Deep neural network-based bandwidth enhancement of photoacoustic data.

PubMed

Gutta, Sreedevi; Kadimesetty, Venkata Suryanarayana; Kalva, Sandeep Kumar; Pramanik, Manojit; Ganapathy, Sriram; Yalavarthy, Phaneendra K

2017-11-01

Photoacoustic (PA) signals collected at the boundary of tissue are always band-limited. A deep neural network was proposed to enhance the bandwidth (BW) of the detected PA signal, thereby improving the quantitative accuracy of the reconstructed PA images. A least square-based deconvolution method that utilizes the Tikhonov regularization framework was used for comparison with the proposed network. The proposed method was evaluated using both numerical and experimental data. The results indicate that the proposed method was capable of enhancing the BW of the detected PA signal, which inturn improves the contrast recovery and quality of reconstructed PA images without adding any significant computational burden. (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).

Fruit fly optimization based least square support vector regression for blind image restoration

NASA Astrophysics Data System (ADS)

Zhang, Jiao; Wang, Rui; Li, Junshan; Yang, Yawei

2014-11-01

The goal of image restoration is to reconstruct the original scene from a degraded observation. It is a critical and challenging task in image processing. Classical restorations require explicit knowledge of the point spread function and a description of the noise as priors. However, it is not practical for many real image processing. The recovery processing needs to be a blind image restoration scenario. Since blind deconvolution is an ill-posed problem, many blind restoration methods need to make additional assumptions to construct restrictions. Due to the differences of PSF and noise energy, blurring images can be quite different. It is difficult to achieve a good balance between proper assumption and high restoration quality in blind deconvolution. Recently, machine learning techniques have been applied to blind image restoration. The least square support vector regression (LSSVR) has been proven to offer strong potential in estimating and forecasting issues. Therefore, this paper proposes a LSSVR-based image restoration method. However, selecting the optimal parameters for support vector machine is essential to the training result. As a novel meta-heuristic algorithm, the fruit fly optimization algorithm (FOA) can be used to handle optimization problems, and has the advantages of fast convergence to the global optimal solution. In the proposed method, the training samples are created from a neighborhood in the degraded image to the central pixel in the original image. The mapping between the degraded image and the original image is learned by training LSSVR. The two parameters of LSSVR are optimized though FOA. The fitness function of FOA is calculated by the restoration error function. With the acquired mapping, the degraded image can be recovered. Experimental results show the proposed method can obtain satisfactory restoration effect. Compared with BP neural network regression, SVR method and Lucy-Richardson algorithm, it speeds up the restoration rate and performs better. Both objective and subjective restoration performances are studied in the comparison experiments.

Temporal and spatial binning of TCSPC data to improve signal-to-noise ratio and imaging speed

NASA Astrophysics Data System (ADS)

Walsh, Alex J.; Beier, Hope T.

2016-03-01

Time-correlated single photon counting (TCSPC) is the most robust method for fluorescence lifetime imaging using laser scanning microscopes. However, TCSPC is inherently slow making it ineffective to capture rapid events due to the single photon product per laser pulse causing extensive acquisition time limitations and the requirement of low fluorescence emission efficiency to avoid bias of measurement towards short lifetimes. Furthermore, thousands of photons per pixel are required for traditional instrument response deconvolution and fluorescence lifetime exponential decay estimation. Instrument response deconvolution and fluorescence exponential decay estimation can be performed in several ways including iterative least squares minimization and Laguerre deconvolution. This paper compares the limitations and accuracy of these fluorescence decay analysis techniques to accurately estimate double exponential decays across many data characteristics including various lifetime values, lifetime component weights, signal-to-noise ratios, and number of photons detected. Furthermore, techniques to improve data fitting, including binning data temporally and spatially, are evaluated as methods to improve decay fits and reduce image acquisition time. Simulation results demonstrate that binning temporally to 36 or 42 time bins, improves accuracy of fits for low photon count data. Such a technique reduces the required number of photons for accurate component estimation if lifetime values are known, such as for commercial fluorescent dyes and FRET experiments, and improve imaging speed 10-fold.

Isotope pattern deconvolution for peptide mass spectrometry by non-negative least squares/least absolute deviation template matching

PubMed Central

2012-01-01

Background The robust identification of isotope patterns originating from peptides being analyzed through mass spectrometry (MS) is often significantly hampered by noise artifacts and the interference of overlapping patterns arising e.g. from post-translational modifications. As the classification of the recorded data points into either ‘noise’ or ‘signal’ lies at the very root of essentially every proteomic application, the quality of the automated processing of mass spectra can significantly influence the way the data might be interpreted within a given biological context. Results We propose non-negative least squares/non-negative least absolute deviation regression to fit a raw spectrum by templates imitating isotope patterns. In a carefully designed validation scheme, we show that the method exhibits excellent performance in pattern picking. It is demonstrated that the method is able to disentangle complicated overlaps of patterns. Conclusions We find that regularization is not necessary to prevent overfitting and that thresholding is an effective and user-friendly way to perform feature selection. The proposed method avoids problems inherent in regularization-based approaches, comes with a set of well-interpretable parameters whose default configuration is shown to generalize well without the need for fine-tuning, and is applicable to spectra of different platforms. The R package IPPD implements the method and is available from the Bioconductor platform (http://bioconductor.fhcrc.org/help/bioc-views/devel/bioc/html/IPPD.html). PMID:23137144

Waveform LiDAR processing: comparison of classic approaches and optimized Gold deconvolution to characterize vegetation structure and terrain elevation

NASA Astrophysics Data System (ADS)

Zhou, T.; Popescu, S. C.; Krause, K.

2016-12-01

Waveform Light Detection and Ranging (LiDAR) data have advantages over discrete-return LiDAR data in accurately characterizing vegetation structure. However, we lack a comprehensive understanding of waveform data processing approaches under different topography and vegetation conditions. The objective of this paper is to highlight a novel deconvolution algorithm, the Gold algorithm, for processing waveform LiDAR data with optimal deconvolution parameters. Further, we present a comparative study of waveform processing methods to provide insight into selecting an approach for a given combination of vegetation and terrain characteristics. We employed two waveform processing methods: 1) direct decomposition, 2) deconvolution and decomposition. In method two, we utilized two deconvolution algorithms - the Richardson Lucy (RL) algorithm and the Gold algorithm. The comprehensive and quantitative comparisons were conducted in terms of the number of detected echoes, position accuracy, the bias of the end products (such as digital terrain model (DTM) and canopy height model (CHM)) from discrete LiDAR data, along with parameter uncertainty for these end products obtained from different methods. This study was conducted at three study sites that include diverse ecological regions, vegetation and elevation gradients. Results demonstrate that two deconvolution algorithms are sensitive to the pre-processing steps of input data. The deconvolution and decomposition method is more capable of detecting hidden echoes with a lower false echo detection rate, especially for the Gold algorithm. Compared to the reference data, all approaches generate satisfactory accuracy assessment results with small mean spatial difference (<1.22 m for DTMs, < 0.77 m for CHMs) and root mean square error (RMSE) (<1.26 m for DTMs, < 1.93 m for CHMs). More specifically, the Gold algorithm is superior to others with smaller root mean square error (RMSE) (< 1.01m), while the direct decomposition approach works better in terms of the percentage of spatial difference within 0.5 and 1 m. The parameter uncertainty analysis demonstrates that the Gold algorithm outperforms other approaches in dense vegetation areas, with the smallest RMSE, and the RL algorithm performs better in sparse vegetation areas in terms of RMSE.

A tool for selective inline quantification of co-eluting proteins in chromatography using spectral analysis and partial least squares regression.

PubMed

Brestrich, Nina; Briskot, Till; Osberghaus, Anna; Hubbuch, Jürgen

2014-07-01

Selective quantification of co-eluting proteins in chromatography is usually performed by offline analytics. This is time-consuming and can lead to late detection of irregularities in chromatography processes. To overcome this analytical bottleneck, a methodology for selective protein quantification in multicomponent mixtures by means of spectral data and partial least squares regression was presented in two previous studies. In this paper, a powerful integration of software and chromatography hardware will be introduced that enables the applicability of this methodology for a selective inline quantification of co-eluting proteins in chromatography. A specific setup consisting of a conventional liquid chromatography system, a diode array detector, and a software interface to Matlab® was developed. The established tool for selective inline quantification was successfully applied for a peak deconvolution of a co-eluting ternary protein mixture consisting of lysozyme, ribonuclease A, and cytochrome c on SP Sepharose FF. Compared to common offline analytics based on collected fractions, no loss of information regarding the retention volumes and peak flanks was observed. A comparison between the mass balances of both analytical methods showed, that the inline quantification tool can be applied for a rapid determination of pool yields. Finally, the achieved inline peak deconvolution was successfully applied to make product purity-based real-time pooling decisions. This makes the established tool for selective inline quantification a valuable approach for inline monitoring and control of chromatographic purification steps and just in time reaction on process irregularities. © 2014 Wiley Periodicals, Inc.

VizieR Online Data Catalog: Magnetic early B-type stars. I. (Shultz+, 2018)

NASA Astrophysics Data System (ADS)

Shultz, M.; Wade, G. A.; Rivinius, Th.; Neiner, C.; Alecian, E.; Bohlender, D.; Monin, D.; Sikora, J.; Mimes Collaboration; Binamics Collaboration

2018-03-01

Longitudinal magnetic field measurements of early B-type stars derived from 1) least-squares deconvolution profiles extracted from high-resolution spectropolarimetric data (ESPaDOnS, Narval, HARPSpol), using masks consisting of metallic lines, metallic + He lines, individual chemical elements, as well as single-line H measurements; and 2) from single-line low-resolution spectropolarimetric observations with dimaPol. (3 data files).

4D PET iterative deconvolution with spatiotemporal regularization for quantitative dynamic PET imaging.

PubMed

Reilhac, Anthonin; Charil, Arnaud; Wimberley, Catriona; Angelis, Georgios; Hamze, Hasar; Callaghan, Paul; Garcia, Marie-Paule; Boisson, Frederic; Ryder, Will; Meikle, Steven R; Gregoire, Marie-Claude

2015-09-01

Quantitative measurements in dynamic PET imaging are usually limited by the poor counting statistics particularly in short dynamic frames and by the low spatial resolution of the detection system, resulting in partial volume effects (PVEs). In this work, we present a fast and easy to implement method for the restoration of dynamic PET images that have suffered from both PVE and noise degradation. It is based on a weighted least squares iterative deconvolution approach of the dynamic PET image with spatial and temporal regularization. Using simulated dynamic [(11)C] Raclopride PET data with controlled biological variations in the striata between scans, we showed that the restoration method provides images which exhibit less noise and better contrast between emitting structures than the original images. In addition, the method is able to recover the true time activity curve in the striata region with an error below 3% while it was underestimated by more than 20% without correction. As a result, the method improves the accuracy and reduces the variability of the kinetic parameter estimates calculated from the corrected images. More importantly it increases the accuracy (from less than 66% to more than 95%) of measured biological variations as well as their statistical detectivity. Crown Copyright © 2015. Published by Elsevier Inc. All rights reserved.

Blind identification of the kinetic parameters in three-compartment models

NASA Astrophysics Data System (ADS)

Riabkov, Dmitri Y.; Di Bella, Edward V. R.

2004-03-01

Quantified knowledge of tissue kinetic parameters in the regions of the brain and other organs can offer information useful in clinical and research applications. Dynamic medical imaging with injection of radioactive or paramagnetic tracer can be used for this measurement. The kinetics of some widely used tracers such as [18F]2-fluoro-2-deoxy-D-glucose can be described by a three-compartment physiological model. The kinetic parameters of the tissue can be estimated from dynamically acquired images. Feasibility of estimation by blind identification, which does not require knowledge of the blood input, is considered analytically and numerically in this work for the three-compartment type of tissue response. The non-uniqueness of the two-region case for blind identification of kinetic parameters in three-compartment model is shown; at least three regions are needed for the blind identification to be unique. Numerical results for the accuracy of these blind identification methods in different conditions were considered. Both a separable variables least-squares (SLS) approach and an eigenvector-based algorithm for multichannel blind deconvolution approach were used. The latter showed poor accuracy. Modifications for non-uniform time sampling were also developed. Also, another method which uses a model for the blood input was compared. Results for the macroparameter K, which reflects the metabolic rate of glucose usage, using three regions with noise showed comparable accuracy for the separable variables least squares method and for the input model-based method, and slightly worse accuracy for SLS with the non-uniform sampling modification.

Gold - A novel deconvolution algorithm with optimization for waveform LiDAR processing

NASA Astrophysics Data System (ADS)

Zhou, Tan; Popescu, Sorin C.; Krause, Keith; Sheridan, Ryan D.; Putman, Eric

2017-07-01

Waveform Light Detection and Ranging (LiDAR) data have advantages over discrete-return LiDAR data in accurately characterizing vegetation structure. However, we lack a comprehensive understanding of waveform data processing approaches under different topography and vegetation conditions. The objective of this paper is to highlight a novel deconvolution algorithm, the Gold algorithm, for processing waveform LiDAR data with optimal deconvolution parameters. Further, we present a comparative study of waveform processing methods to provide insight into selecting an approach for a given combination of vegetation and terrain characteristics. We employed two waveform processing methods: (1) direct decomposition, (2) deconvolution and decomposition. In method two, we utilized two deconvolution algorithms - the Richardson-Lucy (RL) algorithm and the Gold algorithm. The comprehensive and quantitative comparisons were conducted in terms of the number of detected echoes, position accuracy, the bias of the end products (such as digital terrain model (DTM) and canopy height model (CHM)) from the corresponding reference data, along with parameter uncertainty for these end products obtained from different methods. This study was conducted at three study sites that include diverse ecological regions, vegetation and elevation gradients. Results demonstrate that two deconvolution algorithms are sensitive to the pre-processing steps of input data. The deconvolution and decomposition method is more capable of detecting hidden echoes with a lower false echo detection rate, especially for the Gold algorithm. Compared to the reference data, all approaches generate satisfactory accuracy assessment results with small mean spatial difference (<1.22 m for DTMs, <0.77 m for CHMs) and root mean square error (RMSE) (<1.26 m for DTMs, <1.93 m for CHMs). More specifically, the Gold algorithm is superior to others with smaller root mean square error (RMSE) (<1.01 m), while the direct decomposition approach works better in terms of the percentage of spatial difference within 0.5 and 1 m. The parameter uncertainty analysis demonstrates that the Gold algorithm outperforms other approaches in dense vegetation areas, with the smallest RMSE, and the RL algorithm performs better in sparse vegetation areas in terms of RMSE. Additionally, the high level of uncertainty occurs more on areas with high slope and high vegetation. This study provides an alternative and innovative approach for waveform processing that will benefit high fidelity processing of waveform LiDAR data to characterize vegetation structures.

Regression-assisted deconvolution.

PubMed

McIntyre, Julie; Stefanski, Leonard A

2011-06-30

We present a semi-parametric deconvolution estimator for the density function of a random variable biX that is measured with error, a common challenge in many epidemiological studies. Traditional deconvolution estimators rely only on assumptions about the distribution of X and the error in its measurement, and ignore information available in auxiliary variables. Our method assumes the availability of a covariate vector statistically related to X by a mean-variance function regression model, where regression errors are normally distributed and independent of the measurement errors. Simulations suggest that the estimator achieves a much lower integrated squared error than the observed-data kernel density estimator when models are correctly specified and the assumption of normal regression errors is met. We illustrate the method using anthropometric measurements of newborns to estimate the density function of newborn length. Copyright © 2011 John Wiley & Sons, Ltd.

Applying Zeeman Doppler imaging to solar spectra

NASA Astrophysics Data System (ADS)

Hussain, G. A. J.; Saar, S. H.; Collier Cameron, A.

2004-03-01

A new generation of spectro-polarimeters with high throughput (e.g. CFHT/ESPADONS and LBT/PEPSI) is becoming available. This opportunity can be exploited using Zeeman Doppler imaging (ZDI), a technique that inverts time-series of Stokes V spectra to map stellar surface magnetic fields (Semel 1989). ZDI is assisted by ``Least squares deconvolution'' (LSD), which sums up the signal from 1000's of photospheric lines to produce a mean deconvolved profile with higher S:N (Donati & Collier Cameron 1997).

Multidimensional deconvolution of optical microscope and ultrasound imaging using adaptive least-mean-square (LMS) inverse filtering

NASA Astrophysics Data System (ADS)

Sapia, Mark Angelo

2000-11-01

Three-dimensional microscope images typically suffer from reduced resolution due to the effects of convolution, optical aberrations and out-of-focus blurring. Two- dimensional ultrasound images are also degraded by convolutional bluffing and various sources of noise. Speckle noise is a major problem in ultrasound images. In microscopy and ultrasound, various methods of digital filtering have been used to improve image quality. Several methods of deconvolution filtering have been used to improve resolution by reversing the convolutional effects, many of which are based on regularization techniques and non-linear constraints. The technique discussed here is a unique linear filter for deconvolving 3D fluorescence microscopy or 2D ultrasound images. The process is to solve for the filter completely in the spatial-domain using an adaptive algorithm to converge to an optimum solution for de-blurring and resolution improvement. There are two key advantages of using an adaptive solution: (1)it efficiently solves for the filter coefficients by taking into account all sources of noise and degraded resolution at the same time, and (2)achieves near-perfect convergence to the ideal linear deconvolution filter. This linear adaptive technique has other advantages such as avoiding artifacts of frequency-domain transformations and concurrent adaptation to suppress noise. Ultimately, this approach results in better signal-to-noise characteristics with virtually no edge-ringing. Many researchers have not adopted linear techniques because of poor convergence, noise instability and negative valued data in the results. The methods presented here overcome many of these well-documented disadvantages and provide results that clearly out-perform other linear methods and may also out-perform regularization and constrained algorithms. In particular, the adaptive solution is most responsible for overcoming the poor performance associated with linear techniques. This linear adaptive approach to deconvolution is demonstrated with results of restoring blurred phantoms for both microscopy and ultrasound and restoring 3D microscope images of biological cells and 2D ultrasound images of human subjects (courtesy of General Electric and Diasonics, Inc.).

SU-E-I-08: Investigation of Deconvolution Methods for Blocker-Based CBCT Scatter Estimation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, C; Jin, M; Ouyang, L

2015-06-15

Purpose: To investigate whether deconvolution methods can improve the scatter estimation under different blurring and noise conditions for blocker-based scatter correction methods for cone-beam X-ray computed tomography (CBCT). Methods: An “ideal” projection image with scatter was first simulated for blocker-based CBCT data acquisition by assuming no blurring effect and no noise. The ideal image was then convolved with long-tail point spread functions (PSF) with different widths to mimic the blurring effect from the finite focal spot and detector response. Different levels of noise were also added. Three deconvolution Methods: 1) inverse filtering; 2) Wiener; and 3) Richardson-Lucy, were used tomore » recover the scatter signal in the blocked region. The root mean square error (RMSE) of estimated scatter serves as a quantitative measure for the performance of different methods under different blurring and noise conditions. Results: Due to the blurring effect, the scatter signal in the blocked region is contaminated by the primary signal in the unblocked region. The direct use of the signal in the blocked region to estimate scatter (“direct method”) leads to large RMSE values, which increase with the increased width of PSF and increased noise. The inverse filtering is very sensitive to noise and practically useless. The Wiener and Richardson-Lucy deconvolution methods significantly improve scatter estimation compared to the direct method. For a typical medium PSF and medium noise condition, both methods (∼20 RMSE) can achieve 4-fold improvement over the direct method (∼80 RMSE). The Wiener method deals better with large noise and Richardson-Lucy works better on wide PSF. Conclusion: We investigated several deconvolution methods to recover the scatter signal in the blocked region for blocker-based scatter correction for CBCT. Our simulation results demonstrate that Wiener and Richardson-Lucy deconvolution can significantly improve the scatter estimation compared to the direct method.« less

A method to measure the presampling MTF in digital radiography using Wiener deconvolution

NASA Astrophysics Data System (ADS)

Zhou, Zhongxing; Zhu, Qingzhen; Gao, Feng; Zhao, Huijuan; Zhang, Lixin; Li, Guohui

2013-03-01

We developed a novel method for determining the presampling modulation transfer function (MTF) of digital radiography systems from slanted edge images based on Wiener deconvolution. The degraded supersampled edge spread function (ESF) was obtained from simulated slanted edge images with known MTF in the presence of poisson noise, and its corresponding ideal ESF without degration was constructed according to its central edge position. To meet the requirements of the absolute integrable condition of Fourier transformation, the origianl ESFs were mirrored to construct the symmetric pattern of ESFs. Then based on Wiener deconvolution technique, the supersampled line spread function (LSF) could be acquired from the symmetric pattern of degraded supersampled ESFs in the presence of ideal symmetric ESFs and system noise. The MTF is then the normalized magnitude of the Fourier transform of the LSF. The determined MTF showed a strong agreement with the theoritical true MTF when appropriated Wiener parameter was chosen. The effects of Wiener parameter value and the width of square-like wave peak in symmetric ESFs were illustrated and discussed. In conclusion, an accurate and simple method to measure the presampling MTF was established using Wiener deconvolution technique according to slanted edge images.

Computer Processing Of Tunable-Diode-Laser Spectra

NASA Technical Reports Server (NTRS)

May, Randy D.

1991-01-01

Tunable-diode-laser spectrometer measuring transmission spectrum of gas operates under control of computer, which also processes measurement data. Measurements in three channels processed into spectra. Computer controls current supplied to tunable diode laser, stepping it through small increments of wavelength while processing spectral measurements at each step. Program includes library of routines for general manipulation and plotting of spectra, least-squares fitting of direct-transmission and harmonic-absorption spectra, and deconvolution for determination of laser linewidth and for removal of instrumental broadening of spectral lines.

DECONV-TOOL: An IDL based deconvolution software package

NASA Technical Reports Server (NTRS)

Varosi, F.; Landsman, W. B.

1992-01-01

There are a variety of algorithms for deconvolution of blurred images, each having its own criteria or statistic to be optimized in order to estimate the original image data. Using the Interactive Data Language (IDL), we have implemented the Maximum Likelihood, Maximum Entropy, Maximum Residual Likelihood, and sigma-CLEAN algorithms in a unified environment called DeConv_Tool. Most of the algorithms have as their goal the optimization of statistics such as standard deviation and mean of residuals. Shannon entropy, log-likelihood, and chi-square of the residual auto-correlation are computed by DeConv_Tool for the purpose of determining the performance and convergence of any particular method and comparisons between methods. DeConv_Tool allows interactive monitoring of the statistics and the deconvolved image during computation. The final results, and optionally, the intermediate results, are stored in a structure convenient for comparison between methods and review of the deconvolution computation. The routines comprising DeConv_Tool are available via anonymous FTP through the IDL Astronomy User's Library.

Constrained maximum consistency multi-path mitigation

NASA Astrophysics Data System (ADS)

Smith, George B.

2003-10-01

Blind deconvolution algorithms can be useful as pre-processors for signal classification algorithms in shallow water. These algorithms remove the distortion of the signal caused by multipath propagation when no knowledge of the environment is available. A framework in which filters that produce signal estimates from each data channel that are as consistent with each other as possible in a least-squares sense has been presented [Smith, J. Acoust. Soc. Am. 107 (2000)]. This framework provides a solution to the blind deconvolution problem. One implementation of this framework yields the cross-relation on which EVAM [Gurelli and Nikias, IEEE Trans. Signal Process. 43 (1995)] and Rietsch [Rietsch, Geophysics 62(6) (1997)] processing are based. In this presentation, partially blind implementations that have good noise stability properties are compared using Classification Operating Characteristics (CLOC) analysis. [Work supported by ONR under Program Element 62747N and NRL, Stennis Space Center, MS.

XAP, a program for deconvolution and analysis of complex X-ray spectra

USGS Publications Warehouse

Quick, James E.; Haleby, Abdul Malik

1989-01-01

The X-ray analysis program (XAP) is a spectral-deconvolution program written in BASIC and specifically designed to analyze complex spectra produced by energy-dispersive X-ray analytical systems (EDS). XAP compensates for spectrometer drift, utilizes digital filtering to remove background from spectra, and solves for element abundances by least-squares, multiple-regression analysis. Rather than base analyses on only a few channels, broad spectral regions of a sample are reconstructed from standard reference spectra. The effects of this approach are (1) elimination of tedious spectrometer adjustments, (2) removal of background independent of sample composition, and (3) automatic correction for peak overlaps. Although the program was written specifically to operate a KEVEX 7000 X-ray fluorescence analytical system, it could be adapted (with minor modifications) to analyze spectra produced by scanning electron microscopes, electron microprobes, and probes, and X-ray defractometer patterns obtained from whole-rock powders.

Blind channel estimation and deconvolution in colored noise using higher-order cumulants

NASA Astrophysics Data System (ADS)

Tugnait, Jitendra K.; Gummadavelli, Uma

1994-10-01

Existing approaches to blind channel estimation and deconvolution (equalization) focus exclusively on channel or inverse-channel impulse response estimation. It is well-known that the quality of the deconvolved output depends crucially upon the noise statistics also. Typically it is assumed that the noise is white and the signal-to-noise ratio is known. In this paper we remove these restrictions. Both the channel impulse response and the noise model are estimated from the higher-order (fourth, e.g.) cumulant function and the (second-order) correlation function of the received data via a least-squares cumulant/correlation matching criterion. It is assumed that the noise higher-order cumulant function vanishes (e.g., Gaussian noise, as is the case for digital communications). Consistency of the proposed approach is established under certain mild sufficient conditions. The approach is illustrated via simulation examples involving blind equalization of digital communications signals.

Deconvolution of Stark broadened spectra for multi-point density measurements in a flow Z-pinch

DOE PAGES

Vogman, G. V.; Shumlak, U.

2011-10-13

Stark broadened emission spectra, once separated from other broadening effects, provide a convenient non-perturbing means of making plasma density measurements. A deconvolution technique has been developed to measure plasma densities in the ZaP flow Z-pinch experiment. The ZaP experiment uses sheared flow to mitigate MHD instabilities. The pinches exhibit Stark broadened emission spectra, which are captured at 20 locations using a multi-chord spectroscopic system. Spectra that are time- and chord-integrated are well approximated by a Voigt function. The proposed method simultaneously resolves plasma electron density and ion temperature by deconvolving the spectral Voigt profile into constituent functions: a Gaussian functionmore » associated with instrument effects and Doppler broadening by temperature; and a Lorentzian function associated with Stark broadening by electron density. The method uses analytic Fourier transforms of the constituent functions to fit the Voigt profile in the Fourier domain. The method is discussed and compared to a basic least-squares fit. The Fourier transform fitting routine requires fewer fitting parameters and shows promise in being less susceptible to instrumental noise and to contamination from neighboring spectral lines. The method is evaluated and tested using simulated lines and is applied to experimental data for the 229.69 nm C III line from multiple chords to determine plasma density and temperature across the diameter of the pinch. As a result, these measurements are used to gain a better understanding of Z-pinch equilibria.« less

Deconvolution of Stark broadened spectra for multi-point density measurements in a flow Z-pinch

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vogman, G. V.; Shumlak, U.

2011-10-15

Stark broadened emission spectra, once separated from other broadening effects, provide a convenient non-perturbing means of making plasma density measurements. A deconvolution technique has been developed to measure plasma densities in the ZaP flow Z-pinch experiment. The ZaP experiment uses sheared flow to mitigate MHD instabilities. The pinches exhibit Stark broadened emission spectra, which are captured at 20 locations using a multi-chord spectroscopic system. Spectra that are time- and chord-integrated are well approximated by a Voigt function. The proposed method simultaneously resolves plasma electron density and ion temperature by deconvolving the spectral Voigt profile into constituent functions: a Gaussian functionmore » associated with instrument effects and Doppler broadening by temperature; and a Lorentzian function associated with Stark broadening by electron density. The method uses analytic Fourier transforms of the constituent functions to fit the Voigt profile in the Fourier domain. The method is discussed and compared to a basic least-squares fit. The Fourier transform fitting routine requires fewer fitting parameters and shows promise in being less susceptible to instrumental noise and to contamination from neighboring spectral lines. The method is evaluated and tested using simulated lines and is applied to experimental data for the 229.69 nm C III line from multiple chords to determine plasma density and temperature across the diameter of the pinch. These measurements are used to gain a better understanding of Z-pinch equilibria.« less

Optimisation of chromatographic resolution using objective functions including both time and spectral information.

PubMed

Torres-Lapasió, J R; Pous-Torres, S; Ortiz-Bolsico, C; García-Alvarez-Coque, M C

2015-01-16

The optimisation of the resolution in high-performance liquid chromatography is traditionally performed attending only to the time information. However, even in the optimal conditions, some peak pairs may remain unresolved. Such incomplete resolution can be still accomplished by deconvolution, which can be carried out with more guarantees of success by including spectral information. In this work, two-way chromatographic objective functions (COFs) that incorporate both time and spectral information were tested, based on the peak purity (analyte peak fraction free of overlapping) and the multivariate selectivity (figure of merit derived from the net analyte signal) concepts. These COFs are sensitive to situations where the components that coelute in a mixture show some spectral differences. Therefore, they are useful to find out experimental conditions where the spectrochromatograms can be recovered by deconvolution. Two-way multivariate selectivity yielded the best performance and was applied to the separation using diode-array detection of a mixture of 25 phenolic compounds, which remained unresolved in the chromatographic order using linear and multi-linear gradients of acetonitrile-water. Peak deconvolution was carried out using the combination of orthogonal projection approach and alternating least squares. Copyright © 2014 Elsevier B.V. All rights reserved.

Parameter estimation of Monod model by the Least-Squares method for microalgae Botryococcus Braunii sp

NASA Astrophysics Data System (ADS)

See, J. J.; Jamaian, S. S.; Salleh, R. M.; Nor, M. E.; Aman, F.

2018-04-01

This research aims to estimate the parameters of Monod model of microalgae Botryococcus Braunii sp growth by the Least-Squares method. Monod equation is a non-linear equation which can be transformed into a linear equation form and it is solved by implementing the Least-Squares linear regression method. Meanwhile, Gauss-Newton method is an alternative method to solve the non-linear Least-Squares problem with the aim to obtain the parameters value of Monod model by minimizing the sum of square error ( SSE). As the result, the parameters of the Monod model for microalgae Botryococcus Braunii sp can be estimated by the Least-Squares method. However, the estimated parameters value obtained by the non-linear Least-Squares method are more accurate compared to the linear Least-Squares method since the SSE of the non-linear Least-Squares method is less than the linear Least-Squares method.

Development and use of Fourier self deconvolution and curve-fitting in the study of coal oxidation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pierce, J.A.

1986-01-01

Techniques have been developed for modeling highly overlapped band multiplets. The method is based on a least-squares fit of spectra by a series of bands of known shape. Using synthetic spectra, it was shown that when bands are separated by less than their full width at half height (FWHH), valid analytical data can only be obtained after the width of each component band is narrowed by Fourier self deconvolution (FSD). The optimum method of spectral fitting determined from the study of synthetic spectra was then applied to the characterization of oxidized coals. A medium volatile bituminous coal which was airmore » oxidized at 200/sup 0/C for different lengths of time, was extracted with chloroform. A comparison of the infrared spectra of the whole coal and the extract indicated that the extracted material contains a smaller amount of carbonyl, ether, and ester groups, while the aromatic content is much higher. Oxidation does not significantly affect the aromatic content of the whole cola. Most of the aromatic groups in the CHCl/sub 3/ extract show evidence of reaction, however. The production of relatively large amounts of intramolecular aromatic anhydrides is seen in the spectrum of the extract of coals which have undergone extensive oxidation,while there is only a slight indication of this anhydride in the whole coal.« less

LES-Modeling of a Partially Premixed Flame using a Deconvolution Turbulence Closure

NASA Astrophysics Data System (ADS)

Wang, Qing; Wu, Hao; Ihme, Matthias

2015-11-01

The modeling of the turbulence/chemistry interaction in partially premixed and multi-stream combustion remains an outstanding issue. By extending a recently developed constrained minimum mean-square error deconvolution (CMMSED) method, to objective of this work is to develop a source-term closure for turbulent multi-stream combustion. In this method, the chemical source term is obtained from a three-stream flamelet model, and CMMSED is used as closure model, thereby eliminating the need for presumed PDF-modeling. The model is applied to LES of a piloted turbulent jet flame with inhomogeneous inlets, and simulation results are compared with experiments. Comparisons with presumed PDF-methods are performed, and issues regarding resolution and conservation of the CMMSED method are examined. The author would like to acknowledge the support of funding from Stanford Graduate Fellowship.

Deconvolution of the PSF of a seismic lens

NASA Astrophysics Data System (ADS)

Yu, Jianhua; Wang, Yue; Schuster, Gerard T.

2002-12-01

We show that if seismic data d is related to the migration image by mmig = LTd. then mmig is a blurred version of the actual reflectivity distribution m, i.e., mmig = (LTL)m. Here L is the acoustic forward modeling operator under the Born approximation where d = Lm. The blurring operator (LTL), or point spread function, distorts the image because of defects in the seismic lens, i.e., small source-receiver recording aperture and irregular/coarse geophone-source spacing. These distortions can be partly suppressed by applying the deblurring operator (LTL)-1 to the migration image to get m = (LTL)-1mmig. This deblurred image is known as a least squares migration (LSM) image if (LTL)-1LT is applied to the data d using a conjugate gradient method, and is known as a migration deconvolved (MD) image if (LTL)-1 is directly applied to the migration image mmig in (kx, ky, z) space. The MD algorithm is an order-of-magnitude faster than LSM, but it employs more restrictive assumptions. We also show that deblurring can be used to filter out coherent noise in the data such as multiple reflections. The procedure is to, e.g., decompose the forward modeling operator into both primary and multiple reflection operators d = (Lprim + Lmulti)m, invert for m, and find the primary reflection data by dprim = Lprimm. This method is named least squares migration filtering (LSMF). The above three algorithms (LSM, MD and LSMF) might be useful for attacking problems in optical imaging.

Chromatographic peak resolution using Microsoft Excel Solver. The merit of time shifting input arrays.

PubMed

Dasgupta, Purnendu K

2008-12-05

Resolution of overlapped chromatographic peaks is generally accomplished by modeling the peaks as Gaussian or modified Gaussian functions. It is possible, even preferable, to use actual single analyte input responses for this purpose and a nonlinear least squares minimization routine such as that provided by Microsoft Excel Solver can then provide the resolution. In practice, the quality of the results obtained varies greatly due to small shifts in retention time. I show here that such deconvolution can be considerably improved if one or more of the response arrays are iteratively shifted in time.

Non-Negative Spherical Deconvolution (NNSD) for estimation of fiber Orientation Distribution Function in single-/multi-shell diffusion MRI.

PubMed

Cheng, Jian; Deriche, Rachid; Jiang, Tianzi; Shen, Dinggang; Yap, Pew-Thian

2014-11-01

Spherical Deconvolution (SD) is commonly used for estimating fiber Orientation Distribution Functions (fODFs) from diffusion-weighted signals. Existing SD methods can be classified into two categories: 1) Continuous Representation based SD (CR-SD), where typically Spherical Harmonic (SH) representation is used for convenient analytical solutions, and 2) Discrete Representation based SD (DR-SD), where the signal profile is represented by a discrete set of basis functions uniformly oriented on the unit sphere. A feasible fODF should be non-negative and should integrate to unity throughout the unit sphere S(2). However, to our knowledge, most existing SH-based SD methods enforce non-negativity only on discretized points and not the whole continuum of S(2). Maximum Entropy SD (MESD) and Cartesian Tensor Fiber Orientation Distributions (CT-FOD) are the only SD methods that ensure non-negativity throughout the unit sphere. They are however computational intensive and are susceptible to errors caused by numerical spherical integration. Existing SD methods are also known to overestimate the number of fiber directions, especially in regions with low anisotropy. DR-SD introduces additional error in peak detection owing to the angular discretization of the unit sphere. This paper proposes a SD framework, called Non-Negative SD (NNSD), to overcome all the limitations above. NNSD is significantly less susceptible to the false-positive peaks, uses SH representation for efficient analytical spherical deconvolution, and allows accurate peak detection throughout the whole unit sphere. We further show that NNSD and most existing SD methods can be extended to work on multi-shell data by introducing a three-dimensional fiber response function. We evaluated NNSD in comparison with Constrained SD (CSD), a quadratic programming variant of CSD, MESD, and an L1-norm regularized non-negative least-squares DR-SD. Experiments on synthetic and real single-/multi-shell data indicate that NNSD improves estimation performance in terms of mean difference of angles, peak detection consistency, and anisotropy contrast between isotropic and anisotropic regions. Copyright © 2014 Elsevier Inc. All rights reserved.

Chromatographic fingerprinting through chemometric techniques for herbal slimming pills: A way of adulterant identification.

PubMed

Shekari, Nafiseh; Vosough, Maryam; Tabar Heidar, Kourosh

2018-05-01

In the current study, gas chromatography-mass spectrometry (GC-MS) fingerprinting of herbal slimming pills assisted by chemometric methods has been presented. Deconvolution of two-way chromatographic signals of nine herbal slimming pills into pure chromatographic and spectral patterns was performed. The peak clusters were resolved using multivariate curve resolution-alternating least squares (MCR-ALS) by employing appropriate constraints. It was revealed that more useful chemical information about the composition of the slimming pills can be obtained by employing sophisticated GC-MS method coupled with proper chemometric tools yielding the extended number of identified constituents. The thorough fingerprinting of the complex mixtures proved the presence of some toxic or carcinogen components, such as toluene, furfural, furfuryl alcohol, styrene, itaconic anhydride, citraconic anhydride, trimethyl phosphate, phenol, pyrocatechol, p-propenylanisole and pyrogallol. In addition, some samples were shown to be adulterated with undeclared ingredients, including stimulants, anorexiant and laxatives such as phenolphthalein, amfepramone, caffeine and sibutramine. Copyright © 2018 Elsevier B.V. All rights reserved.

A Study of Applying Pulsed Remote Field Eddy Current in Ferromagnetic Pipes Testing

PubMed Central

Luo, Qingwang; Shi, Yibing; Wang, Zhigang; Zhang, Wei; Li, Yanjun

2017-01-01

Pulsed Remote Field Eddy Current Testing (PRFECT) attracts the attention in the testing of ferromagnetic pipes because of its continuous spectrum. This paper simulated the practical PRFECT of pipes by using ANSYS software and employed Least Squares Support Vector Regression (LSSVR) to extract the zero-crossing time to analyze the pipe thickness. As a result, a secondary peak is found in zero-crossing time when transmitter passed by a defect. The secondary peak will lead to wrong quantification and the localization of defects, especially when defects are found only at the transmitter location. Aiming to eliminate the secondary peaks, double sensing coils are set in the transition zone and Wiener deconvolution filter is applied. In the proposed method, position dependent response of the differential signals from the double sensing coils is calibrated by employing zero-mean normalization. The methods proposed in this paper are validated by analyzing the simulation signals and can improve the practicality of PRFECT of ferromagnetic pipes. PMID:28475141

A Study of Applying Pulsed Remote Field Eddy Current in Ferromagnetic Pipes Testing.

PubMed

Luo, Qingwang; Shi, Yibing; Wang, Zhigang; Zhang, Wei; Li, Yanjun

2017-05-05

Pulsed Remote Field Eddy Current Testing (PRFECT) attracts the attention in the testing of ferromagnetic pipes because of its continuous spectrum. This paper simulated the practical PRFECT of pipes by using ANSYS software and employed Least Squares Support Vector Regression (LSSVR) to extract the zero-crossing time to analyze the pipe thickness. As a result, a secondary peak is found in zero-crossing time when transmitter passed by a defect. The secondary peak will lead to wrong quantification and the localization of defects, especially when defects are found only at the transmitter location. Aiming to eliminate the secondary peaks, double sensing coils are set in the transition zone and Wiener deconvolution filter is applied. In the proposed method, position dependent response of the differential signals from the double sensing coils is calibrated by employing zero-mean normalization. The methods proposed in this paper are validated by analyzing the simulation signals and can improve the practicality of PRFECT of ferromagnetic pipes.

A Robust Gold Deconvolution Approach for LiDAR Waveform Data Processing to Characterize Vegetation Structure

NASA Astrophysics Data System (ADS)

Zhou, T.; Popescu, S. C.; Krause, K.; Sheridan, R.; Ku, N. W.

2014-12-01

Increasing attention has been paid in the remote sensing community to the next generation Light Detection and Ranging (lidar) waveform data systems for extracting information on topography and the vertical structure of vegetation. However, processing waveform lidar data raises some challenges compared to analyzing discrete return data. The overall goal of this study was to present a robust de-convolution algorithm- Gold algorithm used to de-convolve waveforms in a lidar dataset acquired within a 60 x 60m study area located in the Harvard Forest in Massachusetts. The waveform lidar data was collected by the National Ecological Observatory Network (NEON). Specific objectives were to: (1) explore advantages and limitations of various waveform processing techniques to derive topography and canopy height information; (2) develop and implement a novel de-convolution algorithm, the Gold algorithm, to extract elevation and canopy metrics; and (3) compare results and assess accuracy. We modeled lidar waveforms with a mixture of Gaussian functions using the Non-least squares (NLS) algorithm implemented in R and derived a Digital Terrain Model (DTM) and canopy height. We compared our waveform-derived topography and canopy height measurements using the Gold de-convolution algorithm to results using the Richardson-Lucy algorithm. Our findings show that the Gold algorithm performed better than the Richardson-Lucy algorithm in terms of recovering the hidden echoes and detecting false echoes for generating a DTM, which indicates that the Gold algorithm could potentially be applied to processing of waveform lidar data to derive information on terrain elevation and canopy characteristics.

A hybrid method for synthetic aperture ladar phase-error compensation

NASA Astrophysics Data System (ADS)

Hua, Zhili; Li, Hongping; Gu, Yongjian

2009-07-01

As a high resolution imaging sensor, synthetic aperture ladar data contain phase-error whose source include uncompensated platform motion and atmospheric turbulence distortion errors. Two previously devised methods, rank one phase-error estimation algorithm and iterative blind deconvolution are reexamined, of which a hybrid method that can recover both the images and PSF's without any a priori information on the PSF is built to speed up the convergence rate by the consideration in the choice of initialization. To be integrated into spotlight mode SAL imaging model respectively, three methods all can effectively reduce the phase-error distortion. For each approach, signal to noise ratio, root mean square error and CPU time are computed, from which we can see the convergence rate of the hybrid method can be improved because a more efficient initialization set of blind deconvolution. Moreover, by making a further discussion of the hybrid method, the weight distribution of ROPE and IBD is found to be an important factor that affects the final result of the whole compensation process.

Fast Fourier-based deconvolution for three-dimensional acoustic source identification with solid spherical arrays

NASA Astrophysics Data System (ADS)

Yang, Yang; Chu, Zhigang; Shen, Linbang; Ping, Guoli; Xu, Zhongming

2018-07-01

Being capable of demystifying the acoustic source identification result fast, Fourier-based deconvolution has been studied and applied widely for the delay and sum (DAS) beamforming with two-dimensional (2D) planar arrays. It is, however so far, still blank in the context of spherical harmonics beamforming (SHB) with three-dimensional (3D) solid spherical arrays. This paper is motivated to settle this problem. Firstly, for the purpose of determining the effective identification region, the premise of deconvolution, a shift-invariant point spread function (PSF), is analyzed with simulations. To make the premise be satisfied approximately, the opening angle in elevation dimension of the surface of interest should be small, while no restriction is imposed to the azimuth dimension. Then, two kinds of deconvolution theories are built for SHB using the zero and the periodic boundary conditions respectively. Both simulations and experiments demonstrate that the periodic boundary condition is superior to the zero one, and fits the 3D acoustic source identification with solid spherical arrays better. Finally, four periodic boundary condition based deconvolution methods are formulated, and their performance is disclosed both with simulations and experimentally. All the four methods offer enhanced spatial resolution and reduced sidelobe contaminations over SHB. The recovered source strength approximates to the exact one multiplied with a coefficient that is the square of the focus distance divided by the distance from the source to the array center, while the recovered pressure contribution is scarcely affected by the focus distance, always approximating to the exact one.

Optimal least-squares finite element method for elliptic problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Povinelli, Louis A.

1991-01-01

An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.

An improved method for polarimetric image restoration in interferometry

NASA Astrophysics Data System (ADS)

Pratley, Luke; Johnston-Hollitt, Melanie

2016-11-01

Interferometric radio astronomy data require the effects of limited coverage in the Fourier plane to be accounted for via a deconvolution process. For the last 40 years this process, known as `cleaning', has been performed almost exclusively on all Stokes parameters individually as if they were independent scalar images. However, here we demonstrate for the case of the linear polarization P, this approach fails to properly account for the complex vector nature resulting in a process which is dependent on the axes under which the deconvolution is performed. We present here an improved method, `Generalized Complex CLEAN', which properly accounts for the complex vector nature of polarized emission and is invariant under rotations of the deconvolution axes. We use two Australia Telescope Compact Array data sets to test standard and complex CLEAN versions of the Högbom and SDI (Steer-Dwedney-Ito) CLEAN algorithms. We show that in general the complex CLEAN version of each algorithm produces more accurate clean components with fewer spurious detections and lower computation cost due to reduced iterations than the current methods. In particular, we find that the complex SDI CLEAN produces the best results for diffuse polarized sources as compared with standard CLEAN algorithms and other complex CLEAN algorithms. Given the move to wide-field, high-resolution polarimetric imaging with future telescopes such as the Square Kilometre Array, we suggest that Generalized Complex CLEAN should be adopted as the deconvolution method for all future polarimetric surveys and in particular that the complex version of an SDI CLEAN should be used.

The first Doppler images of the eclipsing binary SZ Piscium

NASA Astrophysics Data System (ADS)

Xiang, Yue; Gu, Shenghong; Cameron, A. Collier; Barnes, J. R.; Zhang, Liyun

2016-02-01

We present the first Doppler images of the active eclipsing binary system SZ Psc, based on the high-resolution spectral data sets obtained in 2004 November and 2006 September-December. The least-squares deconvolution technique was applied to derive high signal-to-noise profiles from the observed spectra of SZ Psc. Absorption features contributed by a third component of the system were detected in the LSD profiles at all observed phases. We estimated the mass and period of the third component to be about 0.9 M⊙ and 1283 ± 10 d, respectively. After removing the contribution of the third body from the least-squares deconvolved profiles, we derived the surface maps of SZ Psc. The resulting Doppler images indicate significant star-spot activities on the surface of the K subgiant component. The distributions of star-spots are more complex than that revealed by previous photometric studies. The cooler K component exhibited pronounced high-latitude spots as well as numerous low- and intermediate-latitude spot groups during the entire observing seasons, but did not show any large, stable polar cap, different from many other active RS CVn-type binaries.

Richardson-Lucy deconvolution as a general tool for combining images with complementary strengths.

PubMed

Ingaramo, Maria; York, Andrew G; Hoogendoorn, Eelco; Postma, Marten; Shroff, Hari; Patterson, George H

2014-03-17

We use Richardson-Lucy (RL) deconvolution to combine multiple images of a simulated object into a single image in the context of modern fluorescence microscopy techniques. RL deconvolution can merge images with very different point-spread functions, such as in multiview light-sheet microscopes,1, 2 while preserving the best resolution information present in each image. We show that RL deconvolution is also easily applied to merge high-resolution, high-noise images with low-resolution, low-noise images, relevant when complementing conventional microscopy with localization microscopy. We also use RL deconvolution to merge images produced by different simulated illumination patterns, relevant to structured illumination microscopy (SIM)3, 4 and image scanning microscopy (ISM). The quality of our ISM reconstructions is at least as good as reconstructions using standard inversion algorithms for ISM data, but our method follows a simpler recipe that requires no mathematical insight. Finally, we apply RL deconvolution to merge a series of ten images with varying signal and resolution levels. This combination is relevant to gated stimulated-emission depletion (STED) microscopy, and shows that merges of high-quality images are possible even in cases for which a non-iterative inversion algorithm is unknown. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Two-dimensional imaging of two types of radicals by the CW-EPR method

NASA Astrophysics Data System (ADS)

Czechowski, Tomasz; Krzyminiewski, Ryszard; Jurga, Jan; Chlewicki, Wojciech

2008-01-01

The CW-EPR method of image reconstruction is based on sample rotation in a magnetic field with a constant gradient (50 G/cm). In order to obtain a projection (radical density distribution) along a given direction, the EPR spectra are recorded with and without the gradient. Deconvolution, then gives the distribution of the spin density. Projection at 36 different angles gives the information that is necessary for reconstruction of the radical distribution. The problem becomes more complex when there are at least two types of radicals in the sample, because the deconvolution procedure does not give satisfactory results. We propose a method to calculate the projections for each radical, based on iterative procedures. The images of density distribution for each radical obtained by our procedure have proved that the method of deconvolution, in combination with iterative fitting, provides correct results. The test was performed on a sample of polymer PPS Br 111 ( p-phenylene sulphide) with glass fibres and minerals. The results indicated a heterogeneous distribution of radicals in the sample volume. The images obtained were in agreement with the known shape of the sample.

Impact of sensor's point spread function on land cover characterization: Assessment and deconvolution

USGS Publications Warehouse

Huang, C.; Townshend, J.R.G.; Liang, S.; Kalluri, S.N.V.; DeFries, R.S.

2002-01-01

Measured and modeled point spread functions (PSF) of sensor systems indicate that a significant portion of the recorded signal of each pixel of a satellite image originates from outside the area represented by that pixel. This hinders the ability to derive surface information from satellite images on a per-pixel basis. In this study, the impact of the PSF of the Moderate Resolution Imaging Spectroradiometer (MODIS) 250 m bands was assessed using four images representing different landscapes. Experimental results showed that though differences between pixels derived with and without PSF effects were small on the average, the PSF generally brightened dark objects and darkened bright objects. This impact of the PSF lowered the performance of a support vector machine (SVM) classifier by 5.4% in overall accuracy and increased the overall root mean square error (RMSE) by 2.4% in estimating subpixel percent land cover. An inversion method based on the known PSF model reduced the signals originating from surrounding areas by as much as 53%. This method differs from traditional PSF inversion deconvolution methods in that the PSF was adjusted with lower weighting factors for signals originating from neighboring pixels than those specified by the PSF model. By using this deconvolution method, the lost classification accuracy due to residual impact of PSF effects was reduced to only 1.66% in overall accuracy. The increase in the RMSE of estimated subpixel land cover proportions due to the residual impact of PSF effects was reduced to 0.64%. Spatial aggregation also effectively reduced the errors in estimated land cover proportion images. About 50% of the estimation errors were removed after applying the deconvolution method and aggregating derived proportion images to twice their dimensional pixel size. ?? 2002 Elsevier Science Inc. All rights reserved.

The multi-line slope method for measuring the effective magnetic field of cool stars: an application to the solar-like cycle of ɛ Eri

NASA Astrophysics Data System (ADS)

Scalia, C.; Leone, F.; Gangi, M.; Giarrusso, M.; Stift, M. J.

2017-12-01

One method for the determination of integrated longitudinal stellar fields from low-resolution spectra is the so-called slope method, which is based on the regression of the Stokes V signal against the first derivative of Stokes I. Here we investigate the possibility of extending this technique to measure the magnetic fields of cool stars from high-resolution spectra. For this purpose we developed a multi-line modification to the slope method, called the multi-line slope method. We tested this technique by analysing synthetic spectra computed with the COSSAM code and real observations obtained with the high-resolution spectropolarimeters Narval, HARPSpol and the Catania Astrophysical Observatory Spectropolarimeter (CAOS). We show that the multi-line slope method is a fast alternative to the least squares deconvolution technique for the measurement of the effective magnetic fields of cool stars. Using a Fourier transform on the effective magnetic field variations of the star ε Eri, we find that the long-term periodicity of the field corresponds to the 2.95-yr period of the stellar dynamo, revealed by the variation of the activity index.

Intelligent peak deconvolution through in-depth study of the data matrix from liquid chromatography coupled with a photo-diode array detector applied to pharmaceutical analysis.

PubMed

Arase, Shuntaro; Horie, Kanta; Kato, Takashi; Noda, Akira; Mito, Yasuhiro; Takahashi, Masatoshi; Yanagisawa, Toshinobu

2016-10-21

Multivariate curve resolution-alternating least squares (MCR-ALS) method was investigated for its potential to accelerate pharmaceutical research and development. The fast and efficient separation of complex mixtures consisting of multiple components, including impurities as well as major drug substances, remains a challenging application for liquid chromatography in the field of pharmaceutical analysis. In this paper we suggest an integrated analysis algorithm functioning on a matrix of data generated from HPLC coupled with photo-diode array detector (HPLC-PDA) and consisting of the mathematical program for the developed multivariate curve resolution method using an expectation maximization (EM) algorithm with a bidirectional exponentially modified Gaussian (BEMG) model function as a constraint for chromatograms and numerous PDA spectra aligned with time axis. The algorithm provided less than ±1.0% error between true and separated peak area values at resolution (R s ) of 0.6 using simulation data for a three-component mixture with an elution order of a/b/c with similarity (a/b)=0.8410, (b/c)=0.9123 and (a/c)=0.9809 of spectra at peak apex. This software concept provides fast and robust separation analysis even when method development efforts fail to achieve complete separation of the target peaks. Additionally, this approach is potentially applicable to peak deconvolution, allowing quantitative analysis of co-eluted compounds having exactly the same molecular weight. This is complementary to the use of LC-MS to perform quantitative analysis on co-eluted compounds using selected ions to differentiate the proportion of response attributable to each compound. Copyright © 2016 Elsevier B.V. All rights reserved.

Imaging of stellar surfaces with the Occamian approach and the least-squares deconvolution technique

NASA Astrophysics Data System (ADS)

Järvinen, S. P.; Berdyugina, S. V.

2010-10-01

Context. We present in this paper a new technique for the indirect imaging of stellar surfaces (Doppler imaging, DI), when low signal-to-noise spectral data have been improved by the least-squares deconvolution (LSD) method and inverted into temperature maps with the Occamian approach. We apply this technique to both simulated and real data and investigate its applicability for different stellar rotation rates and noise levels in data. Aims: Our goal is to boost the signal of spots in spectral lines and to reduce the effect of photon noise without loosing the temperature information in the lines. Methods: We simulated data from a test star, to which we added different amounts of noise, and employed the inversion technique based on the Occamian approach with and without LSD. In order to be able to infer a temperature map from LSD profiles, we applied the LSD technique for the first time to both the simulated observations and theoretical local line profiles, which remain dependent on temperature and limb angles. We also investigated how the excitation energy of individual lines effects the obtained solution by using three submasks that have lines with low, medium, and high excitation energy levels. Results: We show that our novel approach enables us to overcome the limitations of the two-temperature approximation, which was previously employed for LSD profiles, and to obtain true temperature maps with stellar atmosphere models. The resulting maps agree well with those obtained using the inversion code without LSD, provided the data are noiseless. However, using LSD is only advisable for poor signal-to-noise data. Further, we show that the Occamian technique, both with and without LSD, approaches the surface temperature distribution reasonably well for an adequate spatial resolution. Thus, the stellar rotation rate has a great influence on the result. For instance, in a slowly rotating star, closely situated spots are usually recovered blurred and unresolved, which affects the obtained temperature range of the map. This limitation is critical for small unresolved cool spots and is common for all DI techniques. Finally the LSD method was carried out for high signal-to-noise observations of the young active star V889 Her: the maps obtained with and without LSD are found to be consistent. Conclusions: Our new technique provides meaningful information on the temperature distribution on the stellar surfaces, which was previously inaccessible in DI with LSD. Our approach can be easily adopted for any other multi-line techniques.

Tmax Determined Using a Bayesian Estimation Deconvolution Algorithm Applied to Bolus Tracking Perfusion Imaging: A Digital Phantom Validation Study.

PubMed

Uwano, Ikuko; Sasaki, Makoto; Kudo, Kohsuke; Boutelier, Timothé; Kameda, Hiroyuki; Mori, Futoshi; Yamashita, Fumio

2017-01-10

The Bayesian estimation algorithm improves the precision of bolus tracking perfusion imaging. However, this algorithm cannot directly calculate Tmax, the time scale widely used to identify ischemic penumbra, because Tmax is a non-physiological, artificial index that reflects the tracer arrival delay (TD) and other parameters. We calculated Tmax from the TD and mean transit time (MTT) obtained by the Bayesian algorithm and determined its accuracy in comparison with Tmax obtained by singular value decomposition (SVD) algorithms. The TD and MTT maps were generated by the Bayesian algorithm applied to digital phantoms with time-concentration curves that reflected a range of values for various perfusion metrics using a global arterial input function. Tmax was calculated from the TD and MTT using constants obtained by a linear least-squares fit to Tmax obtained from the two SVD algorithms that showed the best benchmarks in a previous study. Correlations between the Tmax values obtained by the Bayesian and SVD methods were examined. The Bayesian algorithm yielded accurate TD and MTT values relative to the true values of the digital phantom. Tmax calculated from the TD and MTT values with the least-squares fit constants showed excellent correlation (Pearson's correlation coefficient = 0.99) and agreement (intraclass correlation coefficient = 0.99) with Tmax obtained from SVD algorithms. Quantitative analyses of Tmax values calculated from Bayesian-estimation algorithm-derived TD and MTT from a digital phantom correlated and agreed well with Tmax values determined using SVD algorithms.

Bayesian uncertainty quantification in linear models for diffusion MRI.

PubMed

Sjölund, Jens; Eklund, Anders; Özarslan, Evren; Herberthson, Magnus; Bånkestad, Maria; Knutsson, Hans

2018-03-29

Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue microstructure. By fitting a model to the dMRI signal it is possible to derive various quantitative features. Several of the most popular dMRI signal models are expansions in an appropriately chosen basis, where the coefficients are determined using some variation of least-squares. However, such approaches lack any notion of uncertainty, which could be valuable in e.g. group analyses. In this work, we use a probabilistic interpretation of linear least-squares methods to recast popular dMRI models as Bayesian ones. This makes it possible to quantify the uncertainty of any derived quantity. In particular, for quantities that are affine functions of the coefficients, the posterior distribution can be expressed in closed-form. We simulated measurements from single- and double-tensor models where the correct values of several quantities are known, to validate that the theoretically derived quantiles agree with those observed empirically. We included results from residual bootstrap for comparison and found good agreement. The validation employed several different models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI) and Constrained Spherical Deconvolution (CSD). We also used in vivo data to visualize maps of quantitative features and corresponding uncertainties, and to show how our approach can be used in a group analysis to downweight subjects with high uncertainty. In summary, we convert successful linear models for dMRI signal estimation to probabilistic models, capable of accurate uncertainty quantification. Copyright © 2018 Elsevier Inc. All rights reserved.

Comparison of Response Surface Construction Methods for Derivative Estimation Using Moving Least Squares, Kriging and Radial Basis Functions

NASA Technical Reports Server (NTRS)

Krishnamurthy, Thiagarajan

2005-01-01

Response construction methods using Moving Least Squares (MLS), Kriging and Radial Basis Functions (RBF) are compared with the Global Least Squares (GLS) method in three numerical examples for derivative generation capability. Also, a new Interpolating Moving Least Squares (IMLS) method adopted from the meshless method is presented. It is found that the response surface construction methods using the Kriging and RBF interpolation yields more accurate results compared with MLS and GLS methods. Several computational aspects of the response surface construction methods also discussed.

Microseismic source locations with deconvolution migration

NASA Astrophysics Data System (ADS)

Wu, Shaojiang; Wang, Yibo; Zheng, Yikang; Chang, Xu

2018-03-01

Identifying and locating microseismic events are critical problems in hydraulic fracturing monitoring for unconventional resources exploration. In contrast to active seismic data, microseismic data are usually recorded with unknown source excitation time and source location. In this study, we introduce deconvolution migration by combining deconvolution interferometry with interferometric cross-correlation migration (CCM). This method avoids the need for the source excitation time and enhances both the spatial resolution and robustness by eliminating the square term of the source wavelets from CCM. The proposed algorithm is divided into the following three steps: (1) generate the virtual gathers by deconvolving the master trace with all other traces in the microseismic gather to remove the unknown excitation time; (2) migrate the virtual gather to obtain a single image of the source location and (3) stack all of these images together to get the final estimation image of the source location. We test the proposed method on complex synthetic and field data set from the surface hydraulic fracturing monitoring, and compare the results with those obtained by interferometric CCM. The results demonstrate that the proposed method can obtain a 50 per cent higher spatial resolution image of the source location, and more robust estimation with smaller errors of the localization especially in the presence of velocity model errors. This method is also beneficial for source mechanism inversion and global seismology applications.

A high order compact least-squares reconstructed discontinuous Galerkin method for the steady-state compressible flows on hybrid grids

NASA Astrophysics Data System (ADS)

Cheng, Jian; Zhang, Fan; Liu, Tiegang

2018-06-01

In this paper, a class of new high order reconstructed DG (rDG) methods based on the compact least-squares (CLS) reconstruction [23,24] is developed for simulating the two dimensional steady-state compressible flows on hybrid grids. The proposed method combines the advantages of the DG discretization with the flexibility of the compact least-squares reconstruction, which exhibits its superior potential in enhancing the level of accuracy and reducing the computational cost compared to the underlying DG methods with respect to the same number of degrees of freedom. To be specific, a third-order compact least-squares rDG(p1p2) method and a fourth-order compact least-squares rDG(p2p3) method are developed and investigated in this work. In this compact least-squares rDG method, the low order degrees of freedom are evolved through the underlying DG(p1) method and DG(p2) method, respectively, while the high order degrees of freedom are reconstructed through the compact least-squares reconstruction, in which the constitutive relations are built by requiring the reconstructed polynomial and its spatial derivatives on the target cell to conserve the cell averages and the corresponding spatial derivatives on the face-neighboring cells. The large sparse linear system resulted by the compact least-squares reconstruction can be solved relatively efficient when it is coupled with the temporal discretization in the steady-state simulations. A number of test cases are presented to assess the performance of the high order compact least-squares rDG methods, which demonstrates their potential to be an alternative approach for the high order numerical simulations of steady-state compressible flows.

Interferometric redatuming by sparse inversion

NASA Astrophysics Data System (ADS)

van der Neut, Joost; Herrmann, Felix J.

2013-02-01

Assuming that transmission responses are known between the surface and a particular depth level in the subsurface, seismic sources can be effectively mapped to this level by a process called interferometric redatuming. After redatuming, the obtained wavefields can be used for imaging below this particular depth level. Interferometric redatuming consists of two steps, namely (i) the decomposition of the observed wavefields into downgoing and upgoing constituents and (ii) a multidimensional deconvolution of the upgoing constituents with the downgoing constituents. While this method works in theory, sensitivity to noise and artefacts due to incomplete acquisition require a different formulation. In this letter, we demonstrate the benefits of formulating the two steps that undergird interferometric redatuming in terms of a transform-domain sparsity-promoting program. By exploiting compressibility of seismic wavefields in the curvelet domain, the method not only becomes robust with respect to noise but we are also able to remove certain artefacts while preserving the frequency content. Although we observe improvements when we promote sparsity in the redatumed data space, we expect better results when interferometric redatuming would be combined or integrated with least-squares migration with sparsity promotion in the image space.

Least Squares Procedures.

ERIC Educational Resources Information Center

Hester, Yvette

Least squares methods are sophisticated mathematical curve fitting procedures used in all classical parametric methods. The linear least squares approximation is most often associated with finding the "line of best fit" or the regression line. Since all statistical analyses are correlational and all classical parametric methods are least…

Extension of least squares spectral resolution algorithm to high-resolution lipidomics data.

PubMed

Zeng, Ying-Xu; Mjøs, Svein Are; David, Fabrice P A; Schmid, Adrien W

2016-03-31

Lipidomics, which focuses on the global study of molecular lipids in biological systems, has been driven tremendously by technical advances in mass spectrometry (MS) instrumentation, particularly high-resolution MS. This requires powerful computational tools that handle the high-throughput lipidomics data analysis. To address this issue, a novel computational tool has been developed for the analysis of high-resolution MS data, including the data pretreatment, visualization, automated identification, deconvolution and quantification of lipid species. The algorithm features the customized generation of a lipid compound library and mass spectral library, which covers the major lipid classes such as glycerolipids, glycerophospholipids and sphingolipids. Next, the algorithm performs least squares resolution of spectra and chromatograms based on the theoretical isotope distribution of molecular ions, which enables automated identification and quantification of molecular lipid species. Currently, this methodology supports analysis of both high and low resolution MS as well as liquid chromatography-MS (LC-MS) lipidomics data. The flexibility of the methodology allows it to be expanded to support more lipid classes and more data interpretation functions, making it a promising tool in lipidomic data analysis. Copyright © 2016 Elsevier B.V. All rights reserved.

Effective Alternating Direction Optimization Methods for Sparsity-Constrained Blind Image Deblurring.

PubMed

Xiong, Naixue; Liu, Ryan Wen; Liang, Maohan; Wu, Di; Liu, Zhao; Wu, Huisi

2017-01-18

Single-image blind deblurring for imaging sensors in the Internet of Things (IoT) is a challenging ill-conditioned inverse problem, which requires regularization techniques to stabilize the image restoration process. The purpose is to recover the underlying blur kernel and latent sharp image from only one blurred image. Under many degraded imaging conditions, the blur kernel could be considered not only spatially sparse, but also piecewise smooth with the support of a continuous curve. By taking advantage of the hybrid sparse properties of the blur kernel, a hybrid regularization method is proposed in this paper to robustly and accurately estimate the blur kernel. The effectiveness of the proposed blur kernel estimation method is enhanced by incorporating both the L 1 -norm of kernel intensity and the squared L 2 -norm of the intensity derivative. Once the accurate estimation of the blur kernel is obtained, the original blind deblurring can be simplified to the direct deconvolution of blurred images. To guarantee robust non-blind deconvolution, a variational image restoration model is presented based on the L 1 -norm data-fidelity term and the total generalized variation (TGV) regularizer of second-order. All non-smooth optimization problems related to blur kernel estimation and non-blind deconvolution are effectively handled by using the alternating direction method of multipliers (ADMM)-based numerical methods. Comprehensive experiments on both synthetic and realistic datasets have been implemented to compare the proposed method with several state-of-the-art methods. The experimental comparisons have illustrated the satisfactory imaging performance of the proposed method in terms of quantitative and qualitative evaluations.

A mathematical deconvolution formulation for superficial dose distribution measurement by Cerenkov light dosimetry.

PubMed

Brost, Eric Edward; Watanabe, Yoichi

2018-06-01

Cerenkov photons are created by high-energy radiation beams used for radiation therapy. In this study, we developed a Cerenkov light dosimetry technique to obtain a two-dimensional dose distribution in a superficial region of medium from the images of Cerenkov photons by using a deconvolution method. An integral equation was derived to represent the Cerenkov photon image acquired by a camera for a given incident high-energy photon beam by using convolution kernels. Subsequently, an equation relating the planar dose at a depth to a Cerenkov photon image using the well-known relationship between the incident beam fluence and the dose distribution in a medium was obtained. The final equation contained a convolution kernel called the Cerenkov dose scatter function (CDSF). The CDSF function was obtained by deconvolving the Cerenkov scatter function (CSF) with the dose scatter function (DSF). The GAMOS (Geant4-based Architecture for Medicine-Oriented Simulations) Monte Carlo particle simulation software was used to obtain the CSF and DSF. The dose distribution was calculated from the Cerenkov photon intensity data using an iterative deconvolution method with the CDSF. The theoretical formulation was experimentally evaluated by using an optical phantom irradiated by high-energy photon beams. The intensity of the deconvolved Cerenkov photon image showed linear dependence on the dose rate and the photon beam energy. The relative intensity showed a field size dependence similar to the beam output factor. Deconvolved Cerenkov images showed improvement in dose profiles compared with the raw image data. In particular, the deconvolution significantly improved the agreement in the high dose gradient region, such as in the penumbra. Deconvolution with a single iteration was found to provide the most accurate solution of the dose. Two-dimensional dose distributions of the deconvolved Cerenkov images agreed well with the reference distributions for both square fields and a multileaf collimator (MLC) defined, irregularly shaped field. The proposed technique improved the accuracy of the Cerenkov photon dosimetry in the penumbra region. The results of this study showed initial validation of the deconvolution method for beam profile measurements in a homogeneous media. The new formulation accounted for the physical processes of Cerenkov photon transport in the medium more accurately than previously published methods. © 2018 American Association of Physicists in Medicine.

SU-E-T-299: Small Fields Profiles Correction Through Detectors Spatial Response Functions and Field Size Dependence Analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Filipuzzi, M; Garrigo, E; Venencia, C

2014-06-01

Purpose: To calculate the spatial response function of various radiation detectors, to evaluate the dependence on the field size and to analyze the small fields profiles corrections by deconvolution techniques. Methods: Crossline profiles were measured on a Novalis Tx 6MV beam with a HDMLC. The configuration setup was SSD=100cm and depth=5cm. Five fields were studied (200×200mm2,100×100mm2, 20×20mm2, 10×10mm2and 5×5mm2) and measured were made with passive detectors (EBT3 radiochromic films and TLD700 thermoluminescent detectors), ionization chambers (PTW30013, PTW31003, CC04 and PTW31016) and diodes (PTW60012 and IBA SFD). The results of passive detectors were adopted as the actual beam profile. To calculatemore » the detectors kernels, modeled by Gaussian functions, an iterative process based on a least squares criterion was used. The deconvolutions of the measured profiles were calculated with the Richardson-Lucy method. Results: The profiles of the passive detectors corresponded with a difference in the penumbra less than 0.1mm. Both diodes resolve the profiles with an overestimation of the penumbra smaller than 0.2mm. For the other detectors, response functions were calculated and resulted in Gaussian functions with a standard deviation approximate to the radius of the detector in study (with a variation less than 3%). The corrected profiles resolve the penumbra with less than 1% error. Major discrepancies were observed for cases in extreme conditions (PTW31003 and 5×5mm2 field size). Conclusion: This work concludes that the response function of a radiation detector is independent on the field size, even for small radiation beams. The profiles correction, using deconvolution techniques and response functions of standard deviation equal to the radius of the detector, gives penumbra values with less than 1% difference to the real profile. The implementation of this technique allows estimating the real profile, freeing from the effects of the detector used for the acquisition.« less

Bilinear Inverse Problems: Theory, Algorithms, and Applications

NASA Astrophysics Data System (ADS)

Ling, Shuyang

We will discuss how several important real-world signal processing problems, such as self-calibration and blind deconvolution, can be modeled as bilinear inverse problems and solved by convex and nonconvex optimization approaches. In Chapter 2, we bring together three seemingly unrelated concepts, self-calibration, compressive sensing and biconvex optimization. We show how several self-calibration problems can be treated efficiently within the framework of biconvex compressive sensing via a new method called SparseLift. More specifically, we consider a linear system of equations y = DAx, where the diagonal matrix D (which models the calibration error) is unknown and x is an unknown sparse signal. By "lifting" this biconvex inverse problem and exploiting sparsity in this model, we derive explicit theoretical guarantees under which both x and D can be recovered exactly, robustly, and numerically efficiently. In Chapter 3, we study the question of the joint blind deconvolution and blind demixing, i.e., extracting a sequence of functions [special characters omitted] from observing only the sum of their convolutions [special characters omitted]. In particular, for the special case s = 1, it becomes the well-known blind deconvolution problem. We present a non-convex algorithm which guarantees exact recovery under conditions that are competitive with convex optimization methods, with the additional advantage of being computationally much more efficient. We discuss several applications of the proposed framework in image processing and wireless communications in connection with the Internet-of-Things. In Chapter 4, we consider three different self-calibration models of practical relevance. We show how their corresponding bilinear inverse problems can be solved by both the simple linear least squares approach and the SVD-based approach. As a consequence, the proposed algorithms are numerically extremely efficient, thus allowing for real-time deployment. Explicit theoretical guarantees and stability theory are derived and the number of sampling complexity is nearly optimal (up to a poly-log factor). Applications in imaging sciences and signal processing are discussed and numerical simulations are presented to demonstrate the effectiveness and efficiency of our approach.

The covariance matrix for the solution vector of an equality-constrained least-squares problem

NASA Technical Reports Server (NTRS)

Lawson, C. L.

1976-01-01

Methods are given for computing the covariance matrix for the solution vector of an equality-constrained least squares problem. The methods are matched to the solution algorithms given in the book, 'Solving Least Squares Problems.'

Application of an improved minimum entropy deconvolution method for railway rolling element bearing fault diagnosis

NASA Astrophysics Data System (ADS)

Cheng, Yao; Zhou, Ning; Zhang, Weihua; Wang, Zhiwei

2018-07-01

Minimum entropy deconvolution is a widely-used tool in machinery fault diagnosis, because it enhances the impulse component of the signal. The filter coefficients that greatly influence the performance of the minimum entropy deconvolution are calculated by an iterative procedure. This paper proposes an improved deconvolution method for the fault detection of rolling element bearings. The proposed method solves the filter coefficients by the standard particle swarm optimization algorithm, assisted by a generalized spherical coordinate transformation. When optimizing the filters performance for enhancing the impulses in fault diagnosis (namely, faulty rolling element bearings), the proposed method outperformed the classical minimum entropy deconvolution method. The proposed method was validated in simulation and experimental signals from railway bearings. In both simulation and experimental studies, the proposed method delivered better deconvolution performance than the classical minimum entropy deconvolution method, especially in the case of low signal-to-noise ratio.

Ultrafast Method for the Analysis of Fluorescence Lifetime Imaging Microscopy Data Based on the Laguerre Expansion Technique

PubMed Central

Jo, Javier A.; Fang, Qiyin; Marcu, Laura

2007-01-01

We report a new deconvolution method for fluorescence lifetime imaging microscopy (FLIM) based on the Laguerre expansion technique. The performance of this method was tested on synthetic and real FLIM images. The following interesting properties of this technique were demonstrated. 1) The fluorescence intensity decay can be estimated simultaneously for all pixels, without a priori assumption of the decay functional form. 2) The computation speed is extremely fast, performing at least two orders of magnitude faster than current algorithms. 3) The estimated maps of Laguerre expansion coefficients provide a new domain for representing FLIM information. 4) The number of images required for the analysis is relatively small, allowing reduction of the acquisition time. These findings indicate that the developed Laguerre expansion technique for FLIM analysis represents a robust and extremely fast deconvolution method that enables practical applications of FLIM in medicine, biology, biochemistry, and chemistry. PMID:19444338

Method of LSD profile asymmetry for estimating the center of mass velocities of pulsating stars

NASA Astrophysics Data System (ADS)

Britavskiy, Nikolay; Pancino, Elena; Romano, Donatella; Tsymbal, Vadim

2015-08-01

We present radial velocity analysis for 20 solar neighborhood RR Lyrae and 3 Population II Cepheids. High-resolution spectra were observed with either TNG/SARG or VLT/UVES over varying phases. To estimate the center of mass (barycentric) velocities of the program stars, we utilized two independent methods. First, the 'classic' method was employed, which is based on RR Lyrae radial velocity curve templates. Second, we provide the new method that used absorption line profile asymmetry to determine both the pulsation and the barycentric velocities even with a low number of high-resolution spectra and in cases where the phase of the observations is uncertain. This new method is based on a Least Squares Deconvolution (LSD) of the line profiles in order to analyze line asymmetry that occurs in the spectra of pulsating stars. By applying this method to our sample stars we attain accurate measurements (± 1 km/s) of the pulsation component of the radial velocity. This results in determination of the barycentric velocity to within 5 km/s even with a low number of high-resolution spectra. A detailed investigation of LSD profile asymmetry shows the variable nature of the project factor at different pulsation phases, which should be taken into account in the detailed spectroscopic analysis of pulsating stars.

Method of LSD profile asymmetry for estimating the center of mass velocities of pulsating stars

NASA Astrophysics Data System (ADS)

Britavskiy, N.; Pancino, E.; Tsymbal, V.; Romano, D.; Cacciari, C.; Clementini, C.

2016-05-01

We present radial velocity analysis for 20 solar neighborhood RR Lyrae and 3 Population II Cepheids. High-resolution spectra were observed with either TNG/SARG or VLT/UVES over varying phases. To estimate the center of mass (barycentric) velocities of the program stars, we utilized two independent methods. First, the 'classic' method was employed, which is based on RR Lyrae radial velocity curve templates. Second, we provide the new method that used absorption line profile asymmetry to determine both the pulsation and the barycentric velocities even with a low number of high-resolution spectra and in cases where the phase of the observations is uncertain. This new method is based on a least squares deconvolution (LSD) of the line profiles in order to an- alyze line asymmetry that occurs in the spectra of pulsating stars. By applying this method to our sample stars we attain accurate measurements (+- 2 kms^-1) of the pulsation component of the radial velocity. This results in determination of the barycentric velocity to within 5 kms^-1 even with a low number of high- resolution spectra. A detailed investigation of LSD profile asymmetry shows the variable nature of the project factor at different pulsation phases, which should be taken into account in the detailed spectroscopic analysis of pulsating stars.

Adaptive Modal Identification for Flutter Suppression Control

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Drew, Michael; Swei, Sean S.

2016-01-01

In this paper, we will develop an adaptive modal identification method for identifying the frequencies and damping of a flutter mode based on model-reference adaptive control (MRAC) and least-squares methods. The least-squares parameter estimation will achieve parameter convergence in the presence of persistent excitation whereas the MRAC parameter estimation does not guarantee parameter convergence. Two adaptive flutter suppression control approaches are developed: one based on MRAC and the other based on the least-squares method. The MRAC flutter suppression control is designed as an integral part of the parameter estimation where the feedback signal is used to estimate the modal information. On the other hand, the separation principle of control and estimation is applied to the least-squares method. The least-squares modal identification is used to perform parameter estimation.

Least-squares collocation meshless approach for radiative heat transfer in absorbing and scattering media

NASA Astrophysics Data System (ADS)

Liu, L. H.; Tan, J. Y.

2007-02-01

A least-squares collocation meshless method is employed for solving the radiative heat transfer in absorbing, emitting and scattering media. The least-squares collocation meshless method for radiative transfer is based on the discrete ordinates equation. A moving least-squares approximation is applied to construct the trial functions. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of residuals of all collocation and auxiliary points. Three numerical examples are studied to illustrate the performance of this new solution method. The numerical results are compared with the other benchmark approximate solutions. By comparison, the results show that the least-squares collocation meshless method is efficient, accurate and stable, and can be used for solving the radiative heat transfer in absorbing, emitting and scattering media.

Improving cell mixture deconvolution by identifying optimal DNA methylation libraries (IDOL).

PubMed

Koestler, Devin C; Jones, Meaghan J; Usset, Joseph; Christensen, Brock C; Butler, Rondi A; Kobor, Michael S; Wiencke, John K; Kelsey, Karl T

2016-03-08

Confounding due to cellular heterogeneity represents one of the foremost challenges currently facing Epigenome-Wide Association Studies (EWAS). Statistical methods leveraging the tissue-specificity of DNA methylation for deconvoluting the cellular mixture of heterogenous biospecimens offer a promising solution, however the performance of such methods depends entirely on the library of methylation markers being used for deconvolution. Here, we introduce a novel algorithm for Identifying Optimal Libraries (IDOL) that dynamically scans a candidate set of cell-specific methylation markers to find libraries that optimize the accuracy of cell fraction estimates obtained from cell mixture deconvolution. Application of IDOL to training set consisting of samples with both whole-blood DNA methylation data (Illumina HumanMethylation450 BeadArray (HM450)) and flow cytometry measurements of cell composition revealed an optimized library comprised of 300 CpG sites. When compared existing libraries, the library identified by IDOL demonstrated significantly better overall discrimination of the entire immune cell landscape (p = 0.038), and resulted in improved discrimination of 14 out of the 15 pairs of leukocyte subtypes. Estimates of cell composition across the samples in the training set using the IDOL library were highly correlated with their respective flow cytometry measurements, with all cell-specific R (2)>0.99 and root mean square errors (RMSEs) ranging from [0.97 % to 1.33 %] across leukocyte subtypes. Independent validation of the optimized IDOL library using two additional HM450 data sets showed similarly strong prediction performance, with all cell-specific R (2)>0.90 and R M S E<4.00 %. In simulation studies, adjustments for cell composition using the IDOL library resulted in uniformly lower false positive rates compared to competing libraries, while also demonstrating an improved capacity to explain epigenome-wide variation in DNA methylation within two large publicly available HM450 data sets. Despite consisting of half as many CpGs compared to existing libraries for whole blood mixture deconvolution, the optimized IDOL library identified herein resulted in outstanding prediction performance across all considered data sets and demonstrated potential to improve the operating characteristics of EWAS involving adjustments for cell distribution. In addition to providing the EWAS community with an optimized library for whole blood mixture deconvolution, our work establishes a systematic and generalizable framework for the assembly of libraries that improve the accuracy of cell mixture deconvolution.

Sinusoidal synthesis based adaptive tracking for rotating machinery fault detection

NASA Astrophysics Data System (ADS)

Li, Gang; McDonald, Geoff L.; Zhao, Qing

2017-01-01

This paper presents a novel Sinusoidal Synthesis Based Adaptive Tracking (SSBAT) technique for vibration-based rotating machinery fault detection. The proposed SSBAT algorithm is an adaptive time series technique that makes use of both frequency and time domain information of vibration signals. Such information is incorporated in a time varying dynamic model. Signal tracking is then realized by applying adaptive sinusoidal synthesis to the vibration signal. A modified Least-Squares (LS) method is adopted to estimate the model parameters. In addition to tracking, the proposed vibration synthesis model is mainly used as a linear time-varying predictor. The health condition of the rotating machine is monitored by checking the residual between the predicted and measured signal. The SSBAT method takes advantage of the sinusoidal nature of vibration signals and transfers the nonlinear problem into a linear adaptive problem in the time domain based on a state-space realization. It has low computation burden and does not need a priori knowledge of the machine under the no-fault condition which makes the algorithm ideal for on-line fault detection. The method is validated using both numerical simulation and practical application data. Meanwhile, the fault detection results are compared with the commonly adopted autoregressive (AR) and autoregressive Minimum Entropy Deconvolution (ARMED) method to verify the feasibility and performance of the SSBAT method.

Deconvolution method for accurate determination of overlapping peak areas in chromatograms.

PubMed

Nelson, T J

1991-12-20

A method is described for deconvoluting chromatograms which contain overlapping peaks. Parameters can be selected to ensure that attenuation of peak areas is uniform over any desired range of peak widths. A simple extension of the method greatly reduces the negative overshoot frequently encountered with deconvolutions. The deconvoluted chromatograms are suitable for integration by conventional methods.

Application of least median of squared orthogonal distance (LMD) and LMD-based reweighted least squares (RLS) methods on the stock-recruitment relationship

NASA Astrophysics Data System (ADS)

Wang, Yan-Jun; Liu, Qun

1999-03-01

Analysis of stock-recruitment (SR) data is most often done by fitting various SR relationship curves to the data. Fish population dynamics data often have stochastic variations and measurement errors, which usually result in a biased regression analysis. This paper presents a robust regression method, least median of squared orthogonal distance (LMD), which is insensitive to abnormal values in the dependent and independent variables in a regression analysis. Outliers that have significantly different variance from the rest of the data can be identified in a residual analysis. Then, the least squares (LS) method is applied to the SR data with defined outliers being down weighted. The application of LMD and LMD-based Reweighted Least Squares (RLS) method to simulated and real fisheries SR data is explored.

Domain Decomposition Algorithms for First-Order System Least Squares Methods

NASA Technical Reports Server (NTRS)

Pavarino, Luca F.

1996-01-01

Least squares methods based on first-order systems have been recently proposed and analyzed for second-order elliptic equations and systems. They produce symmetric and positive definite discrete systems by using standard finite element spaces, which are not required to satisfy the inf-sup condition. In this paper, several domain decomposition algorithms for these first-order least squares methods are studied. Some representative overlapping and substructuring algorithms are considered in their additive and multiplicative variants. The theoretical and numerical results obtained show that the classical convergence bounds (on the iteration operator) for standard Galerkin discretizations are also valid for least squares methods.

Improving Calculation Accuracies of Accumulation-Mode Fractions Based on Spectral of Aerosol Optical Depths

NASA Astrophysics Data System (ADS)

Ying, Zhang; Zhengqiang, Li; Yan, Wang

2014-03-01

Anthropogenic aerosols are released into the atmosphere, which cause scattering and absorption of incoming solar radiation, thus exerting a direct radiative forcing on the climate system. Anthropogenic Aerosol Optical Depth (AOD) calculations are important in the research of climate changes. Accumulation-Mode Fractions (AMFs) as an anthropogenic aerosol parameter, which are the fractions of AODs between the particulates with diameters smaller than 1μm and total particulates, could be calculated by AOD spectral deconvolution algorithm, and then the anthropogenic AODs are obtained using AMFs. In this study, we present a parameterization method coupled with an AOD spectral deconvolution algorithm to calculate AMFs in Beijing over 2011. All of data are derived from AErosol RObotic NETwork (AERONET) website. The parameterization method is used to improve the accuracies of AMFs compared with constant truncation radius method. We find a good correlation using parameterization method with the square relation coefficient of 0.96, and mean deviation of AMFs is 0.028. The parameterization method could also effectively solve AMF underestimate in winter. It is suggested that the variations of Angstrom indexes in coarse mode have significant impacts on AMF inversions.

Ordinary Least Squares and Quantile Regression: An Inquiry-Based Learning Approach to a Comparison of Regression Methods

ERIC Educational Resources Information Center

Helmreich, James E.; Krog, K. Peter

2018-01-01

We present a short, inquiry-based learning course on concepts and methods underlying ordinary least squares (OLS), least absolute deviation (LAD), and quantile regression (QR). Students investigate squared, absolute, and weighted absolute distance functions (metrics) as location measures. Using differential calculus and properties of convex…

A spectral mimetic least-squares method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bochev, Pavel; Gerritsma, Marc

We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are alsomore » satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.« less

A spectral mimetic least-squares method

DOE PAGES

Bochev, Pavel; Gerritsma, Marc

2014-09-01

We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are alsomore » satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.« less

Adaptive slab laser beam quality improvement using a weighted least-squares reconstruction algorithm.

PubMed

Chen, Shanqiu; Dong, LiZhi; Chen, XiaoJun; Tan, Yi; Liu, Wenjin; Wang, Shuai; Yang, Ping; Xu, Bing; Ye, YuTang

2016-04-10

Adaptive optics is an important technology for improving beam quality in solid-state slab lasers. However, there are uncorrectable aberrations in partial areas of the beam. In the criterion of the conventional least-squares reconstruction method, it makes the zones with small aberrations nonsensitive and hinders this zone from being further corrected. In this paper, a weighted least-squares reconstruction method is proposed to improve the relative sensitivity of zones with small aberrations and to further improve beam quality. Relatively small weights are applied to the zones with large residual aberrations. Comparisons of results show that peak intensity in the far field improved from 1242 analog digital units (ADU) to 2248 ADU, and beam quality β improved from 2.5 to 2.0. This indicates the weighted least-squares method has better performance than the least-squares reconstruction method when there are large zonal uncorrectable aberrations in the slab laser system.

Least squares regression methods for clustered ROC data with discrete covariates.

PubMed

Tang, Liansheng Larry; Zhang, Wei; Li, Qizhai; Ye, Xuan; Chan, Leighton

2016-07-01

The receiver operating characteristic (ROC) curve is a popular tool to evaluate and compare the accuracy of diagnostic tests to distinguish the diseased group from the nondiseased group when test results from tests are continuous or ordinal. A complicated data setting occurs when multiple tests are measured on abnormal and normal locations from the same subject and the measurements are clustered within the subject. Although least squares regression methods can be used for the estimation of ROC curve from correlated data, how to develop the least squares methods to estimate the ROC curve from the clustered data has not been studied. Also, the statistical properties of the least squares methods under the clustering setting are unknown. In this article, we develop the least squares ROC methods to allow the baseline and link functions to differ, and more importantly, to accommodate clustered data with discrete covariates. The methods can generate smooth ROC curves that satisfy the inherent continuous property of the true underlying curve. The least squares methods are shown to be more efficient than the existing nonparametric ROC methods under appropriate model assumptions in simulation studies. We apply the methods to a real example in the detection of glaucomatous deterioration. We also derive the asymptotic properties of the proposed methods. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Untargeted metabolomic profiling of seminal plasma in nonobstructive azoospermia men: A noninvasive detection of spermatogenesis.

PubMed

Gilany, Kambiz; Mani-Varnosfaderani, Ahmad; Minai-Tehrani, Arash; Mirzajani, Fateme; Ghassempour, Alireza; Sadeghi, Mohammed Reza; Amini, Mehdi; Rezadoost, Hassan

2017-08-01

Male factor infertility is involved in almost half of all infertile couples. Lack of the ejaculated sperm owing to testicular malfunction has been reported in 6-10% of infertile men, a condition named nonobstructive azoospermia (NOA). In this study, we investigated untargeted metabolomic profiling of the seminal plasma in NOA men using gas chromatography-mass spectrometry and advance chemometrics. In this regard, the seminal plasma fluids of 11 NOA men with TESE-negative, nine NOA men with TESE-positive and 10 fertile healthy men (as a control group) were collected. Quadratic discriminate analysis (QDA) technique was implemented on total ion chromatograms (TICs) for identification of discriminatory retention times. We developed multivariate classification models using the QDA technique. Our results revealed that the developed QDA models could predict the classes of samples using their TIC data. The receiver operating characteristic curves for these models were >0.88. After recognition of discriminatory retention time's asymmetric penalized least square, evolving factor analysis, correlation optimized warping and alternating least squares strategies were applied for preprocessing and deconvolution of the overlapped chromatographic peaks. We could identify 36 discriminatory metabolites. These metabolites may be considered discriminatory biomarkers for different groups in NOA. Copyright © 2017 John Wiley & Sons, Ltd.

Solid-phase cadmium speciation in soil using L3-edge XANES spectroscopy with partial least-squares regression.

PubMed

Siebers, Nina; Kruse, Jens; Eckhardt, Kai-Uwe; Hu, Yongfeng; Leinweber, Peter

2012-07-01

Cadmium (Cd) has a high toxicity and resolving its speciation in soil is challenging but essential for estimating the environmental risk. In this study partial least-square (PLS) regression was tested for its capability to deconvolute Cd L(3)-edge X-ray absorption near-edge structure (XANES) spectra of multi-compound mixtures. For this, a library of Cd reference compound spectra and a spectrum of a soil sample were acquired. A good coefficient of determination (R(2)) of Cd compounds in mixtures was obtained for the PLS model using binary and ternary mixtures of various Cd reference compounds proving the validity of this approach. In order to describe complex systems like soil, multi-compound mixtures of a variety of Cd compounds must be included in the PLS model. The obtained PLS regression model was then applied to a highly Cd-contaminated soil revealing Cd(3)(PO(4))(2) (36.1%), Cd(NO(3))(2)·4H(2)O (24.5%), Cd(OH)(2) (21.7%), CdCO(3) (17.1%) and CdCl(2) (0.4%). These preliminary results proved that PLS regression is a promising approach for a direct determination of Cd speciation in the solid phase of a soil sample.

Electron paramagnetic resonance image reconstruction with total variation and curvelets regularization

NASA Astrophysics Data System (ADS)

Durand, Sylvain; Frapart, Yves-Michel; Kerebel, Maud

2017-11-01

Spatial electron paramagnetic resonance imaging (EPRI) is a recent method to localize and characterize free radicals in vivo or in vitro, leading to applications in material and biomedical sciences. To improve the quality of the reconstruction obtained by EPRI, a variational method is proposed to inverse the image formation model. It is based on a least-square data-fidelity term and the total variation and Besov seminorm for the regularization term. To fully comprehend the Besov seminorm, an implementation using the curvelet transform and the L 1 norm enforcing the sparsity is proposed. It allows our model to reconstruct both image where acquisition information are missing and image with details in textured areas, thus opening possibilities to reduce acquisition times. To implement the minimization problem using the algorithm developed by Chambolle and Pock, a thorough analysis of the direct model is undertaken and the latter is inverted while avoiding the use of filtered backprojection (FBP) and of non-uniform Fourier transform. Numerical experiments are carried out on simulated data, where the proposed model outperforms both visually and quantitatively the classical model using deconvolution and FBP. Improved reconstructions on real data, acquired on an irradiated distal phalanx, were successfully obtained.

LSD-based analysis of high-resolution stellar spectra

NASA Astrophysics Data System (ADS)

Tsymbal, V.; Tkachenko, A.; Van, Reeth T.

2014-11-01

We present a generalization of the method of least-squares deconvolution (LSD), a powerful tool for extracting high S/N average line profiles from stellar spectra. The generalization of the method is effected by extending it towards the multiprofile LSD and by introducing the possibility to correct the line strengths from the initial mask. We illustrate the new approach by two examples: (a) the detection of astroseismic signatures from low S/N spectra of single stars, and (b) disentangling spectra of multiple stellar objects. The analysis is applied to spectra obtained with 2-m class telescopes in the course of spectroscopic ground-based support for space missions such as CoRoT and Kepler. Usually, rather high S/N is required, so smaller telescopes can only compete successfully with more advanced ones when one can apply a technique that enables a remarkable increase in the S/N of the spectra which they observe. Since the LSD profiles have a potential for reconstruction what is common in all the spectral profiles, it should have a particular practical application to faint stars observed with 2-m class telescopes and whose spectra show remarkable LPVs.

Understanding Least Squares through Monte Carlo Calculations

ERIC Educational Resources Information Center

Tellinghuisen, Joel

2005-01-01

The method of least squares (LS) is considered as an important data analysis tool available to physical scientists. The mathematics of linear least squares(LLS) is summarized in a very compact matrix rotation that renders it practically "formulaic".

An adaptive sparse deconvolution method for distinguishing the overlapping echoes of ultrasonic guided waves for pipeline crack inspection

NASA Astrophysics Data System (ADS)

Chang, Yong; Zi, Yanyang; Zhao, Jiyuan; Yang, Zhe; He, Wangpeng; Sun, Hailiang

2017-03-01

In guided wave pipeline inspection, echoes reflected from closely spaced reflectors generally overlap, meaning useful information is lost. To solve the overlapping problem, sparse deconvolution methods have been developed in the past decade. However, conventional sparse deconvolution methods have limitations in handling guided wave signals, because the input signal is directly used as the prototype of the convolution matrix, without considering the waveform change caused by the dispersion properties of the guided wave. In this paper, an adaptive sparse deconvolution (ASD) method is proposed to overcome these limitations. First, the Gaussian echo model is employed to adaptively estimate the column prototype of the convolution matrix instead of directly using the input signal as the prototype. Then, the convolution matrix is constructed upon the estimated results. Third, the split augmented Lagrangian shrinkage (SALSA) algorithm is introduced to solve the deconvolution problem with high computational efficiency. To verify the effectiveness of the proposed method, guided wave signals obtained from pipeline inspection are investigated numerically and experimentally. Compared to conventional sparse deconvolution methods, e.g. the {{l}1} -norm deconvolution method, the proposed method shows better performance in handling the echo overlap problem in the guided wave signal.

Two-dimensional wavefront reconstruction based on double-shearing and least squares fitting

NASA Astrophysics Data System (ADS)

Liang, Peiying; Ding, Jianping; Zhu, Yangqing; Dong, Qian; Huang, Yuhua; Zhu, Zhen

2017-06-01

The two-dimensional wavefront reconstruction method based on double-shearing and least squares fitting is proposed in this paper. Four one-dimensional phase estimates of the measured wavefront, which correspond to the two shears and the two orthogonal directions, could be calculated from the differential phase, which solves the problem of the missing spectrum, and then by using the least squares method the two-dimensional wavefront reconstruction could be done. The numerical simulations of the proposed algorithm are carried out to verify the feasibility of this method. The influence of noise generated from different shear amount and different intensity on the accuracy of the reconstruction is studied and compared with the results from the algorithm based on single-shearing and least squares fitting. Finally, a two-grating lateral shearing interference experiment is carried out to verify the wavefront reconstruction algorithm based on doubleshearing and least squares fitting.

Separation of Atmospheric and Surface Spectral Features in Mars Global Surveyor Thermal Emission Spectrometer (TES) Spectra

NASA Technical Reports Server (NTRS)

Smith, Michael D.; Bandfield, Joshua L.; Christensen, Philip R.

2000-01-01

We present two algorithms for the separation of spectral features caused by atmospheric and surface components in Thermal Emission Spectrometer (TES) data. One algorithm uses radiative transfer and successive least squares fitting to find spectral shapes first for atmospheric dust, then for water-ice aerosols, and then, finally, for surface emissivity. A second independent algorithm uses a combination of factor analysis, target transformation, and deconvolution to simultaneously find dust, water ice, and surface emissivity spectral shapes. Both algorithms have been applied to TES spectra, and both find very similar atmospheric and surface spectral shapes. For TES spectra taken during aerobraking and science phasing periods in nadir-geometry these two algorithms give meaningful and usable surface emissivity spectra that can be used for mineralogical identification.

A fast least-squares algorithm for population inference

PubMed Central

2013-01-01

Background Population inference is an important problem in genetics used to remove population stratification in genome-wide association studies and to detect migration patterns or shared ancestry. An individual’s genotype can be modeled as a probabilistic function of ancestral population memberships, Q, and the allele frequencies in those populations, P. The parameters, P and Q, of this binomial likelihood model can be inferred using slow sampling methods such as Markov Chain Monte Carlo methods or faster gradient based approaches such as sequential quadratic programming. This paper proposes a least-squares simplification of the binomial likelihood model motivated by a Euclidean interpretation of the genotype feature space. This results in a faster algorithm that easily incorporates the degree of admixture within the sample of individuals and improves estimates without requiring trial-and-error tuning. Results We show that the expected value of the least-squares solution across all possible genotype datasets is equal to the true solution when part of the problem has been solved, and that the variance of the solution approaches zero as its size increases. The Least-squares algorithm performs nearly as well as Admixture for these theoretical scenarios. We compare least-squares, Admixture, and FRAPPE for a variety of problem sizes and difficulties. For particularly hard problems with a large number of populations, small number of samples, or greater degree of admixture, least-squares performs better than the other methods. On simulated mixtures of real population allele frequencies from the HapMap project, Admixture estimates sparsely mixed individuals better than Least-squares. The least-squares approach, however, performs within 1.5% of the Admixture error. On individual genotypes from the HapMap project, Admixture and least-squares perform qualitatively similarly and within 1.2% of each other. Significantly, the least-squares approach nearly always converges 1.5- to 6-times faster. Conclusions The computational advantage of the least-squares approach along with its good estimation performance warrants further research, especially for very large datasets. As problem sizes increase, the difference in estimation performance between all algorithms decreases. In addition, when prior information is known, the least-squares approach easily incorporates the expected degree of admixture to improve the estimate. PMID:23343408

A fast least-squares algorithm for population inference.

PubMed

Parry, R Mitchell; Wang, May D

2013-01-23

Population inference is an important problem in genetics used to remove population stratification in genome-wide association studies and to detect migration patterns or shared ancestry. An individual's genotype can be modeled as a probabilistic function of ancestral population memberships, Q, and the allele frequencies in those populations, P. The parameters, P and Q, of this binomial likelihood model can be inferred using slow sampling methods such as Markov Chain Monte Carlo methods or faster gradient based approaches such as sequential quadratic programming. This paper proposes a least-squares simplification of the binomial likelihood model motivated by a Euclidean interpretation of the genotype feature space. This results in a faster algorithm that easily incorporates the degree of admixture within the sample of individuals and improves estimates without requiring trial-and-error tuning. We show that the expected value of the least-squares solution across all possible genotype datasets is equal to the true solution when part of the problem has been solved, and that the variance of the solution approaches zero as its size increases. The Least-squares algorithm performs nearly as well as Admixture for these theoretical scenarios. We compare least-squares, Admixture, and FRAPPE for a variety of problem sizes and difficulties. For particularly hard problems with a large number of populations, small number of samples, or greater degree of admixture, least-squares performs better than the other methods. On simulated mixtures of real population allele frequencies from the HapMap project, Admixture estimates sparsely mixed individuals better than Least-squares. The least-squares approach, however, performs within 1.5% of the Admixture error. On individual genotypes from the HapMap project, Admixture and least-squares perform qualitatively similarly and within 1.2% of each other. Significantly, the least-squares approach nearly always converges 1.5- to 6-times faster. The computational advantage of the least-squares approach along with its good estimation performance warrants further research, especially for very large datasets. As problem sizes increase, the difference in estimation performance between all algorithms decreases. In addition, when prior information is known, the least-squares approach easily incorporates the expected degree of admixture to improve the estimate.

A model-free method for mass spectrometer response correction. [for oxygen consumption and cardiac output calculation

NASA Technical Reports Server (NTRS)

Shykoff, Barbara E.; Swanson, Harvey T.

1987-01-01

A new method for correction of mass spectrometer output signals is described. Response-time distortion is reduced independently of any model of mass spectrometer behavior. The delay of the system is found first from the cross-correlation function of a step change and its response. A two-sided time-domain digital correction filter (deconvolution filter) is generated next from the same step response data using a regression procedure. Other data are corrected using the filter and delay. The mean squared error between a step response and a step is reduced considerably more after the use of a deconvolution filter than after the application of a second-order model correction. O2 consumption and CO2 production values calculated from data corrupted by a simulated dynamic process return to near the uncorrupted values after correction. Although a clean step response or the ensemble average of several responses contaminated with noise is needed for the generation of the filter, random noise of magnitude not above 0.5 percent added to the response to be corrected does not impair the correction severely.

Orthogonalizing EM: A design-based least squares algorithm.

PubMed

Xiong, Shifeng; Dai, Bin; Huling, Jared; Qian, Peter Z G

We introduce an efficient iterative algorithm, intended for various least squares problems, based on a design of experiments perspective. The algorithm, called orthogonalizing EM (OEM), works for ordinary least squares and can be easily extended to penalized least squares. The main idea of the procedure is to orthogonalize a design matrix by adding new rows and then solve the original problem by embedding the augmented design in a missing data framework. We establish several attractive theoretical properties concerning OEM. For the ordinary least squares with a singular regression matrix, an OEM sequence converges to the Moore-Penrose generalized inverse-based least squares estimator. For ordinary and penalized least squares with various penalties, it converges to a point having grouping coherence for fully aliased regression matrices. Convergence and the convergence rate of the algorithm are examined. Finally, we demonstrate that OEM is highly efficient for large-scale least squares and penalized least squares problems, and is considerably faster than competing methods when n is much larger than p . Supplementary materials for this article are available online.

A Two-Layer Least Squares Support Vector Machine Approach to Credit Risk Assessment

NASA Astrophysics Data System (ADS)

Liu, Jingli; Li, Jianping; Xu, Weixuan; Shi, Yong

Least squares support vector machine (LS-SVM) is a revised version of support vector machine (SVM) and has been proved to be a useful tool for pattern recognition. LS-SVM had excellent generalization performance and low computational cost. In this paper, we propose a new method called two-layer least squares support vector machine which combines kernel principle component analysis (KPCA) and linear programming form of least square support vector machine. With this method sparseness and robustness is obtained while solving large dimensional and large scale database. A U.S. commercial credit card database is used to test the efficiency of our method and the result proved to be a satisfactory one.

[The research on separating and extracting overlapping spectral feature lines in LIBS using damped least squares method].

PubMed

Wang, Yin; Zhao, Nan-jing; Liu, Wen-qing; Yu, Yang; Fang, Li; Meng, De-shuo; Hu, Li; Zhang, Da-hai; Ma, Min-jun; Xiao, Xue; Wang, Yu; Liu, Jian-guo

2015-02-01

In recent years, the technology of laser induced breakdown spectroscopy has been developed rapidly. As one kind of new material composition detection technology, laser induced breakdown spectroscopy can simultaneously detect multi elements fast and simply without any complex sample preparation and realize field, in-situ material composition detection of the sample to be tested. This kind of technology is very promising in many fields. It is very important to separate, fit and extract spectral feature lines in laser induced breakdown spectroscopy, which is the cornerstone of spectral feature recognition and subsequent elements concentrations inversion research. In order to realize effective separation, fitting and extraction of spectral feature lines in laser induced breakdown spectroscopy, the original parameters for spectral lines fitting before iteration were analyzed and determined. The spectral feature line of' chromium (Cr I : 427.480 nm) in fly ash gathered from a coal-fired power station, which was overlapped with another line(FeI: 427.176 nm), was separated from the other one and extracted by using damped least squares method. Based on Gauss-Newton iteration, damped least squares method adds damping factor to step and adjust step length dynamically according to the feedback information after each iteration, in order to prevent the iteration from diverging and make sure that the iteration could converge fast. Damped least squares method helps to obtain better results of separating, fitting and extracting spectral feature lines and give more accurate intensity values of these spectral feature lines: The spectral feature lines of chromium in samples which contain different concentrations of chromium were separated and extracted. And then, the intensity values of corresponding spectral lines were given by using damped least squares method and least squares method separately. The calibration curves were plotted, which showed the relationship between spectral line intensity values and chromium concentrations in different samples. And then their respective linear correlations were compared. The experimental results showed that the linear correlation of the intensity values of spectral feature lines and the concentrations of chromium in different samples, which was obtained by damped least squares method, was better than that one obtained by least squares method. And therefore, damped least squares method was stable, reliable and suitable for separating, fitting and extracting spectral feature lines in laser induced breakdown spectroscopy.

Detecting the Spectrum of the Atlantic's Thermo-haline Circulation: Deconvolved Climate Proxies Show How Polar Climates Communicate

NASA Astrophysics Data System (ADS)

Reischmann, Elizabeth; Yang, Xiao; Rial, José

2014-05-01

Deconvolution is widely used in a wide variety of scientific fields, including its significant use in seismology, as a tool to recover real input from a system's impulse response and output. Our research uses spectral division deconvolution in the context of studying the impulse response of the possible relationship between the nonlinear climates of the Polar Regions by using select δ18O ice cores from both poles. This is feasible in spite of the fact that the records may be the result of nonlinear processes because the two polar climates are synchronized for the period studied, forming a Hilbert transform pair. In order to perform this analysis, the age models of three Greenland and four Antarctica records have been matched using a Monte Carlo method with the methane-matched pair GRIP and BYRD as a basis of calculations. For all of the twelve resulting pairs, various deconvolutions schemes (Weiner, Damped Least Squares, Tikhonov, Truncated Singular Value Decomposition) give consistent, quasi-periodic, impulse responses of the system. Multitaper analysis then demonstrates strong, millennia scale, quasi-periodic oscillations in these system responses with a range of 2,500 to 1,000 years. However, these results are directionally dependent, with the transfer function from north to south differing from that of south north. High amplitude power peaks at 5,000 to 1,7000 years characterize the former, while the latter contains peaks at 2,500 to 1,700 years. These predominant periodicities are also found in the data, some of which have been identified as solar forcing, but others of which may indicate internal oscillations of the climate system (1.6-1.4ky). The approximately 1,500 year period transfer function, which does not have a corresponding solar forcing, may indicate one of these internal periodicities of the system, perhaps even indicating the long-term presence of the Deep Water circulation, also known as the thermo-haline circulation (THC). Simplified models of the polar climate fluctuations are shown to support these findings.

The Use of Alternative Regression Methods in Social Sciences and the Comparison of Least Squares and M Estimation Methods in Terms of the Determination of Coefficient

ERIC Educational Resources Information Center

Coskuntuncel, Orkun

2013-01-01

The purpose of this study is two-fold; the first aim being to show the effect of outliers on the widely used least squares regression estimator in social sciences. The second aim is to compare the classical method of least squares with the robust M-estimator using the "determination of coefficient" (R[superscript 2]). For this purpose,…

Simplified Least Squares Shadowing sensitivity analysis for chaotic ODEs and PDEs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chater, Mario, E-mail: chaterm@mit.edu; Ni, Angxiu, E-mail: niangxiu@mit.edu; Wang, Qiqi, E-mail: qiqi@mit.edu

This paper develops a variant of the Least Squares Shadowing (LSS) method, which has successfully computed the derivative for several chaotic ODEs and PDEs. The development in this paper aims to simplify Least Squares Shadowing method by improving how time dilation is treated. Instead of adding an explicit time dilation term as in the original method, the new variant uses windowing, which can be more efficient and simpler to implement, especially for PDEs.

Comparing least-squares and quantile regression approaches to analyzing median hospital charges.

PubMed

Olsen, Cody S; Clark, Amy E; Thomas, Andrea M; Cook, Lawrence J

2012-07-01

Emergency department (ED) and hospital charges obtained from administrative data sets are useful descriptors of injury severity and the burden to EDs and the health care system. However, charges are typically positively skewed due to costly procedures, long hospital stays, and complicated or prolonged treatment for few patients. The median is not affected by extreme observations and is useful in describing and comparing distributions of hospital charges. A least-squares analysis employing a log transformation is one approach for estimating median hospital charges, corresponding confidence intervals (CIs), and differences between groups; however, this method requires certain distributional properties. An alternate method is quantile regression, which allows estimation and inference related to the median without making distributional assumptions. The objective was to compare the log-transformation least-squares method to the quantile regression approach for estimating median hospital charges, differences in median charges between groups, and associated CIs. The authors performed simulations using repeated sampling of observed statewide ED and hospital charges and charges randomly generated from a hypothetical lognormal distribution. The median and 95% CI and the multiplicative difference between the median charges of two groups were estimated using both least-squares and quantile regression methods. Performance of the two methods was evaluated. In contrast to least squares, quantile regression produced estimates that were unbiased and had smaller mean square errors in simulations of observed ED and hospital charges. Both methods performed well in simulations of hypothetical charges that met least-squares method assumptions. When the data did not follow the assumed distribution, least-squares estimates were often biased, and the associated CIs had lower than expected coverage as sample size increased. Quantile regression analyses of hospital charges provide unbiased estimates even when lognormal and equal variance assumptions are violated. These methods may be particularly useful in describing and analyzing hospital charges from administrative data sets. © 2012 by the Society for Academic Emergency Medicine.

New method to incorporate Type B uncertainty into least-squares procedures in radionuclide metrology.

PubMed

Han, Jubong; Lee, K B; Lee, Jong-Man; Park, Tae Soon; Oh, J S; Oh, Pil-Jei

2016-03-01

We discuss a new method to incorporate Type B uncertainty into least-squares procedures. The new method is based on an extension of the likelihood function from which a conventional least-squares function is derived. The extended likelihood function is the product of the original likelihood function with additional PDFs (Probability Density Functions) that characterize the Type B uncertainties. The PDFs are considered to describe one's incomplete knowledge on correction factors being called nuisance parameters. We use the extended likelihood function to make point and interval estimations of parameters in the basically same way as the least-squares function used in the conventional least-squares method is derived. Since the nuisance parameters are not of interest and should be prevented from appearing in the final result, we eliminate such nuisance parameters by using the profile likelihood. As an example, we present a case study for a linear regression analysis with a common component of Type B uncertainty. In this example we compare the analysis results obtained from using our procedure with those from conventional methods. Copyright © 2015. Published by Elsevier Ltd.

Using Least Squares for Error Propagation

ERIC Educational Resources Information Center

Tellinghuisen, Joel

2015-01-01

The method of least-squares (LS) has a built-in procedure for estimating the standard errors (SEs) of the adjustable parameters in the fit model: They are the square roots of the diagonal elements of the covariance matrix. This means that one can use least-squares to obtain numerical values of propagated errors by defining the target quantities as…

Multi-element least square HDMR methods and their applications for stochastic multiscale model reduction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang, Lijian, E-mail: ljjiang@hnu.edu.cn; Li, Xinping, E-mail: exping@126.com

Stochastic multiscale modeling has become a necessary approach to quantify uncertainty and characterize multiscale phenomena for many practical problems such as flows in stochastic porous media. The numerical treatment of the stochastic multiscale models can be very challengeable as the existence of complex uncertainty and multiple physical scales in the models. To efficiently take care of the difficulty, we construct a computational reduced model. To this end, we propose a multi-element least square high-dimensional model representation (HDMR) method, through which the random domain is adaptively decomposed into a few subdomains, and a local least square HDMR is constructed in eachmore » subdomain. These local HDMRs are represented by a finite number of orthogonal basis functions defined in low-dimensional random spaces. The coefficients in the local HDMRs are determined using least square methods. We paste all the local HDMR approximations together to form a global HDMR approximation. To further reduce computational cost, we present a multi-element reduced least-square HDMR, which improves both efficiency and approximation accuracy in certain conditions. To effectively treat heterogeneity properties and multiscale features in the models, we integrate multiscale finite element methods with multi-element least-square HDMR for stochastic multiscale model reduction. This approach significantly reduces the original model's complexity in both the resolution of the physical space and the high-dimensional stochastic space. We analyze the proposed approach, and provide a set of numerical experiments to demonstrate the performance of the presented model reduction techniques. - Highlights: • Multi-element least square HDMR is proposed to treat stochastic models. • Random domain is adaptively decomposed into some subdomains to obtain adaptive multi-element HDMR. • Least-square reduced HDMR is proposed to enhance computation efficiency and approximation accuracy in certain conditions. • Integrating MsFEM and multi-element least square HDMR can significantly reduce computation complexity.« less

Three Perspectives on Teaching Least Squares

ERIC Educational Resources Information Center

Scariano, Stephen M.; Calzada, Maria

2004-01-01

The method of Least Squares is the most widely used technique for fitting a straight line to data, and it is typically discussed in several undergraduate courses. This article focuses on three developmentally different approaches for solving the Least Squares problem that are suitable for classroom exposition.

Simultaneous quantitative analysis of olmesartan, amlodipine and hydrochlorothiazide in their combined dosage form utilizing classical and alternating least squares based chemometric methods.

PubMed

Darwish, Hany W; Bakheit, Ahmed H; Abdelhameed, Ali S

2016-03-01

Simultaneous spectrophotometric analysis of a multi-component dosage form of olmesartan, amlodipine and hydrochlorothiazide used for the treatment of hypertension has been carried out using various chemometric methods. Multivariate calibration methods include classical least squares (CLS) executed by net analyte processing (NAP-CLS), orthogonal signal correction (OSC-CLS) and direct orthogonal signal correction (DOSC-CLS) in addition to multivariate curve resolution-alternating least squares (MCR-ALS). Results demonstrated the efficiency of the proposed methods as quantitative tools of analysis as well as their qualitative capability. The three analytes were determined precisely using the aforementioned methods in an external data set and in a dosage form after optimization of experimental conditions. Finally, the efficiency of the models was validated via comparison with the partial least squares (PLS) method in terms of accuracy and precision.

An error analysis of least-squares finite element method of velocity-pressure-vorticity formulation for Stokes problem

NASA Technical Reports Server (NTRS)

Chang, Ching L.; Jiang, Bo-Nan

1990-01-01

A theoretical proof of the optimal rate of convergence for the least-squares method is developed for the Stokes problem based on the velocity-pressure-vorticity formula. The 2D Stokes problem is analyzed to define the product space and its inner product, and the a priori estimates are derived to give the finite-element approximation. The least-squares method is found to converge at the optimal rate for equal-order interpolation.

Fast analytical spectral filtering methods for magnetic resonance perfusion quantification.

PubMed

Reddy, Kasireddy V; Mitra, Abhishek; Yalavarthy, Phaneendra K

2016-08-01

The deconvolution in the perfusion weighted imaging (PWI) plays an important role in quantifying the MR perfusion parameters. The PWI application to stroke and brain tumor studies has become a standard clinical practice. The standard approach for this deconvolution is oscillatory-limited singular value decomposition (oSVD) and frequency domain deconvolution (FDD). The FDD is widely recognized as the fastest approach currently available for deconvolution of MR perfusion data. In this work, two fast deconvolution methods (namely analytical fourier filtering and analytical showalter spectral filtering) are proposed. Through systematic evaluation, the proposed methods are shown to be computationally efficient and quantitatively accurate compared to FDD and oSVD.

2-D weighted least-squares phase unwrapping

DOEpatents

Ghiglia, Dennis C.; Romero, Louis A.

1995-01-01

Weighted values of interferometric signals are unwrapped by determining the least squares solution of phase unwrapping for unweighted values of the interferometric signals; and then determining the least squares solution of phase unwrapping for weighted values of the interferometric signals by preconditioned conjugate gradient methods using the unweighted solutions as preconditioning values. An output is provided that is representative of the least squares solution of phase unwrapping for weighted values of the interferometric signals.

2-D weighted least-squares phase unwrapping

DOEpatents

Ghiglia, D.C.; Romero, L.A.

1995-06-13

Weighted values of interferometric signals are unwrapped by determining the least squares solution of phase unwrapping for unweighted values of the interferometric signals; and then determining the least squares solution of phase unwrapping for weighted values of the interferometric signals by preconditioned conjugate gradient methods using the unweighted solutions as preconditioning values. An output is provided that is representative of the least squares solution of phase unwrapping for weighted values of the interferometric signals. 6 figs.

Spacecraft inertia estimation via constrained least squares

NASA Technical Reports Server (NTRS)

Keim, Jason A.; Acikmese, Behcet A.; Shields, Joel F.

2006-01-01

This paper presents a new formulation for spacecraft inertia estimation from test data. Specifically, the inertia estimation problem is formulated as a constrained least squares minimization problem with explicit bounds on the inertia matrix incorporated as LMIs [linear matrix inequalities). The resulting minimization problem is a semidefinite optimization that can be solved efficiently with guaranteed convergence to the global optimum by readily available algorithms. This method is applied to data collected from a robotic testbed consisting of a freely rotating body. The results show that the constrained least squares approach produces more accurate estimates of the inertia matrix than standard unconstrained least squares estimation methods.

Orthogonalizing EM: A design-based least squares algorithm

PubMed Central

Xiong, Shifeng; Dai, Bin; Huling, Jared; Qian, Peter Z. G.

2016-01-01

We introduce an efficient iterative algorithm, intended for various least squares problems, based on a design of experiments perspective. The algorithm, called orthogonalizing EM (OEM), works for ordinary least squares and can be easily extended to penalized least squares. The main idea of the procedure is to orthogonalize a design matrix by adding new rows and then solve the original problem by embedding the augmented design in a missing data framework. We establish several attractive theoretical properties concerning OEM. For the ordinary least squares with a singular regression matrix, an OEM sequence converges to the Moore-Penrose generalized inverse-based least squares estimator. For ordinary and penalized least squares with various penalties, it converges to a point having grouping coherence for fully aliased regression matrices. Convergence and the convergence rate of the algorithm are examined. Finally, we demonstrate that OEM is highly efficient for large-scale least squares and penalized least squares problems, and is considerably faster than competing methods when n is much larger than p. Supplementary materials for this article are available online. PMID:27499558

Uncertainty based pressure reconstruction from velocity measurement with generalized least squares

NASA Astrophysics Data System (ADS)

Zhang, Jiacheng; Scalo, Carlo; Vlachos, Pavlos

2017-11-01

A method using generalized least squares reconstruction of instantaneous pressure field from velocity measurement and velocity uncertainty is introduced and applied to both planar and volumetric flow data. Pressure gradients are computed on a staggered grid from flow acceleration. The variance-covariance matrix of the pressure gradients is evaluated from the velocity uncertainty by approximating the pressure gradient error to a linear combination of velocity errors. An overdetermined system of linear equations which relates the pressure and the computed pressure gradients is formulated and then solved using generalized least squares with the variance-covariance matrix of the pressure gradients. By comparing the reconstructed pressure field against other methods such as solving the pressure Poisson equation, the omni-directional integration, and the ordinary least squares reconstruction, generalized least squares method is found to be more robust to the noise in velocity measurement. The improvement on pressure result becomes more remarkable when the velocity measurement becomes less accurate and more heteroscedastic. The uncertainty of the reconstructed pressure field is also quantified and compared across the different methods.

Simple and Reliable Determination of Intravoxel Incoherent Motion Parameters for the Differential Diagnosis of Head and Neck Tumors

PubMed Central

Sasaki, Miho; Sumi, Misa; Eida, Sato; Katayama, Ikuo; Hotokezaka, Yuka; Nakamura, Takashi

2014-01-01

Intravoxel incoherent motion (IVIM) imaging can characterize diffusion and perfusion of normal and diseased tissues, and IVIM parameters are authentically determined by using cumbersome least-squares method. We evaluated a simple technique for the determination of IVIM parameters using geometric analysis of the multiexponential signal decay curve as an alternative to the least-squares method for the diagnosis of head and neck tumors. Pure diffusion coefficients (D), microvascular volume fraction (f), perfusion-related incoherent microcirculation (D*), and perfusion parameter that is heavily weighted towards extravascular space (P) were determined geometrically (Geo D, Geo f, and Geo P) or by least-squares method (Fit D, Fit f, and Fit D*) in normal structures and 105 head and neck tumors. The IVIM parameters were compared for their levels and diagnostic abilities between the 2 techniques. The IVIM parameters were not able to determine in 14 tumors with the least-squares method alone and in 4 tumors with the geometric and least-squares methods. The geometric IVIM values were significantly different (p<0.001) from Fit values (+2±4% and −7±24% for D and f values, respectively). Geo D and Fit D differentiated between lymphomas and SCCs with similar efficacy (78% and 80% accuracy, respectively). Stepwise approaches using combinations of Geo D and Geo P, Geo D and Geo f, or Fit D and Fit D* differentiated between pleomorphic adenomas, Warthin tumors, and malignant salivary gland tumors with the same efficacy (91% accuracy = 21/23). However, a stepwise differentiation using Fit D and Fit f was less effective (83% accuracy = 19/23). Considering cumbersome procedures with the least squares method compared with the geometric method, we concluded that the geometric determination of IVIM parameters can be an alternative to least-squares method in the diagnosis of head and neck tumors. PMID:25402436

Generalizations of Tikhonov's regularized method of least squares to non-Euclidean vector norms

NASA Astrophysics Data System (ADS)

Volkov, V. V.; Erokhin, V. I.; Kakaev, V. V.; Onufrei, A. Yu.

2017-09-01

Tikhonov's regularized method of least squares and its generalizations to non-Euclidean norms, including polyhedral, are considered. The regularized method of least squares is reduced to mathematical programming problems obtained by "instrumental" generalizations of the Tikhonov lemma on the minimal (in a certain norm) solution of a system of linear algebraic equations with respect to an unknown matrix. Further studies are needed for problems concerning the development of methods and algorithms for solving reduced mathematical programming problems in which the objective functions and admissible domains are constructed using polyhedral vector norms.

A component prediction method for flue gas of natural gas combustion based on nonlinear partial least squares method.

PubMed

Cao, Hui; Yan, Xingyu; Li, Yaojiang; Wang, Yanxia; Zhou, Yan; Yang, Sanchun

2014-01-01

Quantitative analysis for the flue gas of natural gas-fired generator is significant for energy conservation and emission reduction. The traditional partial least squares method may not deal with the nonlinear problems effectively. In the paper, a nonlinear partial least squares method with extended input based on radial basis function neural network (RBFNN) is used for components prediction of flue gas. For the proposed method, the original independent input matrix is the input of RBFNN and the outputs of hidden layer nodes of RBFNN are the extension term of the original independent input matrix. Then, the partial least squares regression is performed on the extended input matrix and the output matrix to establish the components prediction model of flue gas. A near-infrared spectral dataset of flue gas of natural gas combustion is used for estimating the effectiveness of the proposed method compared with PLS. The experiments results show that the root-mean-square errors of prediction values of the proposed method for methane, carbon monoxide, and carbon dioxide are, respectively, reduced by 4.74%, 21.76%, and 5.32% compared to those of PLS. Hence, the proposed method has higher predictive capabilities and better robustness.

New deconvolution method for microscopic images based on the continuous Gaussian radial basis function interpolation model.

PubMed

Chen, Zhaoxue; Chen, Hao

2014-01-01

A deconvolution method based on the Gaussian radial basis function (GRBF) interpolation is proposed. Both the original image and Gaussian point spread function are expressed as the same continuous GRBF model, thus image degradation is simplified as convolution of two continuous Gaussian functions, and image deconvolution is converted to calculate the weighted coefficients of two-dimensional control points. Compared with Wiener filter and Lucy-Richardson algorithm, the GRBF method has an obvious advantage in the quality of restored images. In order to overcome such a defect of long-time computing, the method of graphic processing unit multithreading or increasing space interval of control points is adopted, respectively, to speed up the implementation of GRBF method. The experiments show that based on the continuous GRBF model, the image deconvolution can be efficiently implemented by the method, which also has a considerable reference value for the study of three-dimensional microscopic image deconvolution.

Assessing Fit and Dimensionality in Least Squares Metric Multidimensional Scaling Using Akaike's Information Criterion

ERIC Educational Resources Information Center

Ding, Cody S.; Davison, Mark L.

2010-01-01

Akaike's information criterion is suggested as a tool for evaluating fit and dimensionality in metric multidimensional scaling that uses least squares methods of estimation. This criterion combines the least squares loss function with the number of estimated parameters. Numerical examples are presented. The results from analyses of both simulation…

Deconvolution of magnetic acoustic change complex (mACC).

PubMed

Bardy, Fabrice; McMahon, Catherine M; Yau, Shu Hui; Johnson, Blake W

2014-11-01

The aim of this study was to design a novel experimental approach to investigate the morphological characteristics of auditory cortical responses elicited by rapidly changing synthesized speech sounds. Six sound-evoked magnetoencephalographic (MEG) responses were measured to a synthesized train of speech sounds using the vowels /e/ and /u/ in 17 normal hearing young adults. Responses were measured to: (i) the onset of the speech train, (ii) an F0 increment; (iii) an F0 decrement; (iv) an F2 decrement; (v) an F2 increment; and (vi) the offset of the speech train using short (jittered around 135ms) and long (1500ms) stimulus onset asynchronies (SOAs). The least squares (LS) deconvolution technique was used to disentangle the overlapping MEG responses in the short SOA condition only. Comparison between the morphology of the recovered cortical responses in the short and long SOAs conditions showed high similarity, suggesting that the LS deconvolution technique was successful in disentangling the MEG waveforms. Waveform latencies and amplitudes were different for the two SOAs conditions and were influenced by the spectro-temporal properties of the sound sequence. The magnetic acoustic change complex (mACC) for the short SOA condition showed significantly lower amplitudes and shorter latencies compared to the long SOA condition. The F0 transition showed a larger reduction in amplitude from long to short SOA compared to the F2 transition. Lateralization of the cortical responses were observed under some stimulus conditions and appeared to be associated with the spectro-temporal properties of the acoustic stimulus. The LS deconvolution technique provides a new tool to study the properties of the auditory cortical response to rapidly changing sound stimuli. The presence of the cortical auditory evoked responses for rapid transition of synthesized speech stimuli suggests that the temporal code is preserved at the level of the auditory cortex. Further, the reduced amplitudes and shorter latencies might reflect intrinsic properties of the cortical neurons to rapidly presented sounds. This is the first demonstration of the separation of overlapping cortical responses to rapidly changing speech sounds and offers a potential new biomarker of discrimination of rapid transition of sound. Crown Copyright © 2014. Published by Elsevier Ireland Ltd. All rights reserved.

Least Squares Moving-Window Spectral Analysis.

PubMed

Lee, Young Jong

2017-08-01

Least squares regression is proposed as a moving-windows method for analysis of a series of spectra acquired as a function of external perturbation. The least squares moving-window (LSMW) method can be considered an extended form of the Savitzky-Golay differentiation for nonuniform perturbation spacing. LSMW is characterized in terms of moving-window size, perturbation spacing type, and intensity noise. Simulation results from LSMW are compared with results from other numerical differentiation methods, such as single-interval differentiation, autocorrelation moving-window, and perturbation correlation moving-window methods. It is demonstrated that this simple LSMW method can be useful for quantitative analysis of nonuniformly spaced spectral data with high frequency noise.

A simple method for processing data with least square method

NASA Astrophysics Data System (ADS)

Wang, Chunyan; Qi, Liqun; Chen, Yongxiang; Pang, Guangning

2017-08-01

The least square method is widely used in data processing and error estimation. The mathematical method has become an essential technique for parameter estimation, data processing, regression analysis and experimental data fitting, and has become a criterion tool for statistical inference. In measurement data analysis, the distribution of complex rules is usually based on the least square principle, i.e., the use of matrix to solve the final estimate and to improve its accuracy. In this paper, a new method is presented for the solution of the method which is based on algebraic computation and is relatively straightforward and easy to understand. The practicability of this method is described by a concrete example.

a Unified Matrix Polynomial Approach to Modal Identification

NASA Astrophysics Data System (ADS)

Allemang, R. J.; Brown, D. L.

1998-04-01

One important current focus of modal identification is a reformulation of modal parameter estimation algorithms into a single, consistent mathematical formulation with a corresponding set of definitions and unifying concepts. Particularly, a matrix polynomial approach is used to unify the presentation with respect to current algorithms such as the least-squares complex exponential (LSCE), the polyreference time domain (PTD), Ibrahim time domain (ITD), eigensystem realization algorithm (ERA), rational fraction polynomial (RFP), polyreference frequency domain (PFD) and the complex mode indication function (CMIF) methods. Using this unified matrix polynomial approach (UMPA) allows a discussion of the similarities and differences of the commonly used methods. the use of least squares (LS), total least squares (TLS), double least squares (DLS) and singular value decomposition (SVD) methods is discussed in order to take advantage of redundant measurement data. Eigenvalue and SVD transformation methods are utilized to reduce the effective size of the resulting eigenvalue-eigenvector problem as well.

A molten globule-like intermediate state detected in the thermal transition of cytochrome c under low salt concentration.

PubMed

Nakamura, Shigeyoshi; Baba, Takayuki; Kidokoro, Shun-Ichi

2007-04-01

To understand the stabilization mechanism of the transient intermediate state in protein folding, it is very important to understand the structure and stability of the molten globule state under a native condition, in which the native state exists stably. The thermal transitions of horse cytochrome c were thermodynamically evaluated by highly precise differential scanning calorimetry (DSC) at pH 3.8-5.0. The heat capacity functions were analyzed using double deconvolution and the nonlinear least-squares method. An intermediate (I) state is clearly confirmed in the thermal native (N)-to-denatured (D) transition of horse cytochrome c. The mole fraction of the intermediate state shows the largest value, 0.4, at nearly 70 degrees C at pH 4.1. This intermediate state was also detected by the circular dichroism (CD) method and was found to have the properties of the molten globule-like structure by three-state analysis of the CD data. The Gibbs free-energy change between N and I, DeltaG(NI), and that between N and D, DeltaG(ND), were evaluated to be 9-22 kJ mol(-1) and 41-45 kJ mol(-1), respectively at 15( ) degrees C and pH 4.1.

An analysis of the least-squares problem for the DSN systematic pointing error model

NASA Technical Reports Server (NTRS)

Alvarez, L. S.

1991-01-01

A systematic pointing error model is used to calibrate antennas in the Deep Space Network. The least squares problem is described and analyzed along with the solution methods used to determine the model's parameters. Specifically studied are the rank degeneracy problems resulting from beam pointing error measurement sets that incorporate inadequate sky coverage. A least squares parameter subset selection method is described and its applicability to the systematic error modeling process is demonstrated on Voyager 2 measurement distribution.

Solution of a Complex Least Squares Problem with Constrained Phase.

PubMed

Bydder, Mark

2010-12-30

The least squares solution of a complex linear equation is in general a complex vector with independent real and imaginary parts. In certain applications in magnetic resonance imaging, a solution is desired such that each element has the same phase. A direct method for obtaining the least squares solution to the phase constrained problem is described.

Use of partial least squares regression to impute SNP genotypes in Italian cattle breeds.

PubMed

Dimauro, Corrado; Cellesi, Massimo; Gaspa, Giustino; Ajmone-Marsan, Paolo; Steri, Roberto; Marras, Gabriele; Macciotta, Nicolò P P

2013-06-05

The objective of the present study was to test the ability of the partial least squares regression technique to impute genotypes from low density single nucleotide polymorphisms (SNP) panels i.e. 3K or 7K to a high density panel with 50K SNP. No pedigree information was used. Data consisted of 2093 Holstein, 749 Brown Swiss and 479 Simmental bulls genotyped with the Illumina 50K Beadchip. First, a single-breed approach was applied by using only data from Holstein animals. Then, to enlarge the training population, data from the three breeds were combined and a multi-breed analysis was performed. Accuracies of genotypes imputed using the partial least squares regression method were compared with those obtained by using the Beagle software. The impact of genotype imputation on breeding value prediction was evaluated for milk yield, fat content and protein content. In the single-breed approach, the accuracy of imputation using partial least squares regression was around 90 and 94% for the 3K and 7K platforms, respectively; corresponding accuracies obtained with Beagle were around 85% and 90%. Moreover, computing time required by the partial least squares regression method was on average around 10 times lower than computing time required by Beagle. Using the partial least squares regression method in the multi-breed resulted in lower imputation accuracies than using single-breed data. The impact of the SNP-genotype imputation on the accuracy of direct genomic breeding values was small. The correlation between estimates of genetic merit obtained by using imputed versus actual genotypes was around 0.96 for the 7K chip. Results of the present work suggested that the partial least squares regression imputation method could be useful to impute SNP genotypes when pedigree information is not available.

Compensating Atmospheric Turbulence Effects at High Zenith Angles with Adaptive Optics Using Advanced Phase Reconstructors

NASA Astrophysics Data System (ADS)

Roggemann, M.; Soehnel, G.; Archer, G.

Atmospheric turbulence degrades the resolution of images of space objects far beyond that predicted by diffraction alone. Adaptive optics telescopes have been widely used for compensating these effects, but as users seek to extend the envelopes of operation of adaptive optics telescopes to more demanding conditions, such as daylight operation, and operation at low elevation angles, the level of compensation provided will degrade. We have been investigating the use of advanced wave front reconstructors and post detection image reconstruction to overcome the effects of turbulence on imaging systems in these more demanding scenarios. In this paper we show results comparing the optical performance of the exponential reconstructor, the least squares reconstructor, and two versions of a reconstructor based on the stochastic parallel gradient descent algorithm in a closed loop adaptive optics system using a conventional continuous facesheet deformable mirror and a Hartmann sensor. The performance of these reconstructors has been evaluated under a range of source visual magnitudes and zenith angles ranging up to 70 degrees. We have also simulated satellite images, and applied speckle imaging, multi-frame blind deconvolution algorithms, and deconvolution algorithms that presume the average point spread function is known to compute object estimates. Our work thus far indicates that the combination of adaptive optics and post detection image processing will extend the useful envelope of the current generation of adaptive optics telescopes.

Rapid perfusion quantification using Welch-Satterthwaite approximation and analytical spectral filtering

NASA Astrophysics Data System (ADS)

Krishnan, Karthik; Reddy, Kasireddy V.; Ajani, Bhavya; Yalavarthy, Phaneendra K.

2017-02-01

CT and MR perfusion weighted imaging (PWI) enable quantification of perfusion parameters in stroke studies. These parameters are calculated from the residual impulse response function (IRF) based on a physiological model for tissue perfusion. The standard approach for estimating the IRF is deconvolution using oscillatory-limited singular value decomposition (oSVD) or Frequency Domain Deconvolution (FDD). FDD is widely recognized as the fastest approach currently available for deconvolution of CT Perfusion/MR PWI. In this work, three faster methods are proposed. The first is a direct (model based) crude approximation to the final perfusion quantities (Blood flow, Blood volume, Mean Transit Time and Delay) using the Welch-Satterthwaite approximation for gamma fitted concentration time curves (CTC). The second method is a fast accurate deconvolution method, we call Analytical Fourier Filtering (AFF). The third is another fast accurate deconvolution technique using Showalter's method, we call Analytical Showalter's Spectral Filtering (ASSF). Through systematic evaluation on phantom and clinical data, the proposed methods are shown to be computationally more than twice as fast as FDD. The two deconvolution based methods, AFF and ASSF, are also shown to be quantitatively accurate compared to FDD and oSVD.

Penalized Nonlinear Least Squares Estimation of Time-Varying Parameters in Ordinary Differential Equations

PubMed Central

Cao, Jiguo; Huang, Jianhua Z.; Wu, Hulin

2012-01-01

Ordinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online. PMID:23155351

Measurement System Characterization in the Presence of Measurement Errors

NASA Technical Reports Server (NTRS)

Commo, Sean A.

2012-01-01

In the calibration of a measurement system, data are collected in order to estimate a mathematical model between one or more factors of interest and a response. Ordinary least squares is a method employed to estimate the regression coefficients in the model. The method assumes that the factors are known without error; yet, it is implicitly known that the factors contain some uncertainty. In the literature, this uncertainty is known as measurement error. The measurement error affects both the estimates of the model coefficients and the prediction, or residual, errors. There are some methods, such as orthogonal least squares, that are employed in situations where measurement errors exist, but these methods do not directly incorporate the magnitude of the measurement errors. This research proposes a new method, known as modified least squares, that combines the principles of least squares with knowledge about the measurement errors. This knowledge is expressed in terms of the variance ratio - the ratio of response error variance to measurement error variance.

Use of inequality constrained least squares estimation in small area estimation

NASA Astrophysics Data System (ADS)

Abeygunawardana, R. A. B.; Wickremasinghe, W. N.

2017-05-01

Traditional surveys provide estimates that are based only on the sample observations collected for the population characteristic of interest. However, these estimates may have unacceptably large variance for certain domains. Small Area Estimation (SAE) deals with determining precise and accurate estimates for population characteristics of interest for such domains. SAE usually uses least squares or maximum likelihood procedures incorporating prior information and current survey data. Many available methods in SAE use constraints in equality form. However there are practical situations where certain inequality restrictions on model parameters are more realistic. It will lead to Inequality Constrained Least Squares (ICLS) estimates if the method used is least squares. In this study ICLS estimation procedure is applied to many proposed small area estimates.

A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging.

PubMed

Koay, Cheng Guan; Chang, Lin-Ching; Carew, John D; Pierpaoli, Carlo; Basser, Peter J

2006-09-01

A unifying theoretical and algorithmic framework for diffusion tensor estimation is presented. Theoretical connections among the least squares (LS) methods, (linear least squares (LLS), weighted linear least squares (WLLS), nonlinear least squares (NLS) and their constrained counterparts), are established through their respective objective functions, and higher order derivatives of these objective functions, i.e., Hessian matrices. These theoretical connections provide new insights in designing efficient algorithms for NLS and constrained NLS (CNLS) estimation. Here, we propose novel algorithms of full Newton-type for the NLS and CNLS estimations, which are evaluated with Monte Carlo simulations and compared with the commonly used Levenberg-Marquardt method. The proposed methods have a lower percent of relative error in estimating the trace and lower reduced chi2 value than those of the Levenberg-Marquardt method. These results also demonstrate that the accuracy of an estimate, particularly in a nonlinear estimation problem, is greatly affected by the Hessian matrix. In other words, the accuracy of a nonlinear estimation is algorithm-dependent. Further, this study shows that the noise variance in diffusion weighted signals is orientation dependent when signal-to-noise ratio (SNR) is low (

The crux of the method: assumptions in ordinary least squares and logistic regression.

PubMed

Long, Rebecca G

2008-10-01

Logistic regression has increasingly become the tool of choice when analyzing data with a binary dependent variable. While resources relating to the technique are widely available, clear discussions of why logistic regression should be used in place of ordinary least squares regression are difficult to find. The current paper compares and contrasts the assumptions of ordinary least squares with those of logistic regression and explains why logistic regression's looser assumptions make it adept at handling violations of the more important assumptions in ordinary least squares.

Landsat-4 (TDRSS-user) orbit determination using batch least-squares and sequential methods

NASA Technical Reports Server (NTRS)

Oza, D. H.; Jones, T. L.; Hakimi, M.; Samii, M. V.; Doll, C. E.; Mistretta, G. D.; Hart, R. C.

1992-01-01

TDRSS user orbit determination is analyzed using a batch least-squares method and a sequential estimation method. It was found that in the batch least-squares method analysis, the orbit determination consistency for Landsat-4, which was heavily tracked by TDRSS during January 1991, was about 4 meters in the rms overlap comparisons and about 6 meters in the maximum position differences in overlap comparisons. The consistency was about 10 to 30 meters in the 3 sigma state error covariance function in the sequential method analysis. As a measure of consistency, the first residual of each pass was within the 3 sigma bound in the residual space.

Understanding AuNP interaction with low-generation PAMAM dendrimers: a CIELab and deconvolution study

NASA Astrophysics Data System (ADS)

Jimenez-Ruiz, A.; Carnerero, J. M.; Castillo, P. M.; Prado-Gotor, R.

2017-01-01

Low-generation polyamidoamine (PAMAM) dendrimers are known to adsorb on the surface of gold nanoparticles (AuNPs) causing aggregation and color changes. In this paper, a thorough study of this affinity using absorption spectroscopy, colorimetric, and emission methods has been carried out. Results show that, for citrate-capped gold nanoparticles, interaction with the dendrimer is not only of an electrostatic character but instead occurs, at least in part, through the dendrimer's uncharged internal amino groups. The possibilities of the CIELab chromaticity system parameters' evolution have also been explored in order to quantify dendrimer interaction with the red-colored nanoparticles. By measuring and quantifying 17 nm citrate-capped AuNP color changes, which are strongly dependant on their aggregation state, binding free energies are obtained for the first time for these systems. Results are confirmed via an alternate fitting method which makes use of deconvolution parameters from absorbance spectra. Binding free energies obtained through the use of both means are in good agreement with each other.

Multiway analysis methods applied to the fluorescence excitation-emission dataset for the simultaneous quantification of valsartan and amlodipine in tablets

NASA Astrophysics Data System (ADS)

Dinç, Erdal; Ertekin, Zehra Ceren; Büker, Eda

2017-09-01

In this study, excitation-emission matrix datasets, which have strong overlapping bands, were processed by using four different chemometric calibration algorithms consisting of parallel factor analysis, Tucker3, three-way partial least squares and unfolded partial least squares for the simultaneous quantitative estimation of valsartan and amlodipine besylate in tablets. In analyses, preliminary separation step was not used before the application of parallel factor analysis Tucker3, three-way partial least squares and unfolded partial least squares approaches for the analysis of the related drug substances in samples. Three-way excitation-emission matrix data array was obtained by concatenating excitation-emission matrices of the calibration set, validation set, and commercial tablet samples. The excitation-emission matrix data array was used to get parallel factor analysis, Tucker3, three-way partial least squares and unfolded partial least squares calibrations and to predict the amounts of valsartan and amlodipine besylate in samples. For all the methods, calibration and prediction of valsartan and amlodipine besylate were performed in the working concentration ranges of 0.25-4.50 μg/mL. The validity and the performance of all the proposed methods were checked by using the validation parameters. From the analysis results, it was concluded that the described two-way and three-way algorithmic methods were very useful for the simultaneous quantitative resolution and routine analysis of the related drug substances in marketed samples.

Iterative dip-steering median filter

NASA Astrophysics Data System (ADS)

Huo, Shoudong; Zhu, Weihong; Shi, Taikun

2017-09-01

Seismic data are always contaminated with high noise components, which present processing challenges especially for signal preservation and its true amplitude response. This paper deals with an extension of the conventional median filter, which is widely used in random noise attenuation. It is known that the standard median filter works well with laterally aligned coherent events but cannot handle steep events, especially events with conflicting dips. In this paper, an iterative dip-steering median filter is proposed for the attenuation of random noise in the presence of multiple dips. The filter first identifies the dominant dips inside an optimized processing window by a Fourier-radial transform in the frequency-wavenumber domain. The optimum size of the processing window depends on the intensity of random noise that needs to be attenuated and the amount of signal to be preserved. It then applies median filter along the dominant dip and retains the signals. Iterations are adopted to process the residual signals along the remaining dominant dips in a descending sequence, until all signals have been retained. The method is tested by both synthetic and field data gathers and also compared with the commonly used f-k least squares de-noising and f-x deconvolution.

Seismic interferometry by multidimensional deconvolution as a means to compensate for anisotropic illumination

NASA Astrophysics Data System (ADS)

Wapenaar, K.; van der Neut, J.; Ruigrok, E.; Draganov, D.; Hunziker, J.; Slob, E.; Thorbecke, J.; Snieder, R.

2008-12-01

It is well-known that under specific conditions the crosscorrelation of wavefields observed at two receivers yields the impulse response between these receivers. This principle is known as 'Green's function retrieval' or 'seismic interferometry'. Recently it has been recognized that in many situations it can be advantageous to replace the correlation process by deconvolution. One of the advantages is that deconvolution compensates for the waveform emitted by the source; another advantage is that it is not necessary to assume that the medium is lossless. The approaches that have been developed to date employ a 1D deconvolution process. We propose a method for seismic interferometry by multidimensional deconvolution and show that under specific circumstances the method compensates for irregularities in the source distribution. This is an important difference with crosscorrelation methods, which rely on the condition that waves are equipartitioned. This condition is for example fulfilled when the sources are regularly distributed along a closed surface and the power spectra of the sources are identical. The proposed multidimensional deconvolution method compensates for anisotropic illumination, without requiring knowledge about the positions and the spectra of the sources.

Accuracy of least-squares methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bochev, Pavel B.; Gunzburger, Max D.

1993-01-01

Recently there has been substantial interest in least-squares finite element methods for velocity-vorticity-pressure formulations of the incompressible Navier-Stokes equations. The main cause for this interest is the fact that algorithms for the resulting discrete equations can be devised which require the solution of only symmetric, positive definite systems of algebraic equations. On the other hand, it is well-documented that methods using the vorticity as a primary variable often yield very poor approximations. Thus, here we study the accuracy of these methods through a series of computational experiments, and also comment on theoretical error estimates. It is found, despite the failure of standard methods for deriving error estimates, that computational evidence suggests that these methods are, at the least, nearly optimally accurate. Thus, in addition to the desirable matrix properties yielded by least-squares methods, one also obtains accurate approximations.

Post-processing of adaptive optics images based on frame selection and multi-frame blind deconvolution

NASA Astrophysics Data System (ADS)

Tian, Yu; Rao, Changhui; Wei, Kai

2008-07-01

The adaptive optics can only partially compensate the image blurred by atmospheric turbulence due to the observing condition and hardware restriction. A post-processing method based on frame selection and multi-frames blind deconvolution to improve images partially corrected by adaptive optics is proposed. The appropriate frames which are suitable for blind deconvolution from the recorded AO close-loop frames series are selected by the frame selection technique and then do the multi-frame blind deconvolution. There is no priori knowledge except for the positive constraint in blind deconvolution. It is benefit for the use of multi-frame images to improve the stability and convergence of the blind deconvolution algorithm. The method had been applied in the image restoration of celestial bodies which were observed by 1.2m telescope equipped with 61-element adaptive optical system at Yunnan Observatory. The results show that the method can effectively improve the images partially corrected by adaptive optics.

Combinatorics of least-squares trees.

PubMed

Mihaescu, Radu; Pachter, Lior

2008-09-09

A recurring theme in the least-squares approach to phylogenetics has been the discovery of elegant combinatorial formulas for the least-squares estimates of edge lengths. These formulas have proved useful for the development of efficient algorithms, and have also been important for understanding connections among popular phylogeny algorithms. For example, the selection criterion of the neighbor-joining algorithm is now understood in terms of the combinatorial formulas of Pauplin for estimating tree length. We highlight a phylogenetically desirable property that weighted least-squares methods should satisfy, and provide a complete characterization of methods that satisfy the property. The necessary and sufficient condition is a multiplicative four-point condition that the variance matrix needs to satisfy. The proof is based on the observation that the Lagrange multipliers in the proof of the Gauss-Markov theorem are tree-additive. Our results generalize and complete previous work on ordinary least squares, balanced minimum evolution, and the taxon-weighted variance model. They also provide a time-optimal algorithm for computation.

First-Order System Least-Squares for Second-Order Elliptic Problems with Discontinuous Coefficients

NASA Technical Reports Server (NTRS)

Manteuffel, Thomas A.; McCormick, Stephen F.; Starke, Gerhard

1996-01-01

The first-order system least-squares methodology represents an alternative to standard mixed finite element methods. Among its advantages is the fact that the finite element spaces approximating the pressure and flux variables are not restricted by the inf-sup condition and that the least-squares functional itself serves as an appropriate error measure. This paper studies the first-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coefficients. Ellipticity of an appropriately scaled least-squares bilinear form of the size of the jumps in the coefficients leading to adequate finite element approximation results. The occurrence of singularities at interface corners and cross-points is discussed. and a weighted least-squares functional is introduced to handle such cases. Numerical experiments are presented for two test problems to illustrate the performance of this approach.

Speckle noise removal applied to ultrasound image of carotid artery based on total least squares model.

PubMed

Yang, Lei; Lu, Jun; Dai, Ming; Ren, Li-Jie; Liu, Wei-Zong; Li, Zhen-Zhou; Gong, Xue-Hao

2016-10-06

An ultrasonic image speckle noise removal method by using total least squares model is proposed and applied onto images of cardiovascular structures such as the carotid artery. On the basis of the least squares principle, the related principle of minimum square method is applied to cardiac ultrasound image speckle noise removal process to establish the model of total least squares, orthogonal projection transformation processing is utilized for the output of the model, and the denoising processing for the cardiac ultrasound image speckle noise is realized. Experimental results show that the improved algorithm can greatly improve the resolution of the image, and meet the needs of clinical medical diagnosis and treatment of the cardiovascular system for the head and neck. Furthermore, the success in imaging of carotid arteries has strong implications in neurological complications such as stroke.

SIMULATIONS OF 2D AND 3D THERMOCAPILLARY FLOWS BY A LEAST-SQUARES FINITE ELEMENT METHOD. (R825200)

EPA Science Inventory

Numerical results for time-dependent 2D and 3D thermocapillary flows are presented in this work. The numerical algorithm is based on the Crank-Nicolson scheme for time integration, Newton's method for linearization, and a least-squares finite element method, together with a matri...

A new linear least squares method for T1 estimation from SPGR signals with multiple TRs

NASA Astrophysics Data System (ADS)

Chang, Lin-Ching; Koay, Cheng Guan; Basser, Peter J.; Pierpaoli, Carlo

2009-02-01

The longitudinal relaxation time, T1, can be estimated from two or more spoiled gradient recalled echo x (SPGR) images with two or more flip angles and one or more repetition times (TRs). The function relating signal intensity and the parameters are nonlinear; T1 maps can be computed from SPGR signals using nonlinear least squares regression. A widely-used linear method transforms the nonlinear model by assuming a fixed TR in SPGR images. This constraint is not desirable since multiple TRs are a clinically practical way to reduce the total acquisition time, to satisfy the required resolution, and/or to combine SPGR data acquired at different times. A new linear least squares method is proposed using the first order Taylor expansion. Monte Carlo simulations of SPGR experiments are used to evaluate the accuracy and precision of the estimated T1 from the proposed linear and the nonlinear methods. We show that the new linear least squares method provides T1 estimates comparable in both precision and accuracy to those from the nonlinear method, allowing multiple TRs and reducing computation time significantly.

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mu, Lin; Wang, Junping; Ye, Xiu

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2017-08-17

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

Hybrid sparse blind deconvolution: an implementation of SOOT algorithm to real data

NASA Astrophysics Data System (ADS)

Pakmanesh, Parvaneh; Goudarzi, Alireza; Kourki, Meisam

2018-06-01

Getting information of seismic data depends on deconvolution as an important processing step; it provides the reflectivity series by signal compression. This compression can be obtained by removing the wavelet effects on the traces. The recently blind deconvolution has provided reliable performance for sparse signal recovery. In this study, two deconvolution methods have been implemented to the seismic data; the convolution of these methods provides a robust spiking deconvolution approach. This hybrid deconvolution is applied using the sparse deconvolution (MM algorithm) and the Smoothed-One-Over-Two algorithm (SOOT) in a chain. The MM algorithm is based on the minimization of the cost function defined by standards l1 and l2. After applying the two algorithms to the seismic data, the SOOT algorithm provided well-compressed data with a higher resolution than the MM algorithm. The SOOT algorithm requires initial values to be applied for real data, such as the wavelet coefficients and reflectivity series that can be achieved through the MM algorithm. The computational cost of the hybrid method is high, and it is necessary to be implemented on post-stack or pre-stack seismic data of complex structure regions.

Generalized Structured Component Analysis

ERIC Educational Resources Information Center

Hwang, Heungsun; Takane, Yoshio

2004-01-01

We propose an alternative method to partial least squares for path analysis with components, called generalized structured component analysis. The proposed method replaces factors by exact linear combinations of observed variables. It employs a well-defined least squares criterion to estimate model parameters. As a result, the proposed method…

Recursive least squares method of regression coefficients estimation as a special case of Kalman filter

NASA Astrophysics Data System (ADS)

Borodachev, S. M.

2016-06-01

The simple derivation of recursive least squares (RLS) method equations is given as special case of Kalman filter estimation of a constant system state under changing observation conditions. A numerical example illustrates application of RLS to multicollinearity problem.

Analysis and computation of a least-squares method for consistent mesh tying

DOE PAGES

Day, David; Bochev, Pavel

2007-07-10

We report in the finite element method, a standard approach to mesh tying is to apply Lagrange multipliers. If the interface is curved, however, discretization generally leads to adjoining surfaces that do not coincide spatially. Straightforward Lagrange multiplier methods lead to discrete formulations failing a first-order patch test [T.A. Laursen, M.W. Heinstein, Consistent mesh-tying methods for topologically distinct discretized surfaces in non-linear solid mechanics, Internat. J. Numer. Methods Eng. 57 (2003) 1197–1242]. This paper presents a theoretical and computational study of a least-squares method for mesh tying [P. Bochev, D.M. Day, A least-squares method for consistent mesh tying, Internat. J.more » Numer. Anal. Modeling 4 (2007) 342–352], applied to the partial differential equation -∇ 2φ+αφ=f. We prove optimal convergence rates for domains represented as overlapping subdomains and show that the least-squares method passes a patch test of the order of the finite element space by construction. To apply the method to subdomain configurations with gaps and overlaps we use interface perturbations to eliminate the gaps. Finally, theoretical error estimates are illustrated by numerical experiments.« less

Iterative and function-continuation Fourier deconvolution methods for enhancing mass spectrometer resolution

NASA Technical Reports Server (NTRS)

Ioup, J. W.; Ioup, G. E.; Rayborn, G. H., Jr.; Wood, G. M., Jr.; Upchurch, B. T.

1984-01-01

Mass spectrometer data in the form of ion current versus mass-to-charge ratio often include overlapping mass peaks, especially in low- and medium-resolution instruments. Numerical deconvolution of such data effectively enhances the resolution by decreasing the overlap of mass peaks. In this paper two approaches to deconvolution are presented: a function-domain iterative technique and a Fourier transform method which uses transform-domain function-continuation. Both techniques include data smoothing to reduce the sensitivity of the deconvolution to noise. The efficacy of these methods is demonstrated through application to representative mass spectrometer data and the deconvolved results are discussed and compared to data obtained from a spectrometer with sufficient resolution to achieve separation of the mass peaks studied. A case for which the deconvolution is seriously affected by Gibbs oscillations is analyzed.

Long-term magnetic field stability of Vega

NASA Astrophysics Data System (ADS)

Alina, D.; Petit, P.; Lignières, F.; Wade, G. A.; Fares, R.; Aurière, M.; Böhm, T.; Carfantan, H.

2012-05-01

We present new spectropolarimetric observations of the normal A-type star Vega, obtained during the summer of 2010 with NARVAL at Télescope Bernard Lyot (Pic du Midi Observatory). This new time-series is constituted of 615 spectra collected over 6 different nights. We use the Least-Square-Deconvolution technique to compute, from each spectrum, a mean line profile with a signal-to-noise ratio close to 20,000. After averaging all 615 polarized observations, we detect a circularly polarized Zeeman signature consistent in shape and amplitude with the signatures previously reported from our observations of 2008 and 2009. The surface magnetic geometry of the star, reconstructed using the technique of Zeeman-Doppler Imaging, agrees with the maps obtained in 2008 and 2009, showing that most recognizable features of the photospheric field of Vega are only weakly distorted by large-scale surface flows (differential rotation or meridional circulation).

Improving space debris detection in GEO ring using image deconvolution

NASA Astrophysics Data System (ADS)

Núñez, Jorge; Núñez, Anna; Montojo, Francisco Javier; Condominas, Marta

2015-07-01

In this paper we present a method based on image deconvolution to improve the detection of space debris, mainly in the geostationary ring. Among the deconvolution methods we chose the iterative Richardson-Lucy (R-L), as the method that achieves better goals with a reasonable amount of computation. For this work, we used two sets of real 4096 × 4096 pixel test images obtained with the Telescope Fabra-ROA at Montsec (TFRM). Using the first set of data, we establish the optimal number of iterations in 7, and applying the R-L method with 7 iterations to the images, we show that the astrometric accuracy does not vary significantly while the limiting magnitude of the deconvolved images increases significantly compared to the original ones. The increase is in average about 1.0 magnitude, which means that objects up to 2.5 times fainter can be detected after deconvolution. The application of the method to the second set of test images, which includes several faint objects, shows that, after deconvolution, up to four previously undetected faint objects are detected in a single frame. Finally, we carried out a study of some economic aspects of applying the deconvolution method, showing that an important economic impact can be envisaged.

DIFFERENTIATION OF AURANTII FRUCTUS IMMATURUS AND FRUCTUS PONICIRI TRIFOLIATAE IMMATURUS BY FLOW-INJECTION WITH ULTRAVIOLET SPECTROSCOPIC DETECTION AND PROTON NUCLEAR MAGNETIC RESONANCE USING PARTIAL LEAST-SQUARES DISCRIMINANT ANALYSIS.

PubMed

Zhang, Mengliang; Zhao, Yang; Harrington, Peter de B; Chen, Pei

2016-03-01

Two simple fingerprinting methods, flow-injection coupled to ultraviolet spectroscopy and proton nuclear magnetic resonance, were used for discriminating between Aurantii fructus immaturus and Fructus poniciri trifoliatae immaturus . Both methods were combined with partial least-squares discriminant analysis. In the flow-injection method, four data representations were evaluated: total ultraviolet absorbance chromatograms, averaged ultraviolet spectra, absorbance at 193, 205, 225, and 283 nm, and absorbance at 225 and 283 nm. Prediction rates of 100% were achieved for all data representations by partial least-squares discriminant analysis using leave-one-sample-out cross-validation. The prediction rate for the proton nuclear magnetic resonance data by partial least-squares discriminant analysis with leave-one-sample-out cross-validation was also 100%. A new validation set of data was collected by flow-injection with ultraviolet spectroscopic detection two weeks later and predicted by partial least-squares discriminant analysis models constructed by the initial data representations with no parameter changes. The classification rates were 95% with the total ultraviolet absorbance chromatograms datasets and 100% with the other three datasets. Flow-injection with ultraviolet detection and proton nuclear magnetic resonance are simple, high throughput, and low-cost methods for discrimination studies.

A class of least-squares filtering and identification algorithms with systolic array architectures

NASA Technical Reports Server (NTRS)

Kalson, Seth Z.; Yao, Kung

1991-01-01

A unified approach is presented for deriving a large class of new and previously known time- and order-recursive least-squares algorithms with systolic array architectures, suitable for high-throughput-rate and VLSI implementations of space-time filtering and system identification problems. The geometrical derivation given is unique in that no assumption is made concerning the rank of the sample data correlation matrix. This method utilizes and extends the concept of oblique projections, as used previously in the derivations of the least-squares lattice algorithms. Exponentially weighted least-squares criteria are considered for both sliding and growing memory.

Least squares estimation of avian molt rates

USGS Publications Warehouse

Johnson, D.H.

1989-01-01

A straightforward least squares method of estimating the rate at which birds molt feathers is presented, suitable for birds captured more than once during the period of molt. The date of molt onset can also be estimated. The method is applied to male and female mourning doves.

Real-time holographic deconvolution techniques for one-way image transmission through an aberrating medium: characterization, modeling, and measurements.

PubMed

Haji-Saeed, B; Sengupta, S K; Testorf, M; Goodhue, W; Khoury, J; Woods, C L; Kierstead, J

2006-05-10

We propose and demonstrate a new photorefractive real-time holographic deconvolution technique for adaptive one-way image transmission through aberrating media by means of four-wave mixing. In contrast with earlier methods, which typically required various codings of the exact phase or two-way image transmission for correcting phase distortion, our technique relies on one-way image transmission through the use of exact phase information. Our technique can simultaneously correct both amplitude and phase distortions. We include several forms of image degradation, various test cases, and experimental results. We characterize the performance as a function of the input beam ratios for four metrics: signal-to-noise ratio, normalized root-mean-square error, edge restoration, and peak-to-total energy ratio. In our characterization we use false-color graphic images to display the best beam-intensity ratio two-dimensional region(s) for each of these metrics. Test cases are simulated at the optimal values of the beam-intensity ratios. We demonstrate our results through both experiment and computer simulation.

Wind Tunnel Strain-Gage Balance Calibration Data Analysis Using a Weighted Least Squares Approach

NASA Technical Reports Server (NTRS)

Ulbrich, N.; Volden, T.

2017-01-01

A new approach is presented that uses a weighted least squares fit to analyze wind tunnel strain-gage balance calibration data. The weighted least squares fit is specifically designed to increase the influence of single-component loadings during the regression analysis. The weighted least squares fit also reduces the impact of calibration load schedule asymmetries on the predicted primary sensitivities of the balance gages. A weighting factor between zero and one is assigned to each calibration data point that depends on a simple count of its intentionally loaded load components or gages. The greater the number of a data point's intentionally loaded load components or gages is, the smaller its weighting factor becomes. The proposed approach is applicable to both the Iterative and Non-Iterative Methods that are used for the analysis of strain-gage balance calibration data in the aerospace testing community. The Iterative Method uses a reasonable estimate of the tare corrected load set as input for the determination of the weighting factors. The Non-Iterative Method, on the other hand, uses gage output differences relative to the natural zeros as input for the determination of the weighting factors. Machine calibration data of a six-component force balance is used to illustrate benefits of the proposed weighted least squares fit. In addition, a detailed derivation of the PRESS residuals associated with a weighted least squares fit is given in the appendices of the paper as this information could not be found in the literature. These PRESS residuals may be needed to evaluate the predictive capabilities of the final regression models that result from a weighted least squares fit of the balance calibration data.

How to deal with the high condition number of the noise covariance matrix of gravity field functionals synthesised from a satellite-only global gravity field model?

NASA Astrophysics Data System (ADS)

Klees, R.; Slobbe, D. C.; Farahani, H. H.

2018-03-01

The posed question arises for instance in regional gravity field modelling using weighted least-squares techniques if the gravity field functionals are synthesised from the spherical harmonic coefficients of a satellite-only global gravity model (GGM), and are used as one of the noisy datasets. The associated noise covariance matrix, appeared to be extremely ill-conditioned with a singular value spectrum that decayed gradually to zero without any noticeable gap. We analysed three methods to deal with the ill-conditioned noise covariance matrix: Tihonov regularisation of the noise covariance matrix in combination with the standard formula for the weighted least-squares estimator, a formula of the weighted least-squares estimator, which does not involve the inverse noise covariance matrix, and an estimator based on Rao's unified theory of least-squares. Our analysis was based on a numerical experiment involving a set of height anomalies synthesised from the GGM GOCO05s, which is provided with a full noise covariance matrix. We showed that the three estimators perform similar, provided that the two regularisation parameters each method knows were chosen properly. As standard regularisation parameter choice rules do not apply here, we suggested a new parameter choice rule, and demonstrated its performance. Using this rule, we found that the differences between the three least-squares estimates were within noise. For the standard formulation of the weighted least-squares estimator with regularised noise covariance matrix, this required an exceptionally strong regularisation, much larger than one expected from the condition number of the noise covariance matrix. The preferred method is the inversion-free formulation of the weighted least-squares estimator, because of its simplicity with respect to the choice of the two regularisation parameters.

Texas two-step: a framework for optimal multi-input single-output deconvolution.

PubMed

Neelamani, Ramesh; Deffenbaugh, Max; Baraniuk, Richard G

2007-11-01

Multi-input single-output deconvolution (MISO-D) aims to extract a deblurred estimate of a target signal from several blurred and noisy observations. This paper develops a new two step framework--Texas Two-Step--to solve MISO-D problems with known blurs. Texas Two-Step first reduces the MISO-D problem to a related single-input single-output deconvolution (SISO-D) problem by invoking the concept of sufficient statistics (SSs) and then solves the simpler SISO-D problem using an appropriate technique. The two-step framework enables new MISO-D techniques (both optimal and suboptimal) based on the rich suite of existing SISO-D techniques. In fact, the properties of SSs imply that a MISO-D algorithm is mean-squared-error optimal if and only if it can be rearranged to conform to the Texas Two-Step framework. Using this insight, we construct new wavelet- and curvelet-based MISO-D algorithms with asymptotically optimal performance. Simulated and real data experiments verify that the framework is indeed effective.

A novel SURE-based criterion for parametric PSF estimation.

PubMed

Xue, Feng; Blu, Thierry

2015-02-01

We propose an unbiased estimate of a filtered version of the mean squared error--the blur-SURE (Stein's unbiased risk estimate)--as a novel criterion for estimating an unknown point spread function (PSF) from the degraded image only. The PSF is obtained by minimizing this new objective functional over a family of Wiener processings. Based on this estimated blur kernel, we then perform nonblind deconvolution using our recently developed algorithm. The SURE-based framework is exemplified with a number of parametric PSF, involving a scaling factor that controls the blur size. A typical example of such parametrization is the Gaussian kernel. The experimental results demonstrate that minimizing the blur-SURE yields highly accurate estimates of the PSF parameters, which also result in a restoration quality that is very similar to the one obtained with the exact PSF, when plugged into our recent multi-Wiener SURE-LET deconvolution algorithm. The highly competitive results obtained outline the great potential of developing more powerful blind deconvolution algorithms based on SURE-like estimates.

Further optimization of SeDDaRA blind image deconvolution algorithm and its DSP implementation

NASA Astrophysics Data System (ADS)

Wen, Bo; Zhang, Qiheng; Zhang, Jianlin

2011-11-01

Efficient algorithm for blind image deconvolution and its high-speed implementation is of great value in practice. Further optimization of SeDDaRA is developed, from algorithm structure to numerical calculation methods. The main optimization covers that, the structure's modularization for good implementation feasibility, reducing the data computation and dependency of 2D-FFT/IFFT, and acceleration of power operation by segmented look-up table. Then the Fast SeDDaRA is proposed and specialized for low complexity. As the final implementation, a hardware system of image restoration is conducted by using the multi-DSP parallel processing. Experimental results show that, the processing time and memory demand of Fast SeDDaRA decreases 50% at least; the data throughput of image restoration system is over 7.8Msps. The optimization is proved efficient and feasible, and the Fast SeDDaRA is able to support the real-time application.

Estimation of parameters in rational reaction rates of molecular biological systems via weighted least squares

NASA Astrophysics Data System (ADS)

Wu, Fang-Xiang; Mu, Lei; Shi, Zhong-Ke

2010-01-01

The models of gene regulatory networks are often derived from statistical thermodynamics principle or Michaelis-Menten kinetics equation. As a result, the models contain rational reaction rates which are nonlinear in both parameters and states. It is challenging to estimate parameters nonlinear in a model although there have been many traditional nonlinear parameter estimation methods such as Gauss-Newton iteration method and its variants. In this article, we develop a two-step method to estimate the parameters in rational reaction rates of gene regulatory networks via weighted linear least squares. This method takes the special structure of rational reaction rates into consideration. That is, in the rational reaction rates, the numerator and the denominator are linear in parameters. By designing a special weight matrix for the linear least squares, parameters in the numerator and the denominator can be estimated by solving two linear least squares problems. The main advantage of the developed method is that it can produce the analytical solutions to the estimation of parameters in rational reaction rates which originally is nonlinear parameter estimation problem. The developed method is applied to a couple of gene regulatory networks. The simulation results show the superior performance over Gauss-Newton method.

Penalized Multi-Way Partial Least Squares for Smooth Trajectory Decoding from Electrocorticographic (ECoG) Recording

PubMed Central

Eliseyev, Andrey; Aksenova, Tetiana

2016-01-01

In the current paper the decoding algorithms for motor-related BCI systems for continuous upper limb trajectory prediction are considered. Two methods for the smooth prediction, namely Sobolev and Polynomial Penalized Multi-Way Partial Least Squares (PLS) regressions, are proposed. The methods are compared to the Multi-Way Partial Least Squares and Kalman Filter approaches. The comparison demonstrated that the proposed methods combined the prediction accuracy of the algorithms of the PLS family and trajectory smoothness of the Kalman Filter. In addition, the prediction delay is significantly lower for the proposed algorithms than for the Kalman Filter approach. The proposed methods could be applied in a wide range of applications beyond neuroscience. PMID:27196417

Effect of genetic algorithm as a variable selection method on different chemometric models applied for the analysis of binary mixture of amoxicillin and flucloxacillin: A comparative study

NASA Astrophysics Data System (ADS)

Attia, Khalid A. M.; Nassar, Mohammed W. I.; El-Zeiny, Mohamed B.; Serag, Ahmed

2016-03-01

Different chemometric models were applied for the quantitative analysis of amoxicillin (AMX), and flucloxacillin (FLX) in their binary mixtures, namely, partial least squares (PLS), spectral residual augmented classical least squares (SRACLS), concentration residual augmented classical least squares (CRACLS) and artificial neural networks (ANNs). All methods were applied with and without variable selection procedure (genetic algorithm GA). The methods were used for the quantitative analysis of the drugs in laboratory prepared mixtures and real market sample via handling the UV spectral data. Robust and simpler models were obtained by applying GA. The proposed methods were found to be rapid, simple and required no preliminary separation steps.

Simulation of Foam Divot Weight on External Tank Utilizing Least Squares and Neural Network Methods

NASA Technical Reports Server (NTRS)

Chamis, Christos C.; Coroneos, Rula M.

2007-01-01

Simulation of divot weight in the insulating foam, associated with the external tank of the U.S. space shuttle, has been evaluated using least squares and neural network concepts. The simulation required models based on fundamental considerations that can be used to predict under what conditions voids form, the size of the voids, and subsequent divot ejection mechanisms. The quadratic neural networks were found to be satisfactory for the simulation of foam divot weight in various tests associated with the external tank. Both linear least squares method and the nonlinear neural network predicted identical results.

A new approach to blind deconvolution of astronomical images

NASA Astrophysics Data System (ADS)

Vorontsov, S. V.; Jefferies, S. M.

2017-05-01

We readdress the strategy of finding approximate regularized solutions to the blind deconvolution problem, when both the object and the point-spread function (PSF) have finite support. Our approach consists in addressing fixed points of an iteration in which both the object x and the PSF y are approximated in an alternating manner, discarding the previous approximation for x when updating x (similarly for y), and considering the resultant fixed points as candidates for a sensible solution. Alternating approximations are performed by truncated iterative least-squares descents. The number of descents in the object- and in the PSF-space play a role of two regularization parameters. Selection of appropriate fixed points (which may not be unique) is performed by relaxing the regularization gradually, using the previous fixed point as an initial guess for finding the next one, which brings an approximation of better spatial resolution. We report the results of artificial experiments with noise-free data, targeted at examining the potential capability of the technique to deconvolve images of high complexity. We also show the results obtained with two sets of satellite images acquired using ground-based telescopes with and without adaptive optics compensation. The new approach brings much better results when compared with an alternating minimization technique based on positivity-constrained conjugate gradients, where the iterations stagnate when addressing data of high complexity. In the alternating-approximation step, we examine the performance of three different non-blind iterative deconvolution algorithms. The best results are provided by the non-negativity-constrained successive over-relaxation technique (+SOR) supplemented with an adaptive scheduling of the relaxation parameter. Results of comparable quality are obtained with steepest descents modified by imposing the non-negativity constraint, at the expense of higher numerical costs. The Richardson-Lucy (or expectation-maximization) algorithm fails to locate stable fixed points in our experiments, due apparently to inappropriate regularization properties.

A note on the blind deconvolution of multiple sparse signals from unknown subspaces

NASA Astrophysics Data System (ADS)

Cosse, Augustin

2017-08-01

This note studies the recovery of multiple sparse signals, xn ∈ ℝL, n = 1, . . . , N, from the knowledge of their convolution with an unknown point spread function h ∈ ℝL. When the point spread function is known to be nonzero, |h[k]| > 0, this blind deconvolution problem can be relaxed into a linear, ill-posed inverse problem in the vector concatenating the unknown inputs xn together with the inverse of the filter, d ∈ ℝL where d[k] := 1/h[k]. When prior information is given on the input subspaces, the resulting overdetermined linear system can be solved efficiently via least squares (see Ling et al. 20161). When no information is given on those subspaces, and the inputs are only known to be sparse, it still remains possible to recover these inputs along with the filter by considering an additional l1 penalty. This note certifies exact recovery of both the unknown PSF and unknown sparse inputs, from the knowledge of their convolutions, as soon as the number of inputs N and the dimension of each input, L , satisfy L ≳ N and N ≳ T2max, up to log factors. Here Tmax = maxn{Tn} and Tn, n = 1, . . . , N denote the supports of the inputs xn. Our proof system combines the recent results on blind deconvolution via least squares to certify invertibility of the linear map encoding the convolutions, with the construction of a dual certificate following the structure first suggested in Candés et al. 2007.2 Unlike in these papers, however, it is not possible to rely on the norm ||(A*TAT)-1|| to certify recovery. We instead use a combination of the Schur Complement and Neumann series to compute an expression for the inverse (A*TAT)-1. Given this expression, it is possible to show that the poorly scaled blocks in (A*TAT)-1 are multiplied by the better scaled ones or vanish in the construction of the certificate. Recovery is certified with high probablility on the choice of the supports and distribution of the signs of each input xn on the support. The paper follows the line of previous work by Wang et al. 20163 where the authors guarantee recovery for subgaussian × Bernoulli inputs satisfying 𝔼xn|k| ∈ [1/10, 1] as soon as N ≳ L. Examples of applications include seismic imaging with unknown source or marine seismic data deghosting, magnetic resonance autocalibration or multiple channel estimation in communication. Numerical experiments are provided along with a discussion on the sample complexity tightness.

Variable selection based on clustering analysis for improvement of polyphenols prediction in green tea using synchronous fluorescence spectra

NASA Astrophysics Data System (ADS)

Shan, Jiajia; Wang, Xue; Zhou, Hao; Han, Shuqing; Riza, Dimas Firmanda Al; Kondo, Naoshi

2018-04-01

Synchronous fluorescence spectra, combined with multivariate analysis were used to predict flavonoids content in green tea rapidly and nondestructively. This paper presented a new and efficient spectral intervals selection method called clustering based partial least square (CL-PLS), which selected informative wavelengths by combining clustering concept and partial least square (PLS) methods to improve models’ performance by synchronous fluorescence spectra. The fluorescence spectra of tea samples were obtained and k-means and kohonen-self organizing map clustering algorithms were carried out to cluster full spectra into several clusters, and sub-PLS regression model was developed on each cluster. Finally, CL-PLS models consisting of gradually selected clusters were built. Correlation coefficient (R) was used to evaluate the effect on prediction performance of PLS models. In addition, variable influence on projection partial least square (VIP-PLS), selectivity ratio partial least square (SR-PLS), interval partial least square (iPLS) models and full spectra PLS model were investigated and the results were compared. The results showed that CL-PLS presented the best result for flavonoids prediction using synchronous fluorescence spectra.

Variable selection based on clustering analysis for improvement of polyphenols prediction in green tea using synchronous fluorescence spectra.

PubMed

Shan, Jiajia; Wang, Xue; Zhou, Hao; Han, Shuqing; Riza, Dimas Firmanda Al; Kondo, Naoshi

2018-03-13

Synchronous fluorescence spectra, combined with multivariate analysis were used to predict flavonoids content in green tea rapidly and nondestructively. This paper presented a new and efficient spectral intervals selection method called clustering based partial least square (CL-PLS), which selected informative wavelengths by combining clustering concept and partial least square (PLS) methods to improve models' performance by synchronous fluorescence spectra. The fluorescence spectra of tea samples were obtained and k-means and kohonen-self organizing map clustering algorithms were carried out to cluster full spectra into several clusters, and sub-PLS regression model was developed on each cluster. Finally, CL-PLS models consisting of gradually selected clusters were built. Correlation coefficient (R) was used to evaluate the effect on prediction performance of PLS models. In addition, variable influence on projection partial least square (VIP-PLS), selectivity ratio partial least square (SR-PLS), interval partial least square (iPLS) models and full spectra PLS model were investigated and the results were compared. The results showed that CL-PLS presented the best result for flavonoids prediction using synchronous fluorescence spectra.

Feasibility study on the least square method for fitting non-Gaussian noise data

NASA Astrophysics Data System (ADS)

Xu, Wei; Chen, Wen; Liang, Yingjie

2018-02-01

This study is to investigate the feasibility of least square method in fitting non-Gaussian noise data. We add different levels of the two typical non-Gaussian noises, Lévy and stretched Gaussian noises, to exact value of the selected functions including linear equations, polynomial and exponential equations, and the maximum absolute and the mean square errors are calculated for the different cases. Lévy and stretched Gaussian distributions have many applications in fractional and fractal calculus. It is observed that the non-Gaussian noises are less accurately fitted than the Gaussian noise, but the stretched Gaussian cases appear to perform better than the Lévy noise cases. It is stressed that the least-squares method is inapplicable to the non-Gaussian noise cases when the noise level is larger than 5%.

Evaluation of deconvolution modelling applied to numerical combustion

NASA Astrophysics Data System (ADS)

Mehl, Cédric; Idier, Jérôme; Fiorina, Benoît

2018-01-01

A possible modelling approach in the large eddy simulation (LES) of reactive flows is to deconvolve resolved scalars. Indeed, by inverting the LES filter, scalars such as mass fractions are reconstructed. This information can be used to close budget terms of filtered species balance equations, such as the filtered reaction rate. Being ill-posed in the mathematical sense, the problem is very sensitive to any numerical perturbation. The objective of the present study is to assess the ability of this kind of methodology to capture the chemical structure of premixed flames. For that purpose, three deconvolution methods are tested on a one-dimensional filtered laminar premixed flame configuration: the approximate deconvolution method based on Van Cittert iterative deconvolution, a Taylor decomposition-based method, and the regularised deconvolution method based on the minimisation of a quadratic criterion. These methods are then extended to the reconstruction of subgrid scale profiles. Two methodologies are proposed: the first one relies on subgrid scale interpolation of deconvolved profiles and the second uses parametric functions to describe small scales. Conducted tests analyse the ability of the method to capture the chemical filtered flame structure and front propagation speed. Results show that the deconvolution model should include information about small scales in order to regularise the filter inversion. a priori and a posteriori tests showed that the filtered flame propagation speed and structure cannot be captured if the filter size is too large.

An Alternating Least Squares Method for the Weighted Approximation of a Symmetric Matrix.

ERIC Educational Resources Information Center

ten Berge, Jos M. F.; Kiers, Henk A. L.

1993-01-01

R. A. Bailey and J. C. Gower explored approximating a symmetric matrix "B" by another, "C," in the least squares sense when the squared discrepancies for diagonal elements receive specific nonunit weights. A solution is proposed where "C" is constrained to be positive semidefinite and of a fixed rank. (SLD)

Least Median of Squares Filtering of Locally Optimal Point Matches for Compressible Flow Image Registration

PubMed Central

Castillo, Edward; Castillo, Richard; White, Benjamin; Rojo, Javier; Guerrero, Thomas

2012-01-01

Compressible flow based image registration operates under the assumption that the mass of the imaged material is conserved from one image to the next. Depending on how the mass conservation assumption is modeled, the performance of existing compressible flow methods is limited by factors such as image quality, noise, large magnitude voxel displacements, and computational requirements. The Least Median of Squares Filtered Compressible Flow (LFC) method introduced here is based on a localized, nonlinear least squares, compressible flow model that describes the displacement of a single voxel that lends itself to a simple grid search (block matching) optimization strategy. Spatially inaccurate grid search point matches, corresponding to erroneous local minimizers of the nonlinear compressible flow model, are removed by a novel filtering approach based on least median of squares fitting and the forward search outlier detection method. The spatial accuracy of the method is measured using ten thoracic CT image sets and large samples of expert determined landmarks (available at www.dir-lab.com). The LFC method produces an average error within the intra-observer error on eight of the ten cases, indicating that the method is capable of achieving a high spatial accuracy for thoracic CT registration. PMID:22797602

A simplified fractional order impedance model and parameter identification method for lithium-ion batteries

PubMed Central

Yang, Qingxia; Xu, Jun; Cao, Binggang; Li, Xiuqing

2017-01-01

Identification of internal parameters of lithium-ion batteries is a useful tool to evaluate battery performance, and requires an effective model and algorithm. Based on the least square genetic algorithm, a simplified fractional order impedance model for lithium-ion batteries and the corresponding parameter identification method were developed. The simplified model was derived from the analysis of the electrochemical impedance spectroscopy data and the transient response of lithium-ion batteries with different states of charge. In order to identify the parameters of the model, an equivalent tracking system was established, and the method of least square genetic algorithm was applied using the time-domain test data. Experiments and computer simulations were carried out to verify the effectiveness and accuracy of the proposed model and parameter identification method. Compared with a second-order resistance-capacitance (2-RC) model and recursive least squares method, small tracing voltage fluctuations were observed. The maximum battery voltage tracing error for the proposed model and parameter identification method is within 0.5%; this demonstrates the good performance of the model and the efficiency of the least square genetic algorithm to estimate the internal parameters of lithium-ion batteries. PMID:28212405

Application of deterministic deconvolution of ground-penetrating radar data in a study of carbonate strata

USGS Publications Warehouse

Xia, J.; Franseen, E.K.; Miller, R.D.; Weis, T.V.

2004-01-01

We successfully applied deterministic deconvolution to real ground-penetrating radar (GPR) data by using the source wavelet that was generated in and transmitted through air as the operator. The GPR data were collected with 400-MHz antennas on a bench adjacent to a cleanly exposed quarry face. The quarry site is characterized by horizontally bedded carbonate strata with shale partings. In order to provide groundtruth for this deconvolution approach, 23 conductive rods were drilled into the quarry face at key locations. The steel rods provided critical information for: (1) correlation between reflections on GPR data and geologic features exposed in the quarry face, (2) GPR resolution limits, (3) accuracy of velocities calculated from common midpoint data and (4) identifying any multiples. Comparing the results of deconvolved data with non-deconvolved data demonstrates the effectiveness of deterministic deconvolution in low dielectric-loss media for increased accuracy of velocity models (improved at least 10-15% in our study after deterministic deconvolution), increased vertical and horizontal resolution of specific geologic features and more accurate representation of geologic features as confirmed from detailed study of the adjacent quarry wall. ?? 2004 Elsevier B.V. All rights reserved.

Fitting a function to time-dependent ensemble averaged data.

PubMed

Fogelmark, Karl; Lomholt, Michael A; Irbäck, Anders; Ambjörnsson, Tobias

2018-05-03

Time-dependent ensemble averages, i.e., trajectory-based averages of some observable, are of importance in many fields of science. A crucial objective when interpreting such data is to fit these averages (for instance, squared displacements) with a function and extract parameters (such as diffusion constants). A commonly overlooked challenge in such function fitting procedures is that fluctuations around mean values, by construction, exhibit temporal correlations. We show that the only available general purpose function fitting methods, correlated chi-square method and the weighted least squares method (which neglects correlation), fail at either robust parameter estimation or accurate error estimation. We remedy this by deriving a new closed-form error estimation formula for weighted least square fitting. The new formula uses the full covariance matrix, i.e., rigorously includes temporal correlations, but is free of the robustness issues, inherent to the correlated chi-square method. We demonstrate its accuracy in four examples of importance in many fields: Brownian motion, damped harmonic oscillation, fractional Brownian motion and continuous time random walks. We also successfully apply our method, weighted least squares including correlation in error estimation (WLS-ICE), to particle tracking data. The WLS-ICE method is applicable to arbitrary fit functions, and we provide a publically available WLS-ICE software.

Parameter estimation using weighted total least squares in the two-compartment exchange model.

PubMed

Garpebring, Anders; Löfstedt, Tommy

2018-01-01

The linear least squares (LLS) estimator provides a fast approach to parameter estimation in the linearized two-compartment exchange model. However, the LLS method may introduce a bias through correlated noise in the system matrix of the model. The purpose of this work is to present a new estimator for the linearized two-compartment exchange model that takes this noise into account. To account for the noise in the system matrix, we developed an estimator based on the weighted total least squares (WTLS) method. Using simulations, the proposed WTLS estimator was compared, in terms of accuracy and precision, to an LLS estimator and a nonlinear least squares (NLLS) estimator. The WTLS method improved the accuracy compared to the LLS method to levels comparable to the NLLS method. This improvement was at the expense of increased computational time; however, the WTLS was still faster than the NLLS method. At high signal-to-noise ratio all methods provided similar precisions while inconclusive results were observed at low signal-to-noise ratio. The proposed method provides improvements in accuracy compared to the LLS method, however, at an increased computational cost. Magn Reson Med 79:561-567, 2017. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Simulation Study of Effects of the Blind Deconvolution on Ultrasound Image

NASA Astrophysics Data System (ADS)

He, Xingwu; You, Junchen

2018-03-01

Ultrasonic image restoration is an essential subject in Medical Ultrasound Imaging. However, without enough and precise system knowledge, some traditional image restoration methods based on the system prior knowledge often fail to improve the image quality. In this paper, we use the simulated ultrasound image to find the effectiveness of the blind deconvolution method for ultrasound image restoration. Experimental results demonstrate that the blind deconvolution method can be applied to the ultrasound image restoration and achieve the satisfactory restoration results without the precise prior knowledge, compared with the traditional image restoration method. And with the inaccurate small initial PSF, the results shows blind deconvolution could improve the overall image quality of ultrasound images, like much better SNR and image resolution, and also show the time consumption of these methods. it has no significant increasing on GPU platform.

On the accuracy of least squares methods in the presence of corner singularities

NASA Technical Reports Server (NTRS)

Cox, C. L.; Fix, G. J.

1985-01-01

Elliptic problems with corner singularities are discussed. Finite element approximations based on variational principles of the least squares type tend to display poor convergence properties in such contexts. Moreover, mesh refinement or the use of special singular elements do not appreciably improve matters. It is shown that if the least squares formulation is done in appropriately weighted space, then optimal convergence results in unweighted spaces like L(2).

Parametric output-only identification of time-varying structures using a kernel recursive extended least squares TARMA approach

NASA Astrophysics Data System (ADS)

Ma, Zhi-Sai; Liu, Li; Zhou, Si-Da; Yu, Lei; Naets, Frank; Heylen, Ward; Desmet, Wim

2018-01-01

The problem of parametric output-only identification of time-varying structures in a recursive manner is considered. A kernelized time-dependent autoregressive moving average (TARMA) model is proposed by expanding the time-varying model parameters onto the basis set of kernel functions in a reproducing kernel Hilbert space. An exponentially weighted kernel recursive extended least squares TARMA identification scheme is proposed, and a sliding-window technique is subsequently applied to fix the computational complexity for each consecutive update, allowing the method to operate online in time-varying environments. The proposed sliding-window exponentially weighted kernel recursive extended least squares TARMA method is employed for the identification of a laboratory time-varying structure consisting of a simply supported beam and a moving mass sliding on it. The proposed method is comparatively assessed against an existing recursive pseudo-linear regression TARMA method via Monte Carlo experiments and shown to be capable of accurately tracking the time-varying dynamics. Furthermore, the comparisons demonstrate the superior achievable accuracy, lower computational complexity and enhanced online identification capability of the proposed kernel recursive extended least squares TARMA approach.

Missing value imputation in DNA microarrays based on conjugate gradient method.

PubMed

Dorri, Fatemeh; Azmi, Paeiz; Dorri, Faezeh

2012-02-01

Analysis of gene expression profiles needs a complete matrix of gene array values; consequently, imputation methods have been suggested. In this paper, an algorithm that is based on conjugate gradient (CG) method is proposed to estimate missing values. k-nearest neighbors of the missed entry are first selected based on absolute values of their Pearson correlation coefficient. Then a subset of genes among the k-nearest neighbors is labeled as the best similar ones. CG algorithm with this subset as its input is then used to estimate the missing values. Our proposed CG based algorithm (CGimpute) is evaluated on different data sets. The results are compared with sequential local least squares (SLLSimpute), Bayesian principle component analysis (BPCAimpute), local least squares imputation (LLSimpute), iterated local least squares imputation (ILLSimpute) and adaptive k-nearest neighbors imputation (KNNKimpute) methods. The average of normalized root mean squares error (NRMSE) and relative NRMSE in different data sets with various missing rates shows CGimpute outperforms other methods. Copyright © 2011 Elsevier Ltd. All rights reserved.

Weighted linear least squares estimation of diffusion MRI parameters: strengths, limitations, and pitfalls.

PubMed

Veraart, Jelle; Sijbers, Jan; Sunaert, Stefan; Leemans, Alexander; Jeurissen, Ben

2013-11-01

Linear least squares estimators are widely used in diffusion MRI for the estimation of diffusion parameters. Although adding proper weights is necessary to increase the precision of these linear estimators, there is no consensus on how to practically define them. In this study, the impact of the commonly used weighting strategies on the accuracy and precision of linear diffusion parameter estimators is evaluated and compared with the nonlinear least squares estimation approach. Simulation and real data experiments were done to study the performance of the weighted linear least squares estimators with weights defined by (a) the squares of the respective noisy diffusion-weighted signals; and (b) the squares of the predicted signals, which are reconstructed from a previous estimate of the diffusion model parameters. The negative effect of weighting strategy (a) on the accuracy of the estimator was surprisingly high. Multi-step weighting strategies yield better performance and, in some cases, even outperformed the nonlinear least squares estimator. If proper weighting strategies are applied, the weighted linear least squares approach shows high performance characteristics in terms of accuracy/precision and may even be preferred over nonlinear estimation methods. Copyright © 2013 Elsevier Inc. All rights reserved.

A Deconvolution Approach for the Mapping of Acoustic Sources (DAMAS) Determined from Phased Microphone Arrays

NASA Technical Reports Server (NTRS)

Brooks, Thomas F.; Humphreys, William M.

2006-01-01

Current processing of acoustic array data is burdened with considerable uncertainty. This study reports an original methodology that serves to demystify array results, reduce misinterpretation, and accurately quantify position and strength of acoustic sources. Traditional array results represent noise sources that are convolved with array beamform response functions, which depend on array geometry, size (with respect to source position and distributions), and frequency. The Deconvolution Approach for the Mapping of Acoustic Sources (DAMAS) method removes beamforming characteristics from output presentations. A unique linear system of equations accounts for reciprocal influence at different locations over the array survey region. It makes no assumption beyond the traditional processing assumption of statistically independent noise sources. The full rank equations are solved with a new robust iterative method. DAMAS is quantitatively validated using archival data from a variety of prior high-lift airframe component noise studies, including flap edge/cove, trailing edge, leading edge, slat, and calibration sources. Presentations are explicit and straightforward, as the noise radiated from a region of interest is determined by simply summing the mean-squared values over that region. DAMAS can fully replace existing array processing and presentations methodology in most applications. It appears to dramatically increase the value of arrays to the field of experimental acoustics.

Doppler imaging of the young late-type star LO Pegasi (BD+22°4409) in 2003 September

NASA Astrophysics Data System (ADS)

Piluso, N.; Lanza, A. F.; Pagano, I.; Lanzafame, A. C.; Donati, J.-F.

2008-06-01

A Doppler image of the zero-age main-sequence (ZAMS) late-type rapidly rotating star LO Pegasi, based on spectra acquired between 2003 September 12 and 15 is presented. The least-squares deconvolution technique is applied to enhance the signal-to-noise ratio of the mean rotational broadened line profiles extracted from the observed spectra. In the present application, an unbroadened spectrum is used as a reference, instead of a simple line list, to improve the deconvolution technique applied to extract the mean profiles. The reconstructed image is similar to those previously obtained from observations taken in 1993 and 1998, and shows that LO Peg photospheric activity is dominated by high-latitude spots with a non-uniform polar cap. The latter seems to be a persistent feature as it has been observed since 1993 with little modifications. Small spots, observed between ~10° and ~60° of latitude, appears to be different with respect to those present in the 1993 and 1998 maps. Based on observations made with the Italian Telescopio Nazionale Galileo operated on the island of La Palma by the Centro Galileo Galilei of INAF (Istituto Nazionale di Astrofisica) at the Spanish Observatorio del Roque del los Muchachos of the Instituto de Astrofísica de Canarias. E-mail: nicolo.piluso@oact.inaf.it (NP); nuccio.lanza@oact.inaf.it (AFL); isabella.pagano@oact.inaf.it (IP); alessandro.lanzafame@oact.inaf.it (ACL); donati@ast.obs-mip.fr (J-FD)

Applied Algebra: The Modeling Technique of Least Squares

ERIC Educational Resources Information Center

Zelkowski, Jeremy; Mayes, Robert

2008-01-01

The article focuses on engaging students in algebra through modeling real-world problems. The technique of least squares is explored, encouraging students to develop a deeper understanding of the method. (Contains 2 figures and a bibliography.)

Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

NASA Astrophysics Data System (ADS)

Adib, Arash; Poorveis, Davood; Mehraban, Farid

2018-03-01

In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.

A Novel Richardson-Lucy Model with Dictionary Basis and Spatial Regularization for Isolating Isotropic Signals.

PubMed

Xu, Tiantian; Feng, Yuanjing; Wu, Ye; Zeng, Qingrun; Zhang, Jun; He, Jianzhong; Zhuge, Qichuan

2017-01-01

Diffusion-weighted magnetic resonance imaging is a non-invasive imaging method that has been increasingly used in neuroscience imaging over the last decade. Partial volume effects (PVEs) exist in sampling signal for many physical and actual reasons, which lead to inaccurate fiber imaging. We overcome the influence of PVEs by separating isotropic signal from diffusion-weighted signal, which can provide more accurate estimation of fiber orientations. In this work, we use a novel response function (RF) and the correspondent fiber orientation distribution function (fODF) to construct different signal models, in which case the fODF is represented using dictionary basis function. We then put forward a new index Piso, which is a part of fODF to quantify white and gray matter. The classic Richardson-Lucy (RL) model is usually used in the field of digital image processing to solve the problem of spherical deconvolution caused by highly ill-posed least-squares algorithm. In this case, we propose an innovative model integrating RL model with spatial regularization to settle the suggested double-models, which improve noise resistance and accuracy of imaging. Experimental results of simulated and real data show that the proposal method, which we call iRL, can robustly reconstruct a more accurate fODF and the quantitative index Piso performs better than fractional anisotropy and general fractional anisotropy.

A Novel Richardson-Lucy Model with Dictionary Basis and Spatial Regularization for Isolating Isotropic Signals

PubMed Central

Feng, Yuanjing; Wu, Ye; Zeng, Qingrun; Zhang, Jun; He, Jianzhong; Zhuge, Qichuan

2017-01-01

Diffusion-weighted magnetic resonance imaging is a non-invasive imaging method that has been increasingly used in neuroscience imaging over the last decade. Partial volume effects (PVEs) exist in sampling signal for many physical and actual reasons, which lead to inaccurate fiber imaging. We overcome the influence of PVEs by separating isotropic signal from diffusion-weighted signal, which can provide more accurate estimation of fiber orientations. In this work, we use a novel response function (RF) and the correspondent fiber orientation distribution function (fODF) to construct different signal models, in which case the fODF is represented using dictionary basis function. We then put forward a new index Piso, which is a part of fODF to quantify white and gray matter. The classic Richardson-Lucy (RL) model is usually used in the field of digital image processing to solve the problem of spherical deconvolution caused by highly ill-posed least-squares algorithm. In this case, we propose an innovative model integrating RL model with spatial regularization to settle the suggested double-models, which improve noise resistance and accuracy of imaging. Experimental results of simulated and real data show that the proposal method, which we call iRL, can robustly reconstruct a more accurate fODF and the quantitative index Piso performs better than fractional anisotropy and general fractional anisotropy. PMID:28081561

Methods and Apparatus for Reducing Multipath Signal Error Using Deconvolution

NASA Technical Reports Server (NTRS)

Kumar, Rajendra (Inventor); Lau, Kenneth H. (Inventor)

1999-01-01

A deconvolution approach to adaptive signal processing has been applied to the elimination of signal multipath errors as embodied in one preferred embodiment in a global positioning system receiver. The method and receiver of the present invention estimates then compensates for multipath effects in a comprehensive manner. Application of deconvolution, along with other adaptive identification and estimation techniques, results in completely novel GPS (Global Positioning System) receiver architecture.

A new method of measuring centre-of-mass velocities of radially pulsating stars from high-resolution spectroscopy

NASA Astrophysics Data System (ADS)

Britavskiy, N.; Pancino, E.; Tsymbal, V.; Romano, D.; Fossati, L.

2018-03-01

We present a radial velocity analysis of 20 solar neighbourhood RR Lyrae and three Population II Cepheid variables. We obtained high-resolution, moderate-to-high signal-to-noise ratio spectra for most stars; these spectra covered different pulsation phases for each star. To estimate the gamma (centre-of-mass) velocities of the programme stars, we use two independent methods. The first, `classic' method is based on RR Lyrae radial velocity curve templates. The second method is based on the analysis of absorption-line profile asymmetry to determine both pulsational and gamma velocities. This second method is based on the least-squares deconvolution (LSD) technique applied to analyse the line asymmetry that occurs in the spectra. We obtain measurements of the pulsation component of the radial velocity with an accuracy of ±3.5 km s-1. The gamma velocity was determined with an accuracy of ±10 km s-1, even for those stars having a small number of spectra. The main advantage of this method is the possibility of obtaining an estimation of gamma velocity even from one spectroscopic observation with uncertain pulsation phase. A detailed investigation of LSD profile asymmetry shows that the projection factor p varies as a function of the pulsation phase - this is a key parameter, which converts observed spectral line radial velocity variations into photospheric pulsation velocities. As a by-product of our study, we present 41 densely spaced synthetic grids of LSD profile bisectors based on atmospheric models of RR Lyr covering all pulsation phases.

Cellulose, Chitosan and Keratin Composite Materials: Facile and Recyclable Synthesis, Conformation and Properties.

PubMed

Tran, Chieu D; Mututuvari, Tamutsiwa M

2016-03-07

A method was developed in which cellulose (CEL) and/or chitosan (CS) were added to keratin (KER) to enable [CEL/CS+KER] composites formed to have better mechanical strength and wider utilization. Butylmethylimmidazolium chloride ([BMIm + Cl - ]), an ionic liquid, was used as the sole solvent, and because the majority of [BMIm + Cl - ] used (at least 88%) was recovered, the method is green and recyclable. FTIR, XRD, 13 C CP-MAS NMR and SEM results confirm that KER, CS and CEL remain chemically intact and distributed homogeneously in the composites. We successfully demonstrate that the widely used method based on the deconvolution of the FTIR bands of amide bonds to determine secondary structure of proteins is relatively subjective as the conformation obtained is strongly dependent on the choice of parameters selected for curve fitting. A new method, based on the partial least squares regression analysis (PLSR) of the amide bands, was developed, and proven to be objective and can provide more accurate information. Results obtained with this method agree well with those by XRD, namely they indicate that although KER retains its second structure when incorporated into the [CEL+CS] composites, it has relatively lower α -helix, higher β -turn and random form compared to that of the KER in native wool. It seems that during dissolution by [BMIm + Cl - ], the inter- and intramolecular forces in KER were broken thereby destroying its secondary structure. During regeneration, these interactions were reestablished to reform partially the secondary structure. However, in the presence of either CEL or CS, the chains seem to prefer the extended form thereby hindering reformation of the α -helix. Consequently, the KER in these matrices may adopt structures with lower content of α -helix and higher β -sheet. As anticipated, results of tensile strength and TGA confirm that adding CEL or CS into KER substantially increase the mechanical strength and thermal stability of the [CS/CEL+KER] composites.

Least-squares finite element methods for compressible Euler equations

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Carey, G. F.

1990-01-01

A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.

Hybrid least squares multivariate spectral analysis methods

DOEpatents

Haaland, David M.

2002-01-01

A set of hybrid least squares multivariate spectral analysis methods in which spectral shapes of components or effects not present in the original calibration step are added in a following estimation or calibration step to improve the accuracy of the estimation of the amount of the original components in the sampled mixture. The "hybrid" method herein means a combination of an initial classical least squares analysis calibration step with subsequent analysis by an inverse multivariate analysis method. A "spectral shape" herein means normally the spectral shape of a non-calibrated chemical component in the sample mixture but can also mean the spectral shapes of other sources of spectral variation, including temperature drift, shifts between spectrometers, spectrometer drift, etc. The "shape" can be continuous, discontinuous, or even discrete points illustrative of the particular effect.

A New Global Regression Analysis Method for the Prediction of Wind Tunnel Model Weight Corrections

NASA Technical Reports Server (NTRS)

Ulbrich, Norbert Manfred; Bridge, Thomas M.; Amaya, Max A.

2014-01-01

A new global regression analysis method is discussed that predicts wind tunnel model weight corrections for strain-gage balance loads during a wind tunnel test. The method determines corrections by combining "wind-on" model attitude measurements with least squares estimates of the model weight and center of gravity coordinates that are obtained from "wind-off" data points. The method treats the least squares fit of the model weight separate from the fit of the center of gravity coordinates. Therefore, it performs two fits of "wind- off" data points and uses the least squares estimator of the model weight as an input for the fit of the center of gravity coordinates. Explicit equations for the least squares estimators of the weight and center of gravity coordinates are derived that simplify the implementation of the method in the data system software of a wind tunnel. In addition, recommendations for sets of "wind-off" data points are made that take typical model support system constraints into account. Explicit equations of the confidence intervals on the model weight and center of gravity coordinates and two different error analyses of the model weight prediction are also discussed in the appendices of the paper.

Assessment of Gait Characteristics in Total Knee Arthroplasty Patients Using a Hierarchical Partial Least Squares Method.

PubMed

Wang, Wei; Ackland, David C; McClelland, Jodie A; Webster, Kate E; Halgamuge, Saman

2018-01-01

Quantitative gait analysis is an important tool in objective assessment and management of total knee arthroplasty (TKA) patients. Studies evaluating gait patterns in TKA patients have tended to focus on discrete data such as spatiotemporal information, joint range of motion and peak values of kinematics and kinetics, or consider selected principal components of gait waveforms for analysis. These strategies may not have the capacity to capture small variations in gait patterns associated with each joint across an entire gait cycle, and may ultimately limit the accuracy of gait classification. The aim of this study was to develop an automatic feature extraction method to analyse patterns from high-dimensional autocorrelated gait waveforms. A general linear feature extraction framework was proposed and a hierarchical partial least squares method derived for discriminant analysis of multiple gait waveforms. The effectiveness of this strategy was verified using a dataset of joint angle and ground reaction force waveforms from 43 patients after TKA surgery and 31 healthy control subjects. Compared with principal component analysis and partial least squares methods, the hierarchical partial least squares method achieved generally better classification performance on all possible combinations of waveforms, with the highest classification accuracy . The novel hierarchical partial least squares method proposed is capable of capturing virtually all significant differences between TKA patients and the controls, and provides new insights into data visualization. The proposed framework presents a foundation for more rigorous classification of gait, and may ultimately be used to evaluate the effects of interventions such as surgery and rehabilitation.

Scalar flux modeling in turbulent flames using iterative deconvolution

NASA Astrophysics Data System (ADS)

Nikolaou, Z. M.; Cant, R. S.; Vervisch, L.

2018-04-01

In the context of large eddy simulations, deconvolution is an attractive alternative for modeling the unclosed terms appearing in the filtered governing equations. Such methods have been used in a number of studies for non-reacting and incompressible flows; however, their application in reacting flows is limited in comparison. Deconvolution methods originate from clearly defined operations, and in theory they can be used in order to model any unclosed term in the filtered equations including the scalar flux. In this study, an iterative deconvolution algorithm is used in order to provide a closure for the scalar flux term in a turbulent premixed flame by explicitly filtering the deconvoluted fields. The assessment of the method is conducted a priori using a three-dimensional direct numerical simulation database of a turbulent freely propagating premixed flame in a canonical configuration. In contrast to most classical a priori studies, the assessment is more stringent as it is performed on a much coarser mesh which is constructed using the filtered fields as obtained from the direct simulations. For the conditions tested in this study, deconvolution is found to provide good estimates both of the scalar flux and of its divergence.

Motion correction of PET brain images through deconvolution: II. Practical implementation and algorithm optimization

NASA Astrophysics Data System (ADS)

Raghunath, N.; Faber, T. L.; Suryanarayanan, S.; Votaw, J. R.

2009-02-01

Image quality is significantly degraded even by small amounts of patient motion in very high-resolution PET scanners. When patient motion is known, deconvolution methods can be used to correct the reconstructed image and reduce motion blur. This paper describes the implementation and optimization of an iterative deconvolution method that uses an ordered subset approach to make it practical and clinically viable. We performed ten separate FDG PET scans using the Hoffman brain phantom and simultaneously measured its motion using the Polaris Vicra tracking system (Northern Digital Inc., Ontario, Canada). The feasibility and effectiveness of the technique was studied by performing scans with different motion and deconvolution parameters. Deconvolution resulted in visually better images and significant improvement as quantified by the Universal Quality Index (UQI) and contrast measures. Finally, the technique was applied to human studies to demonstrate marked improvement. Thus, the deconvolution technique presented here appears promising as a valid alternative to existing motion correction methods for PET. It has the potential for deblurring an image from any modality if the causative motion is known and its effect can be represented in a system matrix.

A new algorithm for stand table projection models.

Treesearch

Quang V. Cao; V. Clark Baldwin

1999-01-01

The constrained least squares method is proposed as an algorithm for projecting stand tables through time. This method consists of three steps: (1) predict survival in each diameter class, (2) predict diameter growth, and (3) use the least squares approach to adjust the stand table to satisfy the constraints of future survival, average diameter, and stand basal area....

The Least-Squares Estimation of Latent Trait Variables.

ERIC Educational Resources Information Center

Tatsuoka, Kikumi

This paper presents a new method for estimating a given latent trait variable by the least-squares approach. The beta weights are obtained recursively with the help of Fourier series and expressed as functions of item parameters of response curves. The values of the latent trait variable estimated by this method and by maximum likelihood method…

Discrimination of Aurantii Fructus Immaturus and Fructus Poniciri Trifoliatae Immaturus by Flow Injection UV Spectroscopy (FIUV) and 1H NMR using Partial Least-squares Discriminant Analysis (PLS-DA)

USDA-ARS?s Scientific Manuscript database

Two simple fingerprinting methods, flow-injection UV spectroscopy (FIUV) and 1H nuclear magnetic resonance (NMR), for discrimination of Aurantii FructusImmaturus and Fructus Poniciri TrifoliataeImmaturususing were described. Both methods were combined with partial least-squares discriminant analysis...

Evaluation of fatty proportion in fatty liver using least squares method with constraints.

PubMed

Li, Xingsong; Deng, Yinhui; Yu, Jinhua; Wang, Yuanyuan; Shamdasani, Vijay

2014-01-01

Backscatter and attenuation parameters are not easily measured in clinical applications due to tissue inhomogeneity in the region of interest (ROI). A least squares method(LSM) that fits the echo signal power spectra from a ROI to a 3-parameter tissue model was used to get attenuation coefficient imaging in fatty liver. Since fat's attenuation value is higher than normal liver parenchyma, a reasonable threshold was chosen to evaluate the fatty proportion in fatty liver. Experimental results using clinical data of fatty liver illustrate that the least squares method can get accurate attenuation estimates. It is proved that the attenuation values have a positive correlation with the fatty proportion, which can be used to evaluate the syndrome of fatty liver.

Evaluation of the Bitterness of Traditional Chinese Medicines using an E-Tongue Coupled with a Robust Partial Least Squares Regression Method.

PubMed

Lin, Zhaozhou; Zhang, Qiao; Liu, Ruixin; Gao, Xiaojie; Zhang, Lu; Kang, Bingya; Shi, Junhan; Wu, Zidan; Gui, Xinjing; Li, Xuelin

2016-01-25

To accurately, safely, and efficiently evaluate the bitterness of Traditional Chinese Medicines (TCMs), a robust predictor was developed using robust partial least squares (RPLS) regression method based on data obtained from an electronic tongue (e-tongue) system. The data quality was verified by the Grubb's test. Moreover, potential outliers were detected based on both the standardized residual and score distance calculated for each sample. The performance of RPLS on the dataset before and after outlier detection was compared to other state-of-the-art methods including multivariate linear regression, least squares support vector machine, and the plain partial least squares regression. Both R² and root-mean-squares error (RMSE) of cross-validation (CV) were recorded for each model. With four latent variables, a robust RMSECV value of 0.3916 with bitterness values ranging from 0.63 to 4.78 were obtained for the RPLS model that was constructed based on the dataset including outliers. Meanwhile, the RMSECV, which was calculated using the models constructed by other methods, was larger than that of the RPLS model. After six outliers were excluded, the performance of all benchmark methods markedly improved, but the difference between the RPLS model constructed before and after outlier exclusion was negligible. In conclusion, the bitterness of TCM decoctions can be accurately evaluated with the RPLS model constructed using e-tongue data.

On the method of least squares. II. [for calculation of covariance matrices and optimization algorithms

NASA Technical Reports Server (NTRS)

Jefferys, W. H.

1981-01-01

A least squares method proposed previously for solving a general class of problems is expanded in two ways. First, covariance matrices related to the solution are calculated and their interpretation is given. Second, improved methods of solving the normal equations related to those of Marquardt (1963) and Fletcher and Powell (1963) are developed for this approach. These methods may converge in cases where Newton's method diverges or converges slowly.

A weak Galerkin least-squares finite element method for div-curl systems

NASA Astrophysics Data System (ADS)

Li, Jichun; Ye, Xiu; Zhang, Shangyou

2018-06-01

In this paper, we introduce a weak Galerkin least-squares method for solving div-curl problem. This finite element method leads to a symmetric positive definite system and has the flexibility to work with general meshes such as hybrid mesh, polytopal mesh and mesh with hanging nodes. Error estimates of the finite element solution are derived. The numerical examples demonstrate the robustness and flexibility of the proposed method.

Kernel Partial Least Squares for Nonlinear Regression and Discrimination

NASA Technical Reports Server (NTRS)

Rosipal, Roman; Clancy, Daniel (Technical Monitor)

2002-01-01

This paper summarizes recent results on applying the method of partial least squares (PLS) in a reproducing kernel Hilbert space (RKHS). A previously proposed kernel PLS regression model was proven to be competitive with other regularized regression methods in RKHS. The family of nonlinear kernel-based PLS models is extended by considering the kernel PLS method for discrimination. Theoretical and experimental results on a two-class discrimination problem indicate usefulness of the method.

Calibration and compensation method of three-axis geomagnetic sensor based on pre-processing total least square iteration

NASA Astrophysics Data System (ADS)

Zhou, Y.; Zhang, X.; Xiao, W.

2018-04-01

As the geomagnetic sensor is susceptible to interference, a pre-processing total least square iteration method is proposed for calibration compensation. Firstly, the error model of the geomagnetic sensor is analyzed and the correction model is proposed, then the characteristics of the model are analyzed and converted into nine parameters. The geomagnetic data is processed by Hilbert transform (HHT) to improve the signal-to-noise ratio, and the nine parameters are calculated by using the combination of Newton iteration method and the least squares estimation method. The sifter algorithm is used to filter the initial value of the iteration to ensure that the initial error is as small as possible. The experimental results show that this method does not need additional equipment and devices, can continuously update the calibration parameters, and better than the two-step estimation method, it can compensate geomagnetic sensor error well.

Solution of a few nonlinear problems in aerodynamics by the finite elements and functional least squares methods. Ph.D. Thesis - Paris Univ.; [mathematical models of transonic flow using nonlinear equations

NASA Technical Reports Server (NTRS)

Periaux, J.

1979-01-01

The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.

Source Pulse Estimation of Mine Shock by Blind Deconvolution

NASA Astrophysics Data System (ADS)

Makowski, R.

The objective of seismic signal deconvolution is to extract from the signal information concerning the rockmass or the signal in the source of the shock. In the case of blind deconvolution, we have to extract information regarding both quantities. Many methods of deconvolution made use of in prospective seismology were found to be of minor utility when applied to shock-induced signals recorded in the mines of the Lubin Copper District. The lack of effectiveness should be attributed to the inadequacy of the model on which the methods are based, with respect to the propagation conditions for that type of signal. Each of the blind deconvolution methods involves a number of assumptions; hence, only if these assumptions are fulfilled, we may expect reliable results.Consequently, we had to formulate a different model for the signals recorded in the copper mines of the Lubin District. The model is based on the following assumptions: (1) The signal emitted by the sh ock source is a short-term signal. (2) The signal transmitting system (rockmass) constitutes a parallel connection of elementary systems. (3) The elementary systems are of resonant type. Such a model seems to be justified by the geological structure as well as by the positions of the shock foci and seismometers. The results of time-frequency transformation also support the dominance of resonant-type propagation.Making use of the model, a new method for the blind deconvolution of seismic signals has been proposed. The adequacy of the new model, as well as the efficiency of the proposed method, has been confirmed by the results of blind deconvolution. The slight approximation errors obtained with a small number of approximating elements additionally corroborate the adequacy of the model.

Partial Deconvolution with Inaccurate Blur Kernel.

PubMed

Ren, Dongwei; Zuo, Wangmeng; Zhang, David; Xu, Jun; Zhang, Lei

2017-10-17

Most non-blind deconvolution methods are developed under the error-free kernel assumption, and are not robust to inaccurate blur kernel. Unfortunately, despite the great progress in blind deconvolution, estimation error remains inevitable during blur kernel estimation. Consequently, severe artifacts such as ringing effects and distortions are likely to be introduced in the non-blind deconvolution stage. In this paper, we tackle this issue by suggesting: (i) a partial map in the Fourier domain for modeling kernel estimation error, and (ii) a partial deconvolution model for robust deblurring with inaccurate blur kernel. The partial map is constructed by detecting the reliable Fourier entries of estimated blur kernel. And partial deconvolution is applied to wavelet-based and learning-based models to suppress the adverse effect of kernel estimation error. Furthermore, an E-M algorithm is developed for estimating the partial map and recovering the latent sharp image alternatively. Experimental results show that our partial deconvolution model is effective in relieving artifacts caused by inaccurate blur kernel, and can achieve favorable deblurring quality on synthetic and real blurry images.Most non-blind deconvolution methods are developed under the error-free kernel assumption, and are not robust to inaccurate blur kernel. Unfortunately, despite the great progress in blind deconvolution, estimation error remains inevitable during blur kernel estimation. Consequently, severe artifacts such as ringing effects and distortions are likely to be introduced in the non-blind deconvolution stage. In this paper, we tackle this issue by suggesting: (i) a partial map in the Fourier domain for modeling kernel estimation error, and (ii) a partial deconvolution model for robust deblurring with inaccurate blur kernel. The partial map is constructed by detecting the reliable Fourier entries of estimated blur kernel. And partial deconvolution is applied to wavelet-based and learning-based models to suppress the adverse effect of kernel estimation error. Furthermore, an E-M algorithm is developed for estimating the partial map and recovering the latent sharp image alternatively. Experimental results show that our partial deconvolution model is effective in relieving artifacts caused by inaccurate blur kernel, and can achieve favorable deblurring quality on synthetic and real blurry images.

Superresolution restoration of an image sequence: adaptive filtering approach.

PubMed

Elad, M; Feuer, A

1999-01-01

This paper presents a new method based on adaptive filtering theory for superresolution restoration of continuous image sequences. The proposed methodology suggests least squares (LS) estimators which adapt in time, based on adaptive filters, least mean squares (LMS) or recursive least squares (RLS). The adaptation enables the treatment of linear space and time-variant blurring and arbitrary motion, both of them assumed known. The proposed new approach is shown to be of relatively low computational requirements. Simulations demonstrating the superresolution restoration algorithms are presented.

Inter-class sparsity based discriminative least square regression.

PubMed

Wen, Jie; Xu, Yong; Li, Zuoyong; Ma, Zhongli; Xu, Yuanrong

2018-06-01

Least square regression is a very popular supervised classification method. However, two main issues greatly limit its performance. The first one is that it only focuses on fitting the input features to the corresponding output labels while ignoring the correlations among samples. The second one is that the used label matrix, i.e., zero-one label matrix is inappropriate for classification. To solve these problems and improve the performance, this paper presents a novel method, i.e., inter-class sparsity based discriminative least square regression (ICS_DLSR), for multi-class classification. Different from other methods, the proposed method pursues that the transformed samples have a common sparsity structure in each class. For this goal, an inter-class sparsity constraint is introduced to the least square regression model such that the margins of samples from the same class can be greatly reduced while those of samples from different classes can be enlarged. In addition, an error term with row-sparsity constraint is introduced to relax the strict zero-one label matrix, which allows the method to be more flexible in learning the discriminative transformation matrix. These factors encourage the method to learn a more compact and discriminative transformation for regression and thus has the potential to perform better than other methods. Extensive experimental results show that the proposed method achieves the best performance in comparison with other methods for multi-class classification. Copyright © 2018 Elsevier Ltd. All rights reserved.

Accuracy of maximum likelihood and least-squares estimates in the lidar slope method with noisy data.

PubMed

Eberhard, Wynn L

2017-04-01

The maximum likelihood estimator (MLE) is derived for retrieving the extinction coefficient and zero-range intercept in the lidar slope method in the presence of random and independent Gaussian noise. Least-squares fitting, weighted by the inverse of the noise variance, is equivalent to the MLE. Monte Carlo simulations demonstrate that two traditional least-squares fitting schemes, which use different weights, are less accurate. Alternative fitting schemes that have some positive attributes are introduced and evaluated. The principal factors governing accuracy of all these schemes are elucidated. Applying these schemes to data with Poisson rather than Gaussian noise alters accuracy little, even when the signal-to-noise ratio is low. Methods to estimate optimum weighting factors in actual data are presented. Even when the weighting estimates are coarse, retrieval accuracy declines only modestly. Mathematical tools are described for predicting retrieval accuracy. Least-squares fitting with inverse variance weighting has optimum accuracy for retrieval of parameters from single-wavelength lidar measurements when noise, errors, and uncertainties are Gaussian distributed, or close to optimum when only approximately Gaussian.

Geodesic least squares regression for scaling studies in magnetic confinement fusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Verdoolaege, Geert

In regression analyses for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. However, concerns have been raised with respect to several assumptions underlying OLS in its application to scaling laws. We here discuss a new regression method that is robust in the presence of significant uncertainty on both the data and the regression model. The method, which we call geodesic least squares regression (GLS), is based on minimization of the Rao geodesic distance on a probabilistic manifold. We demonstrate the superiority ofmore » the method using synthetic data and we present an application to the scaling law for the power threshold for the transition to the high confinement regime in magnetic confinement fusion devices.« less

A Generalized Least Squares Regression Approach for Computing Effect Sizes in Single-Case Research: Application Examples

ERIC Educational Resources Information Center

Maggin, Daniel M.; Swaminathan, Hariharan; Rogers, Helen J.; O'Keeffe, Breda V.; Sugai, George; Horner, Robert H.

2011-01-01

A new method for deriving effect sizes from single-case designs is proposed. The strategy is applicable to small-sample time-series data with autoregressive errors. The method uses Generalized Least Squares (GLS) to model the autocorrelation of the data and estimate regression parameters to produce an effect size that represents the magnitude of…

Gamma-Ray Simulated Spectrum Deconvolution of a LaBr₃ 1-in. x 1-in. Scintillator for Nondestructive ATR Fuel Burnup On-Site Predictions

DOE PAGES

Navarro, Jorge; Ring, Terry A.; Nigg, David W.

2015-03-01

A deconvolution method for a LaBr₃ 1"x1" detector for nondestructive Advanced Test Reactor (ATR) fuel burnup applications was developed. The method consisted of obtaining the detector response function, applying a deconvolution algorithm to 1”x1” LaBr₃ simulated, data along with evaluating the effects that deconvolution have on nondestructively determining ATR fuel burnup. The simulated response function of the detector was obtained using MCNPX as well with experimental data. The Maximum-Likelihood Expectation Maximization (MLEM) deconvolution algorithm was selected to enhance one-isotope source-simulated and fuel- simulated spectra. The final evaluation of the study consisted of measuring the performance of the fuel burnup calibrationmore » curve for the convoluted and deconvoluted cases. The methodology was developed in order to help design a reliable, high resolution, rugged and robust detection system for the ATR fuel canal capable of collecting high performance data for model validation, along with a system that can calculate burnup and using experimental scintillator detector data.« less

Load forecasting via suboptimal seasonal autoregressive models and iteratively reweighted least squares estimation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mbamalu, G.A.N.; El-Hawary, M.E.

The authors propose suboptimal least squares or IRWLS procedures for estimating the parameters of a seasonal multiplicative AR model encountered during power system load forecasting. The proposed method involves using an interactive computer environment to estimate the parameters of a seasonal multiplicative AR process. The method comprises five major computational steps. The first determines the order of the seasonal multiplicative AR process, and the second uses the least squares or the IRWLS to estimate the optimal nonseasonal AR model parameters. In the third step one obtains the intermediate series by back forecast, which is followed by using the least squaresmore » or the IRWLS to estimate the optimal season AR parameters. The final step uses the estimated parameters to forecast future load. The method is applied to predict the Nova Scotia Power Corporation's 168 lead time hourly load. The results obtained are documented and compared with results based on the Box and Jenkins method.« less

Using deconvolution to improve the metrological performance of the grid method

NASA Astrophysics Data System (ADS)

Grédiac, Michel; Sur, Frédéric; Badulescu, Claudiu; Mathias, Jean-Denis

2013-06-01

The use of various deconvolution techniques to enhance strain maps obtained with the grid method is addressed in this study. Since phase derivative maps obtained with the grid method can be approximated by their actual counterparts convolved by the envelope of the kernel used to extract phases and phase derivatives, non-blind restoration techniques can be used to perform deconvolution. Six deconvolution techniques are presented and employed to restore a synthetic phase derivative map, namely direct deconvolution, regularized deconvolution, the Richardson-Lucy algorithm and Wiener filtering, the last two with two variants concerning their practical implementations. Obtained results show that the noise that corrupts the grid images must be thoroughly taken into account to limit its effect on the deconvolved strain maps. The difficulty here is that the noise on the grid image yields a spatially correlated noise on the strain maps. In particular, numerical experiments on synthetic data show that direct and regularized deconvolutions are unstable when noisy data are processed. The same remark holds when Wiener filtering is employed without taking into account noise autocorrelation. On the other hand, the Richardson-Lucy algorithm and Wiener filtering with noise autocorrelation provide deconvolved maps where the impact of noise remains controlled within a certain limit. It is also observed that the last technique outperforms the Richardson-Lucy algorithm. Two short examples of actual strain fields restoration are finally shown. They deal with asphalt and shape memory alloy specimens. The benefits and limitations of deconvolution are presented and discussed in these two cases. The main conclusion is that strain maps are correctly deconvolved when the signal-to-noise ratio is high and that actual noise in the actual strain maps must be more specifically characterized than in the current study to address higher noise levels with Wiener filtering.

Addressing the identification problem in age-period-cohort analysis: a tutorial on the use of partial least squares and principal components analysis.

PubMed

Tu, Yu-Kang; Krämer, Nicole; Lee, Wen-Chung

2012-07-01

In the analysis of trends in health outcomes, an ongoing issue is how to separate and estimate the effects of age, period, and cohort. As these 3 variables are perfectly collinear by definition, regression coefficients in a general linear model are not unique. In this tutorial, we review why identification is a problem, and how this problem may be tackled using partial least squares and principal components regression analyses. Both methods produce regression coefficients that fulfill the same collinearity constraint as the variables age, period, and cohort. We show that, because the constraint imposed by partial least squares and principal components regression is inherent in the mathematical relation among the 3 variables, this leads to more interpretable results. We use one dataset from a Taiwanese health-screening program to illustrate how to use partial least squares regression to analyze the trends in body heights with 3 continuous variables for age, period, and cohort. We then use another dataset of hepatocellular carcinoma mortality rates for Taiwanese men to illustrate how to use partial least squares regression to analyze tables with aggregated data. We use the second dataset to show the relation between the intrinsic estimator, a recently proposed method for the age-period-cohort analysis, and partial least squares regression. We also show that the inclusion of all indicator variables provides a more consistent approach. R code for our analyses is provided in the eAppendix.

Total variation superiorized conjugate gradient method for image reconstruction

NASA Astrophysics Data System (ADS)

Zibetti, Marcelo V. W.; Lin, Chuan; Herman, Gabor T.

2018-03-01

The conjugate gradient (CG) method is commonly used for the relatively-rapid solution of least squares problems. In image reconstruction, the problem can be ill-posed and also contaminated by noise; due to this, approaches such as regularization should be utilized. Total variation (TV) is a useful regularization penalty, frequently utilized in image reconstruction for generating images with sharp edges. When a non-quadratic norm is selected for regularization, as is the case for TV, then it is no longer possible to use CG. Non-linear CG is an alternative, but it does not share the efficiency that CG shows with least squares and methods such as fast iterative shrinkage-thresholding algorithms (FISTA) are preferred for problems with TV norm. A different approach to including prior information is superiorization. In this paper it is shown that the conjugate gradient method can be superiorized. Five different CG variants are proposed, including preconditioned CG. The CG methods superiorized by the total variation norm are presented and their performance in image reconstruction is demonstrated. It is illustrated that some of the proposed variants of the superiorized CG method can produce reconstructions of superior quality to those produced by FISTA and in less computational time, due to the speed of the original CG for least squares problems. In the Appendix we examine the behavior of one of the superiorized CG methods (we call it S-CG); one of its input parameters is a positive number ɛ. It is proved that, for any given ɛ that is greater than the half-squared-residual for the least squares solution, S-CG terminates in a finite number of steps with an output for which the half-squared-residual is less than or equal to ɛ. Importantly, it is also the case that the output will have a lower value of TV than what would be provided by unsuperiorized CG for the same value ɛ of the half-squared residual.

Application of an NLME-Stochastic Deconvolution Approach to Level A IVIVC Modeling.

PubMed

Kakhi, Maziar; Suarez-Sharp, Sandra; Shepard, Terry; Chittenden, Jason

2017-07-01

Stochastic deconvolution is a parameter estimation method that calculates drug absorption using a nonlinear mixed-effects model in which the random effects associated with absorption represent a Wiener process. The present work compares (1) stochastic deconvolution and (2) numerical deconvolution, using clinical pharmacokinetic (PK) data generated for an in vitro-in vivo correlation (IVIVC) study of extended release (ER) formulations of a Biopharmaceutics Classification System class III drug substance. The preliminary analysis found that numerical and stochastic deconvolution yielded superimposable fraction absorbed (F abs ) versus time profiles when supplied with exactly the same externally determined unit impulse response parameters. In a separate analysis, a full population-PK/stochastic deconvolution was applied to the clinical PK data. Scenarios were considered in which immediate release (IR) data were either retained or excluded to inform parameter estimation. The resulting F abs profiles were then used to model level A IVIVCs. All the considered stochastic deconvolution scenarios, and numerical deconvolution, yielded on average similar results with respect to the IVIVC validation. These results could be achieved with stochastic deconvolution without recourse to IR data. Unlike numerical deconvolution, this also implies that in crossover studies where certain individuals do not receive an IR treatment, their ER data alone can still be included as part of the IVIVC analysis. Published by Elsevier Inc.

A novel partial volume effects correction technique integrating deconvolution associated with denoising within an iterative PET image reconstruction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Merlin, Thibaut, E-mail: thibaut.merlin@telecom-bretagne.eu; Visvikis, Dimitris; Fernandez, Philippe

2015-02-15

Purpose: Partial volume effect (PVE) plays an important role in both qualitative and quantitative PET image accuracy, especially for small structures. A previously proposed voxelwise PVE correction method applied on PET reconstructed images involves the use of Lucy–Richardson deconvolution incorporating wavelet-based denoising to limit the associated propagation of noise. The aim of this study is to incorporate the deconvolution, coupled with the denoising step, directly inside the iterative reconstruction process to further improve PVE correction. Methods: The list-mode ordered subset expectation maximization (OSEM) algorithm has been modified accordingly with the application of the Lucy–Richardson deconvolution algorithm to the current estimationmore » of the image, at each reconstruction iteration. Acquisitions of the NEMA NU2-2001 IQ phantom were performed on a GE DRX PET/CT system to study the impact of incorporating the deconvolution inside the reconstruction [with and without the point spread function (PSF) model] in comparison to its application postreconstruction and to standard iterative reconstruction incorporating the PSF model. The impact of the denoising step was also evaluated. Images were semiquantitatively assessed by studying the trade-off between the intensity recovery and the noise level in the background estimated as relative standard deviation. Qualitative assessments of the developed methods were additionally performed on clinical cases. Results: Incorporating the deconvolution without denoising within the reconstruction achieved superior intensity recovery in comparison to both standard OSEM reconstruction integrating a PSF model and application of the deconvolution algorithm in a postreconstruction process. The addition of the denoising step permitted to limit the SNR degradation while preserving the intensity recovery. Conclusions: This study demonstrates the feasibility of incorporating the Lucy–Richardson deconvolution associated with a wavelet-based denoising in the reconstruction process to better correct for PVE. Future work includes further evaluations of the proposed method on clinical datasets and the use of improved PSF models.« less

More efficient parameter estimates for factor analysis of ordinal variables by ridge generalized least squares.

PubMed

Yuan, Ke-Hai; Jiang, Ge; Cheng, Ying

2017-11-01

Data in psychology are often collected using Likert-type scales, and it has been shown that factor analysis of Likert-type data is better performed on the polychoric correlation matrix than on the product-moment covariance matrix, especially when the distributions of the observed variables are skewed. In theory, factor analysis of the polychoric correlation matrix is best conducted using generalized least squares with an asymptotically correct weight matrix (AGLS). However, simulation studies showed that both least squares (LS) and diagonally weighted least squares (DWLS) perform better than AGLS, and thus LS or DWLS is routinely used in practice. In either LS or DWLS, the associations among the polychoric correlation coefficients are completely ignored. To mend such a gap between statistical theory and empirical work, this paper proposes new methods, called ridge GLS, for factor analysis of ordinal data. Monte Carlo results show that, for a wide range of sample sizes, ridge GLS methods yield uniformly more accurate parameter estimates than existing methods (LS, DWLS, AGLS). A real-data example indicates that estimates by ridge GLS are 9-20% more efficient than those by existing methods. Rescaled and adjusted test statistics as well as sandwich-type standard errors following the ridge GLS methods also perform reasonably well. © 2017 The British Psychological Society.

Imaging resolution and properties analysis of super resolution microscopy with parallel detection under different noise, detector and image restoration conditions

NASA Astrophysics Data System (ADS)

Yu, Zhongzhi; Liu, Shaocong; Sun, Shiyi; Kuang, Cuifang; Liu, Xu

2018-06-01

Parallel detection, which can use the additional information of a pinhole plane image taken at every excitation scan position, could be an efficient method to enhance the resolution of a confocal laser scanning microscope. In this paper, we discuss images obtained under different conditions and using different image restoration methods with parallel detection to quantitatively compare the imaging quality. The conditions include different noise levels and different detector array settings. The image restoration methods include linear deconvolution and pixel reassignment with Richard-Lucy deconvolution and with maximum-likelihood estimation deconvolution. The results show that the linear deconvolution share properties such as high-efficiency and the best performance under all different conditions, and is therefore expected to be of use for future biomedical routine research.

An augmented classical least squares method for quantitative Raman spectral analysis against component information loss.

PubMed

Zhou, Yan; Cao, Hui

2013-01-01

We propose an augmented classical least squares (ACLS) calibration method for quantitative Raman spectral analysis against component information loss. The Raman spectral signals with low analyte concentration correlations were selected and used as the substitutes for unknown quantitative component information during the CLS calibration procedure. The number of selected signals was determined by using the leave-one-out root-mean-square error of cross-validation (RMSECV) curve. An ACLS model was built based on the augmented concentration matrix and the reference spectral signal matrix. The proposed method was compared with partial least squares (PLS) and principal component regression (PCR) using one example: a data set recorded from an experiment of analyte concentration determination using Raman spectroscopy. A 2-fold cross-validation with Venetian blinds strategy was exploited to evaluate the predictive power of the proposed method. The one-way variance analysis (ANOVA) was used to access the predictive power difference between the proposed method and existing methods. Results indicated that the proposed method is effective at increasing the robust predictive power of traditional CLS model against component information loss and its predictive power is comparable to that of PLS or PCR.

Theoretical study of the incompressible Navier-Stokes equations by the least-squares method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Loh, Ching Y.; Povinelli, Louis A.

1994-01-01

Usually the theoretical analysis of the Navier-Stokes equations is conducted via the Galerkin method which leads to difficult saddle-point problems. This paper demonstrates that the least-squares method is a useful alternative tool for the theoretical study of partial differential equations since it leads to minimization problems which can often be treated by an elementary technique. The principal part of the Navier-Stokes equations in the first-order velocity-pressure-vorticity formulation consists of two div-curl systems, so the three-dimensional div-curl system is thoroughly studied at first. By introducing a dummy variable and by using the least-squares method, this paper shows that the div-curl system is properly determined and elliptic, and has a unique solution. The same technique then is employed to prove that the Stokes equations are properly determined and elliptic, and that four boundary conditions on a fixed boundary are required for three-dimensional problems. This paper also shows that under four combinations of non-standard boundary conditions the solution of the Stokes equations is unique. This paper emphasizes the application of the least-squares method and the div-curl method to derive a high-order version of differential equations and additional boundary conditions. In this paper, an elementary method (integration by parts) is used to prove Friedrichs' inequalities related to the div and curl operators which play an essential role in the analysis.

Evaluation of the Bitterness of Traditional Chinese Medicines using an E-Tongue Coupled with a Robust Partial Least Squares Regression Method

PubMed Central

Lin, Zhaozhou; Zhang, Qiao; Liu, Ruixin; Gao, Xiaojie; Zhang, Lu; Kang, Bingya; Shi, Junhan; Wu, Zidan; Gui, Xinjing; Li, Xuelin

2016-01-01

To accurately, safely, and efficiently evaluate the bitterness of Traditional Chinese Medicines (TCMs), a robust predictor was developed using robust partial least squares (RPLS) regression method based on data obtained from an electronic tongue (e-tongue) system. The data quality was verified by the Grubb’s test. Moreover, potential outliers were detected based on both the standardized residual and score distance calculated for each sample. The performance of RPLS on the dataset before and after outlier detection was compared to other state-of-the-art methods including multivariate linear regression, least squares support vector machine, and the plain partial least squares regression. Both R2 and root-mean-squares error (RMSE) of cross-validation (CV) were recorded for each model. With four latent variables, a robust RMSECV value of 0.3916 with bitterness values ranging from 0.63 to 4.78 were obtained for the RPLS model that was constructed based on the dataset including outliers. Meanwhile, the RMSECV, which was calculated using the models constructed by other methods, was larger than that of the RPLS model. After six outliers were excluded, the performance of all benchmark methods markedly improved, but the difference between the RPLS model constructed before and after outlier exclusion was negligible. In conclusion, the bitterness of TCM decoctions can be accurately evaluated with the RPLS model constructed using e-tongue data. PMID:26821026

Avoiding hard chromatographic segmentation: A moving window approach for the automated resolution of gas chromatography-mass spectrometry-based metabolomics signals by multivariate methods.

PubMed

Domingo-Almenara, Xavier; Perera, Alexandre; Brezmes, Jesus

2016-11-25

Gas chromatography-mass spectrometry (GC-MS) produces large and complex datasets characterized by co-eluted compounds and at trace levels, and with a distinct compound ion-redundancy as a result of the high fragmentation by the electron impact ionization. Compounds in GC-MS can be resolved by taking advantage of the multivariate nature of GC-MS data by applying multivariate resolution methods. However, multivariate methods have to be applied in small regions of the chromatogram, and therefore chromatograms are segmented prior to the application of the algorithms. The automation of this segmentation process is a challenging task as it implies separating between informative data and noise from the chromatogram. This study demonstrates the capabilities of independent component analysis-orthogonal signal deconvolution (ICA-OSD) and multivariate curve resolution-alternating least squares (MCR-ALS) with an overlapping moving window implementation to avoid the typical hard chromatographic segmentation. Also, after being resolved, compounds are aligned across samples by an automated alignment algorithm. We evaluated the proposed methods through a quantitative analysis of GC-qTOF MS data from 25 serum samples. The quantitative performance of both moving window ICA-OSD and MCR-ALS-based implementations was compared with the quantification of 33 compounds by the XCMS package. Results shown that most of the R 2 coefficients of determination exhibited a high correlation (R 2 >0.90) in both ICA-OSD and MCR-ALS moving window-based approaches. Copyright © 2016 Elsevier B.V. All rights reserved.

Adaptive recovery of motion blur point spread function from differently exposed images

NASA Astrophysics Data System (ADS)

Albu, Felix; Florea, Corneliu; Drîmbarean, Alexandru; Zamfir, Adrian

2010-01-01

Motion due to digital camera movement during the image capture process is a major factor that degrades the quality of images and many methods for camera motion removal have been developed. Central to all techniques is the correct recovery of what is known as the Point Spread Function (PSF). A very popular technique to estimate the PSF relies on using a pair of gyroscopic sensors to measure the hand motion. However, the errors caused either by the loss of the translational component of the movement or due to the lack of precision in gyro-sensors measurements impede the achievement of a good quality restored image. In order to compensate for this, we propose a method that begins with an estimation of the PSF obtained from 2 gyro sensors and uses a pair of under-exposed image together with the blurred image to adaptively improve it. The luminance of the under-exposed image is equalized with that of the blurred image. An initial estimation of the PSF is generated from the output signal of 2 gyro sensors. The PSF coefficients are updated using 2D-Least Mean Square (LMS) algorithms with a coarse-to-fine approach on a grid of points selected from both images. This refined PSF is used to process the blurred image using known deblurring methods. Our results show that the proposed method leads to superior PSF support and coefficient estimation. Also the quality of the restored image is improved compared to 2 gyro only approach or to blind image de-convolution results.

Joint de-blurring and nonuniformity correction method for infrared microscopy imaging

NASA Astrophysics Data System (ADS)

Jara, Anselmo; Torres, Sergio; Machuca, Guillermo; Ramírez, Wagner; Gutiérrez, Pablo A.; Viafora, Laura A.; Godoy, Sebastián E.; Vera, Esteban

2018-05-01

In this work, we present a new technique to simultaneously reduce two major degradation artifacts found in mid-wavelength infrared microscopy imagery, namely the inherent focal-plane array nonuniformity noise and the scene defocus presented due to the point spread function of the infrared microscope. We correct both nuisances using a novel, recursive method that combines the constant range nonuniformity correction algorithm with a frame-by-frame deconvolution approach. The ability of the method to jointly compensate for both nonuniformity noise and blur is demonstrated using two different real mid-wavelength infrared microscopic video sequences, which were captured from two microscopic living organisms using a Janos-Sofradir mid-wavelength infrared microscopy setup. The performance of the proposed method is assessed on real and simulated infrared data by computing the root mean-square error and the roughness-laplacian pattern index, which was specifically developed for the present work.

Multi-frame partially saturated images blind deconvolution

NASA Astrophysics Data System (ADS)

Ye, Pengzhao; Feng, Huajun; Xu, Zhihai; Li, Qi; Chen, Yueting

2016-12-01

When blurred images have saturated or over-exposed pixels, conventional blind deconvolution approaches often fail to estimate accurate point spread function (PSF) and will introduce local ringing artifacts. In this paper, we propose a method to deal with the problem under the modified multi-frame blind deconvolution framework. First, in the kernel estimation step, a light streak detection scheme using multi-frame blurred images is incorporated into the regularization constraint. Second, we deal with image regions affected by the saturated pixels separately by modeling a weighted matrix during each multi-frame deconvolution iteration process. Both synthetic and real-world examples show that more accurate PSFs can be estimated and restored images have richer details and less negative effects compared to state of art methods.

Linear Least Squares for Correlated Data

NASA Technical Reports Server (NTRS)

Dean, Edwin B.

1988-01-01

Throughout the literature authors have consistently discussed the suspicion that regression results were less than satisfactory when the independent variables were correlated. Camm, Gulledge, and Womer, and Womer and Marcotte provide excellent applied examples of these concerns. Many authors have obtained partial solutions for this problem as discussed by Womer and Marcotte and Wonnacott and Wonnacott, which result in generalized least squares algorithms to solve restrictive cases. This paper presents a simple but relatively general multivariate method for obtaining linear least squares coefficients which are free of the statistical distortion created by correlated independent variables.

The least-squares mixing models to generate fraction images derived from remote sensing multispectral data

NASA Technical Reports Server (NTRS)

Shimabukuro, Yosio Edemir; Smith, James A.

1991-01-01

Constrained-least-squares and weighted-least-squares mixing models for generating fraction images derived from remote sensing multispectral data are presented. An experiment considering three components within the pixels-eucalyptus, soil (understory), and shade-was performed. The generated fraction images for shade (shade image) derived from these two methods were compared by considering the performance and computer time. The derived shade images are related to the observed variation in forest structure, i.e., the fraction of inferred shade in the pixel is related to different eucalyptus ages.

Neither fixed nor random: weighted least squares meta-analysis.

PubMed

Stanley, T D; Doucouliagos, Hristos

2015-06-15

This study challenges two core conventional meta-analysis methods: fixed effect and random effects. We show how and explain why an unrestricted weighted least squares estimator is superior to conventional random-effects meta-analysis when there is publication (or small-sample) bias and better than a fixed-effect weighted average if there is heterogeneity. Statistical theory and simulations of effect sizes, log odds ratios and regression coefficients demonstrate that this unrestricted weighted least squares estimator provides satisfactory estimates and confidence intervals that are comparable to random effects when there is no publication (or small-sample) bias and identical to fixed-effect meta-analysis when there is no heterogeneity. When there is publication selection bias, the unrestricted weighted least squares approach dominates random effects; when there is excess heterogeneity, it is clearly superior to fixed-effect meta-analysis. In practical applications, an unrestricted weighted least squares weighted average will often provide superior estimates to both conventional fixed and random effects. Copyright © 2015 John Wiley & Sons, Ltd.

Untangling the Diverse Interior and Multiple Exterior Guest Interactions of a Supramolecular Host by the Simultaneous Analysis of Complementary Observables.

PubMed

Sgarlata, Carmelo; Raymond, Kenneth N

2016-07-05

The entropic and enthalpic driving forces for encapsulation versus sequential exterior guest binding to the [Ga4L6](12-) supramolecular host in solution are very different, which significantly complicates the determination of these thermodynamic parameters. The simultaneous use of complementary techniques, such as NMR, UV-vis, and isothermal titration calorimetry, enables the disentanglement of such multiple host-guest interactions. Indeed, data collected by each technique measure different components of the host-guest equilibria and together provide a complete picture of the solution thermodynamics. Unfortunately, commercially available programs do not allow for global analysis of different physical observables. We thus resorted to a novel procedure for the simultaneous refinement of multiple parameters (ΔG°, ΔH°, and ΔS°) by treating different observables through a weighted nonlinear least-squares analysis of a constrained model. The refinement procedure is discussed for the multiple binding of the Et4N(+) guest, but it is broadly applicable to the deconvolution of other intricate host-guest equilibria.

Least median of squares and iteratively re-weighted least squares as robust linear regression methods for fluorimetric determination of α-lipoic acid in capsules in ideal and non-ideal cases of linearity.

PubMed

Korany, Mohamed A; Gazy, Azza A; Khamis, Essam F; Ragab, Marwa A A; Kamal, Miranda F

2018-06-01

This study outlines two robust regression approaches, namely least median of squares (LMS) and iteratively re-weighted least squares (IRLS) to investigate their application in instrument analysis of nutraceuticals (that is, fluorescence quenching of merbromin reagent upon lipoic acid addition). These robust regression methods were used to calculate calibration data from the fluorescence quenching reaction (∆F and F-ratio) under ideal or non-ideal linearity conditions. For each condition, data were treated using three regression fittings: Ordinary Least Squares (OLS), LMS and IRLS. Assessment of linearity, limits of detection (LOD) and quantitation (LOQ), accuracy and precision were carefully studied for each condition. LMS and IRLS regression line fittings showed significant improvement in correlation coefficients and all regression parameters for both methods and both conditions. In the ideal linearity condition, the intercept and slope changed insignificantly, but a dramatic change was observed for the non-ideal condition and linearity intercept. Under both linearity conditions, LOD and LOQ values after the robust regression line fitting of data were lower than those obtained before data treatment. The results obtained after statistical treatment indicated that the linearity ranges for drug determination could be expanded to lower limits of quantitation by enhancing the regression equation parameters after data treatment. Analysis results for lipoic acid in capsules, using both fluorimetric methods, treated by parametric OLS and after treatment by robust LMS and IRLS were compared for both linearity conditions. Copyright © 2018 John Wiley & Sons, Ltd.

Arrhenius time-scaled least squares: a simple, robust approach to accelerated stability data analysis for bioproducts.

PubMed

Rauk, Adam P; Guo, Kevin; Hu, Yanling; Cahya, Suntara; Weiss, William F

2014-08-01

Defining a suitable product presentation with an acceptable stability profile over its intended shelf-life is one of the principal challenges in bioproduct development. Accelerated stability studies are routinely used as a tool to better understand long-term stability. Data analysis often employs an overall mass action kinetics description for the degradation and the Arrhenius relationship to capture the temperature dependence of the observed rate constant. To improve predictive accuracy and precision, the current work proposes a least-squares estimation approach with a single nonlinear covariate and uses a polynomial to describe the change in a product attribute with respect to time. The approach, which will be referred to as Arrhenius time-scaled (ATS) least squares, enables accurate, precise predictions to be achieved for degradation profiles commonly encountered during bioproduct development. A Monte Carlo study is conducted to compare the proposed approach with the common method of least-squares estimation on the logarithmic form of the Arrhenius equation and nonlinear estimation of a first-order model. The ATS least squares method accommodates a range of degradation profiles, provides a simple and intuitive approach for data presentation, and can be implemented with ease. © 2014 Wiley Periodicals, Inc. and the American Pharmacists Association.

Least-Squares Regression and Spectral Residual Augmented Classical Least-Squares Chemometric Models for Stability-Indicating Analysis of Agomelatine and Its Degradation Products: A Comparative Study.

PubMed

Naguib, Ibrahim A; Abdelrahman, Maha M; El Ghobashy, Mohamed R; Ali, Nesma A

2016-01-01

Two accurate, sensitive, and selective stability-indicating methods are developed and validated for simultaneous quantitative determination of agomelatine (AGM) and its forced degradation products (Deg I and Deg II), whether in pure forms or in pharmaceutical formulations. Partial least-squares regression (PLSR) and spectral residual augmented classical least-squares (SRACLS) are two chemometric models that are being subjected to a comparative study through handling UV spectral data in range (215-350 nm). For proper analysis, a three-factor, four-level experimental design was established, resulting in a training set consisting of 16 mixtures containing different ratios of interfering species. An independent test set consisting of eight mixtures was used to validate the prediction ability of the suggested models. The results presented indicate the ability of mentioned multivariate calibration models to analyze AGM, Deg I, and Deg II with high selectivity and accuracy. The analysis results of the pharmaceutical formulations were statistically compared to the reference HPLC method, with no significant differences observed regarding accuracy and precision. The SRACLS model gives comparable results to the PLSR model; however, it keeps the qualitative spectral information of the classical least-squares algorithm for analyzed components.

Potential energy surface fitting by a statistically localized, permutationally invariant, local interpolating moving least squares method for the many-body potential: Method and application to N{sub 4}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bender, Jason D.; Doraiswamy, Sriram; Candler, Graham V., E-mail: truhlar@umn.edu, E-mail: candler@aem.umn.edu

2014-02-07

Fitting potential energy surfaces to analytic forms is an important first step for efficient molecular dynamics simulations. Here, we present an improved version of the local interpolating moving least squares method (L-IMLS) for such fitting. Our method has three key improvements. First, pairwise interactions are modeled separately from many-body interactions. Second, permutational invariance is incorporated in the basis functions, using permutationally invariant polynomials in Morse variables, and in the weight functions. Third, computational cost is reduced by statistical localization, in which we statistically correlate the cutoff radius with data point density. We motivate our discussion in this paper with amore » review of global and local least-squares-based fitting methods in one dimension. Then, we develop our method in six dimensions, and we note that it allows the analytic evaluation of gradients, a feature that is important for molecular dynamics. The approach, which we call statistically localized, permutationally invariant, local interpolating moving least squares fitting of the many-body potential (SL-PI-L-IMLS-MP, or, more simply, L-IMLS-G2), is used to fit a potential energy surface to an electronic structure dataset for N{sub 4}. We discuss its performance on the dataset and give directions for further research, including applications to trajectory calculations.« less

A comparison of waveform processing algorithms for single-wavelength LiDAR bathymetry

NASA Astrophysics Data System (ADS)

Wang, Chisheng; Li, Qingquan; Liu, Yanxiong; Wu, Guofeng; Liu, Peng; Ding, Xiaoli

2015-03-01

Due to the low-cost and lightweight units, single-wavelength LiDAR bathymetric systems are an ideal option for shallow-water (<12 m) bathymetry. However, one disadvantage of such systems is the lack of near-infrared and Raman channels, which results in difficulties in extracting the water surface. Therefore, the choice of a suitable waveform processing method is extremely important to guarantee the accuracy of the bathymetric retrieval. In this paper, we test six algorithms for single-wavelength bathymetric waveform processing, i.e. peak detection (PD), the average square difference function (ASDF), Gaussian decomposition (GD), quadrilateral fitting (QF), Richardson-Lucy deconvolution (RLD), and Wiener filter deconvolution (WD). To date, most of these algorithms have previously only been applied in topographic LiDAR waveforms captured over land. A simulated dataset and an Optech Aquarius dataset were used to assess the algorithms, with the focus being on their capability of extracting the depth and the bottom response. The influences of a number of water and equipment parameters were also investigated by the use of a Monte Carlo method. The results showed that the RLD method had a superior performance in terms of a high detection rate and low errors in the retrieved depth and magnitude. The attenuation coefficient, noise level, water depth, and bottom reflectance had significant influences on the measurement error of the retrieved depth, while the effects of scan angle and water surface roughness were not so obvious.

PROPOSED MODIFICATIONS OF K2-TEMPERATURE RELATION AND LEAST SQUARES ESTIMATES OF BOD (BIOCHEMICAL OXYGEN DEMAND) PARAMETERS

EPA Science Inventory

A technique is presented for finding the least squares estimates for the ultimate biochemical oxygen demand (BOD) and rate coefficient for the BOD reaction without resorting to complicated computer algorithms or subjective graphical methods. This may be used in stream water quali...

Why Might Relative Fit Indices Differ between Estimators?

ERIC Educational Resources Information Center

Weng, Li-Jen; Cheng, Chung-Ping

1997-01-01

Relative fit indices using the null model as the reference point in computation may differ across estimation methods, as this article illustrates by comparing maximum likelihood, ordinary least squares, and generalized least squares estimation in structural equation modeling. The illustration uses a covariance matrix for six observed variables…

Forecasting Error Calculation with Mean Absolute Deviation and Mean Absolute Percentage Error

NASA Astrophysics Data System (ADS)

Khair, Ummul; Fahmi, Hasanul; Hakim, Sarudin Al; Rahim, Robbi

2017-12-01

Prediction using a forecasting method is one of the most important things for an organization, the selection of appropriate forecasting methods is also important but the percentage error of a method is more important in order for decision makers to adopt the right culture, the use of the Mean Absolute Deviation and Mean Absolute Percentage Error to calculate the percentage of mistakes in the least square method resulted in a percentage of 9.77% and it was decided that the least square method be worked for time series and trend data.

A least-squares finite element method for incompressible Navier-Stokes problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1992-01-01

A least-squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to a saddle-point problem by the classic mixed method and can thus accommodate equal-order interpolations. This method has no parameter to tune. The associated algebraic system is symmetric, and positive definite. Numerical results for the cavity flow at Reynolds number up to 10,000 and the backward-facing step flow at Reynolds number up to 900 are presented.

Advantages of soft versus hard constraints in self-modeling curve resolution problems. Alternating least squares with penalty functions.

PubMed

Gemperline, Paul J; Cash, Eric

2003-08-15

A new algorithm for self-modeling curve resolution (SMCR) that yields improved results by incorporating soft constraints is described. The method uses least squares penalty functions to implement constraints in an alternating least squares algorithm, including nonnegativity, unimodality, equality, and closure constraints. By using least squares penalty functions, soft constraints are formulated rather than hard constraints. Significant benefits are (obtained using soft constraints, especially in the form of fewer distortions due to noise in resolved profiles. Soft equality constraints can also be used to introduce incomplete or partial reference information into SMCR solutions. Four different examples demonstrating application of the new method are presented, including resolution of overlapped HPLC-DAD peaks, flow injection analysis data, and batch reaction data measured by UV/visible and near-infrared spectroscopy (NIR). Each example was selected to show one aspect of the significant advantages of soft constraints over traditionally used hard constraints. Incomplete or partial reference information into self-modeling curve resolution models is described. The method offers a substantial improvement in the ability to resolve time-dependent concentration profiles from mixture spectra recorded as a function of time.

Nimbus 7 earth radiation budget wide field of view climate data set improvement. I - The earth albedo from deconvolution of shortwave measurements

NASA Technical Reports Server (NTRS)

Hucek, Richard R.; Ardanuy, Philip E.; Kyle, H. Lee

1987-01-01

A deconvolution method for extracting the top of the atmosphere (TOA) mean, daily albedo field from a set of wide-FOV (WFOV) shortwave radiometer measurements is proposed. The method is based on constructing a synthetic measurement for each satellite observation. The albedo field is represented as a truncated series of spherical harmonic functions, and these linear equations are presented. Simulation studies were conducted to determine the sensitivity of the method. It is observed that a maximum of about 289 pieces of data can be extracted from a set of Nimbus 7 WFOV satellite measurements. The albedos derived using the deconvolution method are compared with albedos derived using the WFOV archival method; the developed albedo field achieved a 20 percent reduction in the global rms regional reflected flux density errors. The deconvolution method is applied to estimate the mean, daily average TOA albedo field for January 1983. A strong and extensive albedo maximum (0.42), which corresponds to the El Nino/Southern Oscillation event of 1982-1983, is detected over the south central Pacific Ocean.

Second-order data obtained by beta-cyclodextrin complexes: a novel approach for multicomponent analysis with three-way multivariate calibration methods.

PubMed

Khani, Rouhollah; Ghasemi, Jahan B; Shemirani, Farzaneh

2014-10-01

This research reports the first application of β-cyclodextrin (β-CD) complexes as a new method for generation of three way data, combined with second-order calibration methods for quantification of a binary mixture of caffeic (CA) and vanillic (VA) acids, as model compounds in fruit juices samples. At first, the basic experimental parameters affecting the formation of inclusion complexes between target analytes and β-CD were investigated and optimized. Then under the optimum conditions, parallel factor analysis (PARAFAC) and bilinear least squares/residual bilinearization (BLLS/RBL) were applied for deconvolution of trilinear data to get spectral and concentration profiles of CA and VA as a function of β-CD concentrations. Due to severe concentration profile overlapping between CA and VA in β-CD concentration dimension, PARAFAC could not be successfully applied to the studied samples. So, BLLS/RBL performed better than PARAFAC. The resolution of the model compounds was possible due to differences in the spectral absorbance changes of the β-CD complexes signals of the investigated analytes, opening a new approach for second-order data generation. The proposed method was validated by comparison with a reference method based on high-performance liquid chromatography photodiode array detection (HPLC-PDA), and no significant differences were found between the reference values and the ones obtained with the proposed method. Such a chemometrics-based protocol may be a very promising tool for more analytical applications in real samples monitoring, due to its advantages of simplicity, rapidity, accuracy, sufficient spectral resolution and concentration prediction even in the presence of unknown interferents. Copyright © 2014 Elsevier B.V. All rights reserved.

Towards robust deconvolution of low-dose perfusion CT: sparse perfusion deconvolution using online dictionary learning.

PubMed

Fang, Ruogu; Chen, Tsuhan; Sanelli, Pina C

2013-05-01

Computed tomography perfusion (CTP) is an important functional imaging modality in the evaluation of cerebrovascular diseases, particularly in acute stroke and vasospasm. However, the post-processed parametric maps of blood flow tend to be noisy, especially in low-dose CTP, due to the noisy contrast enhancement profile and the oscillatory nature of the results generated by the current computational methods. In this paper, we propose a robust sparse perfusion deconvolution method (SPD) to estimate cerebral blood flow in CTP performed at low radiation dose. We first build a dictionary from high-dose perfusion maps using online dictionary learning and then perform deconvolution-based hemodynamic parameters estimation on the low-dose CTP data. Our method is validated on clinical data of patients with normal and pathological CBF maps. The results show that we achieve superior performance than existing methods, and potentially improve the differentiation between normal and ischemic tissue in the brain. Copyright © 2013 Elsevier B.V. All rights reserved.

Towards robust deconvolution of low-dose perfusion CT: Sparse perfusion deconvolution using online dictionary learning

PubMed Central

Fang, Ruogu; Chen, Tsuhan; Sanelli, Pina C.

2014-01-01

Computed tomography perfusion (CTP) is an important functional imaging modality in the evaluation of cerebrovascular diseases, particularly in acute stroke and vasospasm. However, the post-processed parametric maps of blood flow tend to be noisy, especially in low-dose CTP, due to the noisy contrast enhancement profile and the oscillatory nature of the results generated by the current computational methods. In this paper, we propose a robust sparse perfusion deconvolution method (SPD) to estimate cerebral blood flow in CTP performed at low radiation dose. We first build a dictionary from high-dose perfusion maps using online dictionary learning and then perform deconvolution-based hemodynamic parameters estimation on the low-dose CTP data. Our method is validated on clinical data of patients with normal and pathological CBF maps. The results show that we achieve superior performance than existing methods, and potentially improve the differentiation between normal and ischemic tissue in the brain. PMID:23542422

SU-C-9A-03: Simultaneous Deconvolution and Segmentation for PET Tumor Delineation Using a Variational Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, L; Tan, S; Lu, W

2014-06-01

Purpose: To implement a new method that integrates deconvolution with segmentation under the variational framework for PET tumor delineation. Methods: Deconvolution and segmentation are both challenging problems in image processing. The partial volume effect (PVE) makes tumor boundaries in PET image blurred which affects the accuracy of tumor segmentation. Deconvolution aims to obtain a PVE-free image, which can help to improve the segmentation accuracy. Conversely, a correct localization of the object boundaries is helpful to estimate the blur kernel, and thus assist in the deconvolution. In this study, we proposed to solve the two problems simultaneously using a variational methodmore » so that they can benefit each other. The energy functional consists of a fidelity term and a regularization term, and the blur kernel was limited to be the isotropic Gaussian kernel. We minimized the energy functional by solving the associated Euler-Lagrange equations and taking the derivative with respect to the parameters of the kernel function. An alternate minimization method was used to iterate between segmentation, deconvolution and blur-kernel recovery. The performance of the proposed method was tested on clinic PET images of patients with non-Hodgkin's lymphoma, and compared with seven other segmentation methods using the dice similarity index (DSI) and volume error (VE). Results: Among all segmentation methods, the proposed one (DSI=0.81, VE=0.05) has the highest accuracy, followed by the active contours without edges (DSI=0.81, VE=0.25), while other methods including the Graph Cut and the Mumford-Shah (MS) method have lower accuracy. A visual inspection shows that the proposed method localizes the real tumor contour very well. Conclusion: The result showed that deconvolution and segmentation can contribute to each other. The proposed variational method solve the two problems simultaneously, and leads to a high performance for tumor segmentation in PET. This work was supported in part by National Natural Science Foundation of China (NNSFC), under Grant Nos. 60971112 and 61375018, and Fundamental Research Funds for the Central Universities, under Grant No. 2012QN086. Wei Lu was supported in part by the National Institutes of Health (NIH) Grant No. R01 CA172638.« less

Stability indicating methods for the analysis of cefprozil in the presence of its alkaline induced degradation product

NASA Astrophysics Data System (ADS)

Attia, Khalid A. M.; Nassar, Mohammed W. I.; El-Zeiny, Mohamed B.; Serag, Ahmed

2016-04-01

Three simple, specific, accurate and precise spectrophotometric methods were developed for the determination of cefprozil (CZ) in the presence of its alkaline induced degradation product (DCZ). The first method was the bivariate method, while the two other multivariate methods were partial least squares (PLS) and spectral residual augmented classical least squares (SRACLS). The multivariate methods were applied with and without variable selection procedure (genetic algorithm GA). These methods were tested by analyzing laboratory prepared mixtures of the above drug with its alkaline induced degradation product and they were applied to its commercial pharmaceutical products.

Simultaneous spectrophotometric determination of four metals by two kinds of partial least squares methods

NASA Astrophysics Data System (ADS)

Gao, Ling; Ren, Shouxin

2005-10-01

Simultaneous determination of Ni(II), Cd(II), Cu(II) and Zn(II) was studied by two methods, kernel partial least squares (KPLS) and wavelet packet transform partial least squares (WPTPLS), with xylenol orange and cetyltrimethyl ammonium bromide as reagents in the medium pH = 9.22 borax-hydrochloric acid buffer solution. Two programs, PKPLS and PWPTPLS, were designed to perform the calculations. Data reduction was performed using kernel matrices and wavelet packet transform, respectively. In the KPLS method, the size of the kernel matrix is only dependent on the number of samples, thus the method was suitable for the data matrix with many wavelengths and fewer samples. Wavelet packet representations of signals provide a local time-frequency description, thus in the wavelet packet domain, the quality of the noise removal can be improved. In the WPTPLS by optimization, wavelet function and decomposition level were selected as Daubeches 12 and 5, respectively. Experimental results showed both methods to be successful even where there was severe overlap of spectra.

Least square neural network model of the crude oil blending process.

PubMed

Rubio, José de Jesús

2016-06-01

In this paper, the recursive least square algorithm is designed for the big data learning of a feedforward neural network. The proposed method as the combination of the recursive least square and feedforward neural network obtains four advantages over the alone algorithms: it requires less number of regressors, it is fast, it has the learning ability, and it is more compact. Stability, convergence, boundedness of parameters, and local minimum avoidance of the proposed technique are guaranteed. The introduced strategy is applied for the modeling of the crude oil blending process. Copyright © 2016 Elsevier Ltd. All rights reserved.

Using Least Squares to Solve Systems of Equations

ERIC Educational Resources Information Center

Tellinghuisen, Joel

2016-01-01

The method of least squares (LS) yields exact solutions for the adjustable parameters when the number of data values n equals the number of parameters "p". This holds also when the fit model consists of "m" different equations and "m = p", which means that LS algorithms can be used to obtain solutions to systems of…

An on-line modified least-mean-square algorithm for training neurofuzzy controllers.

PubMed

Tan, Woei Wan

2007-04-01

The problem hindering the use of data-driven modelling methods for training controllers on-line is the lack of control over the amount by which the plant is excited. As the operating schedule determines the information available on-line, the knowledge of the process may degrade if the setpoint remains constant for an extended period. This paper proposes an identification algorithm that alleviates "learning interference" by incorporating fuzzy theory into the normalized least-mean-square update rule. The ability of the proposed methodology to achieve faster learning is examined by employing the algorithm to train a neurofuzzy feedforward controller for controlling a liquid level process. Since the proposed identification strategy has similarities with the normalized least-mean-square update rule and the recursive least-square estimator, the on-line learning rates of these algorithms are also compared.

Least-squares finite element method for fluid dynamics

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Povinelli, Louis A.

1989-01-01

An overview is given of new developments of the least squares finite element method (LSFEM) in fluid dynamics. Special emphasis is placed on the universality of LSFEM; the symmetry and positiveness of the algebraic systems obtained from LSFEM; the accommodation of LSFEM to equal order interpolations for incompressible viscous flows; and the natural numerical dissipation of LSFEM for convective transport problems and high speed compressible flows. The performance of LSFEM is illustrated by numerical examples.

Dereplication of Natural Products Using GC-TOF Mass Spectrometry: Improved Metabolite Identification by Spectral Deconvolution Ratio Analysis.

PubMed

Carnevale Neto, Fausto; Pilon, Alan C; Selegato, Denise M; Freire, Rafael T; Gu, Haiwei; Raftery, Daniel; Lopes, Norberto P; Castro-Gamboa, Ian

2016-01-01

Dereplication based on hyphenated techniques has been extensively applied in plant metabolomics, thereby avoiding re-isolation of known natural products. However, due to the complex nature of biological samples and their large concentration range, dereplication requires the use of chemometric tools to comprehensively extract information from the acquired data. In this work we developed a reliable GC-MS-based method for the identification of non-targeted plant metabolites by combining the Ratio Analysis of Mass Spectrometry deconvolution tool (RAMSY) with Automated Mass Spectral Deconvolution and Identification System software (AMDIS). Plants species from Solanaceae, Chrysobalanaceae and Euphorbiaceae were selected as model systems due to their molecular diversity, ethnopharmacological potential, and economical value. The samples were analyzed by GC-MS after methoximation and silylation reactions. Dereplication was initiated with the use of a factorial design of experiments to determine the best AMDIS configuration for each sample, considering linear retention indices and mass spectral data. A heuristic factor (CDF, compound detection factor) was developed and applied to the AMDIS results in order to decrease the false-positive rates. Despite the enhancement in deconvolution and peak identification, the empirical AMDIS method was not able to fully deconvolute all GC-peaks, leading to low MF values and/or missing metabolites. RAMSY was applied as a complementary deconvolution method to AMDIS to peaks exhibiting substantial overlap, resulting in recovery of low-intensity co-eluted ions. The results from this combination of optimized AMDIS with RAMSY attested to the ability of this approach as an improved dereplication method for complex biological samples such as plant extracts.

Dereplication of Natural Products Using GC-TOF Mass Spectrometry: Improved Metabolite Identification by Spectral Deconvolution Ratio Analysis

PubMed Central

Carnevale Neto, Fausto; Pilon, Alan C.; Selegato, Denise M.; Freire, Rafael T.; Gu, Haiwei; Raftery, Daniel; Lopes, Norberto P.; Castro-Gamboa, Ian

2016-01-01

Dereplication based on hyphenated techniques has been extensively applied in plant metabolomics, thereby avoiding re-isolation of known natural products. However, due to the complex nature of biological samples and their large concentration range, dereplication requires the use of chemometric tools to comprehensively extract information from the acquired data. In this work we developed a reliable GC-MS-based method for the identification of non-targeted plant metabolites by combining the Ratio Analysis of Mass Spectrometry deconvolution tool (RAMSY) with Automated Mass Spectral Deconvolution and Identification System software (AMDIS). Plants species from Solanaceae, Chrysobalanaceae and Euphorbiaceae were selected as model systems due to their molecular diversity, ethnopharmacological potential, and economical value. The samples were analyzed by GC-MS after methoximation and silylation reactions. Dereplication was initiated with the use of a factorial design of experiments to determine the best AMDIS configuration for each sample, considering linear retention indices and mass spectral data. A heuristic factor (CDF, compound detection factor) was developed and applied to the AMDIS results in order to decrease the false-positive rates. Despite the enhancement in deconvolution and peak identification, the empirical AMDIS method was not able to fully deconvolute all GC-peaks, leading to low MF values and/or missing metabolites. RAMSY was applied as a complementary deconvolution method to AMDIS to peaks exhibiting substantial overlap, resulting in recovery of low-intensity co-eluted ions. The results from this combination of optimized AMDIS with RAMSY attested to the ability of this approach as an improved dereplication method for complex biological samples such as plant extracts. PMID:27747213

A method of PSF generation for 3D brightfield deconvolution.

PubMed

Tadrous, P J

2010-02-01

This paper addresses the problem of 3D deconvolution of through focus widefield microscope datasets (Z-stacks). One of the most difficult stages in brightfield deconvolution is finding the point spread function. A theoretically calculated point spread function (called a 'synthetic PSF' in this paper) requires foreknowledge of many system parameters and still gives only approximate results. A point spread function measured from a sub-resolution bead suffers from low signal-to-noise ratio, compounded in the brightfield setting (by contrast to fluorescence) by absorptive, refractive and dispersal effects. This paper describes a method of point spread function estimation based on measurements of a Z-stack through a thin sample. This Z-stack is deconvolved by an idealized point spread function derived from the same Z-stack to yield a point spread function of high signal-to-noise ratio that is also inherently tailored to the imaging system. The theory is validated by a practical experiment comparing the non-blind 3D deconvolution of the yeast Saccharomyces cerevisiae with the point spread function generated using the method presented in this paper (called the 'extracted PSF') to a synthetic point spread function. Restoration of both high- and low-contrast brightfield structures is achieved with fewer artefacts using the extracted point spread function obtained with this method. Furthermore the deconvolution progresses further (more iterations are allowed before the error function reaches its nadir) with the extracted point spread function compared to the synthetic point spread function indicating that the extracted point spread function is a better fit to the brightfield deconvolution model than the synthetic point spread function.

Exploring the limits of cryospectroscopy: Least-squares based approaches for analyzing the self-association of HCl

NASA Astrophysics Data System (ADS)

De Beuckeleer, Liene I.; Herrebout, Wouter A.

2016-02-01

To rationalize the concentration dependent behavior observed for a large spectral data set of HCl recorded in liquid argon, least-squares based numerical methods are developed and validated. In these methods, for each wavenumber a polynomial is used to mimic the relation between monomer concentrations and measured absorbances. Least-squares fitting of higher degree polynomials tends to overfit and thus leads to compensation effects where a contribution due to one species is compensated for by a negative contribution of another. The compensation effects are corrected for by carefully analyzing, using AIC and BIC information criteria, the differences observed between consecutive fittings when the degree of the polynomial model is systematically increased, and by introducing constraints prohibiting negative absorbances to occur for the monomer or for one of the oligomers. The method developed should allow other, more complicated self-associating systems to be analyzed with a much higher accuracy than before.

Peelle's pertinent puzzle using the Monte Carlo technique

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kawano, Toshihiko; Talou, Patrick; Burr, Thomas

2009-01-01

We try to understand the long-standing problem of the Peelle's Pertinent Puzzle (PPP) using the Monte Carlo technique. We allow the probability density functions to be any kind of form to assume the impact of distribution, and obtain the least-squares solution directly from numerical simulations. We found that the standard least squares method gives the correct answer if a weighting function is properly provided. Results from numerical simulations show that the correct answer of PPP is 1.1 {+-} 0.25 if the common error is multiplicative. The thought-provoking answer of 0.88 is also correct, if the common error is additive, andmore » if the error is proportional to the measured values. The least squares method correctly gives us the most probable case, where the additive component has a negative value. Finally, the standard method fails for PPP due to a distorted (non Gaussian) joint distribution.« less

A Christoffel function weighted least squares algorithm for collocation approximations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Narayan, Akil; Jakeman, John D.; Zhou, Tao

Here, we propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation framework. Our investigation is motivated by applications in the collocation approximation of parametric functions, which frequently entails construction of surrogates via orthogonal polynomials. A standard Monte Carlo approach would draw samples according to the density defining the orthogonal polynomial family. Our proposed algorithm instead samples with respect to the (weighted) pluripotential equilibrium measure of the domain, and subsequently solves a weighted least-squares problem, with weights given by evaluations of the Christoffel function. We present theoretical analysis tomore » motivate the algorithm, and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest.« less

A Christoffel function weighted least squares algorithm for collocation approximations

DOE PAGES

Narayan, Akil; Jakeman, John D.; Zhou, Tao

2016-11-28

Here, we propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation framework. Our investigation is motivated by applications in the collocation approximation of parametric functions, which frequently entails construction of surrogates via orthogonal polynomials. A standard Monte Carlo approach would draw samples according to the density defining the orthogonal polynomial family. Our proposed algorithm instead samples with respect to the (weighted) pluripotential equilibrium measure of the domain, and subsequently solves a weighted least-squares problem, with weights given by evaluations of the Christoffel function. We present theoretical analysis tomore » motivate the algorithm, and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest.« less

Real-Time Adaptive Least-Squares Drag Minimization for Performance Adaptive Aeroelastic Wing

NASA Technical Reports Server (NTRS)

Ferrier, Yvonne L.; Nguyen, Nhan T.; Ting, Eric

2016-01-01

This paper contains a simulation study of a real-time adaptive least-squares drag minimization algorithm for an aeroelastic model of a flexible wing aircraft. The aircraft model is based on the NASA Generic Transport Model (GTM). The wing structures incorporate a novel aerodynamic control surface known as the Variable Camber Continuous Trailing Edge Flap (VCCTEF). The drag minimization algorithm uses the Newton-Raphson method to find the optimal VCCTEF deflections for minimum drag in the context of an altitude-hold flight control mode at cruise conditions. The aerodynamic coefficient parameters used in this optimization method are identified in real-time using Recursive Least Squares (RLS). The results demonstrate the potential of the VCCTEF to improve aerodynamic efficiency for drag minimization for transport aircraft.

Method for exploiting bias in factor analysis using constrained alternating least squares algorithms

DOEpatents

Keenan, Michael R.

2008-12-30

Bias plays an important role in factor analysis and is often implicitly made use of, for example, to constrain solutions to factors that conform to physical reality. However, when components are collinear, a large range of solutions may exist that satisfy the basic constraints and fit the data equally well. In such cases, the introduction of mathematical bias through the application of constraints may select solutions that are less than optimal. The biased alternating least squares algorithm of the present invention can offset mathematical bias introduced by constraints in the standard alternating least squares analysis to achieve factor solutions that are most consistent with physical reality. In addition, these methods can be used to explicitly exploit bias to provide alternative views and provide additional insights into spectral data sets.

Parallel block schemes for large scale least squares computations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Golub, G.H.; Plemmons, R.J.; Sameh, A.

1986-04-01

Large scale least squares computations arise in a variety of scientific and engineering problems, including geodetic adjustments and surveys, medical image analysis, molecular structures, partial differential equations and substructuring methods in structural engineering. In each of these problems, matrices often arise which possess a block structure which reflects the local connection nature of the underlying physical problem. For example, such super-large nonlinear least squares computations arise in geodesy. Here the coordinates of positions are calculated by iteratively solving overdetermined systems of nonlinear equations by the Gauss-Newton method. The US National Geodetic Survey will complete this year (1986) the readjustment ofmore » the North American Datum, a problem which involves over 540 thousand unknowns and over 6.5 million observations (equations). The observation matrix for these least squares computations has a block angular form with 161 diagnonal blocks, each containing 3 to 4 thousand unknowns. In this paper parallel schemes are suggested for the orthogonal factorization of matrices in block angular form and for the associated backsubstitution phase of the least squares computations. In addition, a parallel scheme for the calculation of certain elements of the covariance matrix for such problems is described. It is shown that these algorithms are ideally suited for multiprocessors with three levels of parallelism such as the Cedar system at the University of Illinois. 20 refs., 7 figs.« less

Improved methods to estimate the effective impervious area in urban catchments using rainfall-runoff data

NASA Astrophysics Data System (ADS)

Ebrahimian, Ali; Wilson, Bruce N.; Gulliver, John S.

2016-05-01

Impervious surfaces are useful indicators of the urbanization impacts on water resources. Effective impervious area (EIA), which is the portion of total impervious area (TIA) that is hydraulically connected to the drainage system, is a better catchment parameter in the determination of actual urban runoff. Development of reliable methods for quantifying EIA rather than TIA is currently one of the knowledge gaps in the rainfall-runoff modeling context. The objective of this study is to improve the rainfall-runoff data analysis method for estimating EIA fraction in urban catchments by eliminating the subjective part of the existing method and by reducing the uncertainty of EIA estimates. First, the theoretical framework is generalized using a general linear least square model and using a general criterion for categorizing runoff events. Issues with the existing method that reduce the precision of the EIA fraction estimates are then identified and discussed. Two improved methods, based on ordinary least square (OLS) and weighted least square (WLS) estimates, are proposed to address these issues. The proposed weighted least squares method is then applied to eleven urban catchments in Europe, Canada, and Australia. The results are compared to map measured directly connected impervious area (DCIA) and are shown to be consistent with DCIA values. In addition, both of the improved methods are applied to nine urban catchments in Minnesota, USA. Both methods were successful in removing the subjective component inherent in the analysis of rainfall-runoff data of the current method. The WLS method is more robust than the OLS method and generates results that are different and more precise than the OLS method in the presence of heteroscedastic residuals in our rainfall-runoff data.

A Comprehensive Study of Gridding Methods for GPS Horizontal Velocity Fields

NASA Astrophysics Data System (ADS)

Wu, Yanqiang; Jiang, Zaisen; Liu, Xiaoxia; Wei, Wenxin; Zhu, Shuang; Zhang, Long; Zou, Zhenyu; Xiong, Xiaohui; Wang, Qixin; Du, Jiliang

2017-03-01

Four gridding methods for GPS velocities are compared in terms of their precision, applicability and robustness by analyzing simulated data with uncertainties from 0.0 to ±3.0 mm/a. When the input data are 1° × 1° grid sampled and the uncertainty of the additional error is greater than ±1.0 mm/a, the gridding results show that the least-squares collocation method is highly robust while the robustness of the Kriging method is low. In contrast, the spherical harmonics and the multi-surface function are moderately robust, and the regional singular values for the multi-surface function method and the edge effects for the spherical harmonics method become more significant with increasing uncertainty of the input data. When the input data (with additional errors of ±2.0 mm/a) are decimated by 50% from the 1° × 1° grid data and then erased in three 6° × 12° regions, the gridding results in these three regions indicate that the least-squares collocation and the spherical harmonics methods have good performances, while the multi-surface function and the Kriging methods may lead to singular values. The gridding techniques are also applied to GPS horizontal velocities with an average error of ±0.8 mm/a over the Chinese mainland and the surrounding areas, and the results show that the least-squares collocation method has the best performance, followed by the Kriging and multi-surface function methods. Furthermore, the edge effects of the spherical harmonics method are significantly affected by the sparseness and geometric distribution of the input data. In general, the least-squares collocation method is superior in terms of its robustness, edge effect, error distribution and stability, while the other methods have several positive features.

Image restoration approach to address reduced modulation contrast in structured illumination microscopy

PubMed Central

Patwary, Nurmohammed; Doblas, Ana; Preza, Chrysanthe

2018-01-01

The performance of structured illumination microscopy (SIM) is hampered in many biological applications due to the inability to modulate the light when imaging deep into the sample. This is in part because sample-induced aberration reduces the modulation contrast of the structured pattern. In this paper, we present an image restoration approach suitable for processing raw incoherent-grid-projection SIM data with a low fringe contrast. Restoration results from simulated and experimental ApoTome SIM data show results with improved signal-to-noise ratio (SNR) and optical sectioning compared to the results obtained from existing methods, such as 2D demodulation and 3D SIM deconvolution. Our proposed method provides satisfactory results (quantified by the achieved SNR and normalized mean square error) even when the modulation contrast of the illumination pattern is as low as 7%. PMID:29675307

QCL spectroscopy combined with the least squares method for substance analysis

NASA Astrophysics Data System (ADS)

Samsonov, D. A.; Tabalina, A. S.; Fufurin, I. L.

2017-11-01

The article briefly describes distinctive features of quantum cascade lasers (QCL). It also describes an experimental set-up for acquiring mid-infrared absorption spectra using QCL. The paper demonstrates experimental results in the form of normed spectra. We tested the application of the least squares method for spectrum analysis. We used this method for substance identification and extraction of concentration data. We compare the results with more common methods of absorption spectroscopy. Eventually, we prove the feasibility of using this simple method for quantitative and qualitative analysis of experimental data acquired with QCL.

SU-G-IeP3-08: Image Reconstruction for Scanning Imaging System Based On Shape-Modulated Point Spreading Function

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Ruixing; Yang, LV; Xu, Kele

Purpose: Deconvolution is a widely used tool in the field of image reconstruction algorithm when the linear imaging system has been blurred by the imperfect system transfer function. However, due to the nature of Gaussian-liked distribution for point spread function (PSF), the components with coherent high frequency in the image are hard to restored in most of the previous scanning imaging system, even the relatively accurate PSF is acquired. We propose a novel method for deconvolution of images which are obtained by using shape-modulated PSF. Methods: We use two different types of PSF - Gaussian shape and donut shape -more » to convolute the original image in order to simulate the process of scanning imaging. By employing deconvolution of the two images with corresponding given priors, the image quality of the deblurred images are compared. Then we find the critical size of the donut shape compared with the Gaussian shape which has similar deconvolution results. Through calculation of tightened focusing process using radially polarized beam, such size of donut is achievable under same conditions. Results: The effects of different relative size of donut and Gaussian shapes are investigated. When the full width at half maximum (FWHM) ratio of donut and Gaussian shape is set about 1.83, similar resolution results are obtained through our deconvolution method. Decreasing the size of donut will favor the deconvolution method. A mask with both amplitude and phase modulation is used to create a donut-shaped PSF compared with the non-modulated Gaussian PSF. Donut with size smaller than our critical value is obtained. Conclusion: The utility of donutshaped PSF are proved useful and achievable in the imaging and deconvolution processing, which is expected to have potential practical applications in high resolution imaging for biological samples.« less

Quality assessment of gasoline using comprehensive two-dimensional gas chromatography combined with unfolded partial least squares: A reliable approach for the detection of gasoline adulteration.

PubMed

Parastar, Hadi; Mostafapour, Sara; Azimi, Gholamhasan

2016-01-01

Comprehensive two-dimensional gas chromatography and flame ionization detection combined with unfolded-partial least squares is proposed as a simple, fast and reliable method to assess the quality of gasoline and to detect its potential adulterants. The data for the calibration set are first baseline corrected using a two-dimensional asymmetric least squares algorithm. The number of significant partial least squares components to build the model is determined using the minimum value of root-mean square error of leave-one out cross validation, which was 4. In this regard, blends of gasoline with kerosene, white spirit and paint thinner as frequently used adulterants are used to make calibration samples. Appropriate statistical parameters of regression coefficient of 0.996-0.998, root-mean square error of prediction of 0.005-0.010 and relative error of prediction of 1.54-3.82% for the calibration set show the reliability of the developed method. In addition, the developed method is externally validated with three samples in validation set (with a relative error of prediction below 10.0%). Finally, to test the applicability of the proposed strategy for the analysis of real samples, five real gasoline samples collected from gas stations are used for this purpose and the gasoline proportions were in range of 70-85%. Also, the relative standard deviations were below 8.5% for different samples in the prediction set. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Dense deconvolution net: Multi path fusion and dense deconvolution for high resolution skin lesion segmentation.

PubMed

He, Xinzi; Yu, Zhen; Wang, Tianfu; Lei, Baiying; Shi, Yiyan

2018-01-01

Dermoscopy imaging has been a routine examination approach for skin lesion diagnosis. Accurate segmentation is the first step for automatic dermoscopy image assessment. The main challenges for skin lesion segmentation are numerous variations in viewpoint and scale of skin lesion region. To handle these challenges, we propose a novel skin lesion segmentation network via a very deep dense deconvolution network based on dermoscopic images. Specifically, the deep dense layer and generic multi-path Deep RefineNet are combined to improve the segmentation performance. The deep representation of all available layers is aggregated to form the global feature maps using skip connection. Also, the dense deconvolution layer is leveraged to capture diverse appearance features via the contextual information. Finally, we apply the dense deconvolution layer to smooth segmentation maps and obtain final high-resolution output. Our proposed method shows the superiority over the state-of-the-art approaches based on the public available 2016 and 2017 skin lesion challenge dataset and achieves the accuracy of 96.0% and 93.9%, which obtained a 6.0% and 1.2% increase over the traditional method, respectively. By utilizing Dense Deconvolution Net, the average time for processing one testing images with our proposed framework was 0.253 s.

Multivariate fault isolation of batch processes via variable selection in partial least squares discriminant analysis.

PubMed

Yan, Zhengbing; Kuang, Te-Hui; Yao, Yuan

2017-09-01

In recent years, multivariate statistical monitoring of batch processes has become a popular research topic, wherein multivariate fault isolation is an important step aiming at the identification of the faulty variables contributing most to the detected process abnormality. Although contribution plots have been commonly used in statistical fault isolation, such methods suffer from the smearing effect between correlated variables. In particular, in batch process monitoring, the high autocorrelations and cross-correlations that exist in variable trajectories make the smearing effect unavoidable. To address such a problem, a variable selection-based fault isolation method is proposed in this research, which transforms the fault isolation problem into a variable selection problem in partial least squares discriminant analysis and solves it by calculating a sparse partial least squares model. As different from the traditional methods, the proposed method emphasizes the relative importance of each process variable. Such information may help process engineers in conducting root-cause diagnosis. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Estimation of suspended-sediment rating curves and mean suspended-sediment loads

USGS Publications Warehouse

Crawford, Charles G.

1991-01-01

A simulation study was done to evaluate: (1) the accuracy and precision of parameter estimates for the bias-corrected, transformed-linear and non-linear models obtained by the method of least squares; (2) the accuracy of mean suspended-sediment loads calculated by the flow-duration, rating-curve method using model parameters obtained by the alternative methods. Parameter estimates obtained by least squares for the bias-corrected, transformed-linear model were considerably more precise than those obtained for the non-linear or weighted non-linear model. The accuracy of parameter estimates obtained for the biascorrected, transformed-linear and weighted non-linear model was similar and was much greater than the accuracy obtained by non-linear least squares. The improved parameter estimates obtained by the biascorrected, transformed-linear or weighted non-linear model yield estimates of mean suspended-sediment load calculated by the flow-duration, rating-curve method that are more accurate and precise than those obtained for the non-linear model.

The MiMeS survey of Magnetism in Massive Stars: magnetic analysis of the O-type stars

NASA Astrophysics Data System (ADS)

Grunhut, J. H.; Wade, G. A.; Neiner, C.; Oksala, M. E.; Petit, V.; Alecian, E.; Bohlender, D. A.; Bouret, J.-C.; Henrichs, H. F.; Hussain, G. A. J.; Kochukhov, O.; MiMeS Collaboration

2017-02-01

We present the analysis performed on spectropolarimetric data of 97 O-type targets included in the framework of the Magnetism in Massive Stars (MiMeS) Survey. Mean least-squares deconvolved Stokes I and V line profiles were extracted for each observation, from which we measured the radial velocity, rotational and non-rotational broadening velocities, and longitudinal magnetic field Bℓ. The investigation of the Stokes I profiles led to the discovery of two new multiline spectroscopic systems (HD 46106, HD 204827) and confirmed the presence of a suspected companion in HD 37041. We present a modified strategy of the least-squares deconvolution technique aimed at optimizing the detection of magnetic signatures while minimizing the detection of spurious signatures in Stokes V. Using this analysis, we confirm the detection of a magnetic field in six targets previously reported as magnetic by the MiMeS collaboration (HD 108, HD 47129A2, HD 57682, HD 148937, CPD-28 2561, and NGC 1624-2), as well as report the presence of signal in Stokes V in three new magnetic candidates (HD 36486, HD 162978, and HD 199579). Overall, we find a magnetic incidence rate of 7 ± 3 per cent, for 108 individual O stars (including all O-type components part of multiline systems), with a median uncertainty of the Bℓ measurements of about 50 G. An inspection of the data reveals no obvious biases affecting the incidence rate or the preference for detecting magnetic signatures in the magnetic stars. Similar to A- and B-type stars, we find no link between the stars' physical properties (e.g. Teff, mass, and age) and the presence of a magnetic field. However, the Of?p stars represent a distinct class of magnetic O-type stars.

Spectrophotometric determination of ternary mixtures of thiamin, riboflavin and pyridoxal in pharmaceutical and human plasma by least-squares support vector machines.

PubMed

Niazi, Ali; Zolgharnein, Javad; Afiuni-Zadeh, Somaie

2007-11-01

Ternary mixtures of thiamin, riboflavin and pyridoxal have been simultaneously determined in synthetic and real samples by applications of spectrophotometric and least-squares support vector machines. The calibration graphs were linear in the ranges of 1.0 - 20.0, 1.0 - 10.0 and 1.0 - 20.0 microg ml(-1) with detection limits of 0.6, 0.5 and 0.7 microg ml(-1) for thiamin, riboflavin and pyridoxal, respectively. The experimental calibration matrix was designed with 21 mixtures of these chemicals. The concentrations were varied between calibration graph concentrations of vitamins. The simultaneous determination of these vitamin mixtures by using spectrophotometric methods is a difficult problem, due to spectral interferences. The partial least squares (PLS) modeling and least-squares support vector machines were used for the multivariate calibration of the spectrophotometric data. An excellent model was built using LS-SVM, with low prediction errors and superior performance in relation to PLS. The root mean square errors of prediction (RMSEP) for thiamin, riboflavin and pyridoxal with PLS and LS-SVM were 0.6926, 0.3755, 0.4322 and 0.0421, 0.0318, 0.0457, respectively. The proposed method was satisfactorily applied to the rapid simultaneous determination of thiamin, riboflavin and pyridoxal in commercial pharmaceutical preparations and human plasma samples.

Intrinsic fluorescence spectroscopy of glutamate dehydrogenase: Integrated behavior and deconvolution analysis

NASA Astrophysics Data System (ADS)

Pompa, P. P.; Cingolani, R.; Rinaldi, R.

2003-07-01

In this paper, we present a deconvolution method aimed at spectrally resolving the broad fluorescence spectra of proteins, namely, of the enzyme bovine liver glutamate dehydrogenase (GDH). The analytical procedure is based on the deconvolution of the emission spectra into three distinct Gaussian fluorescing bands Gj. The relative changes of the Gj parameters are directly related to the conformational changes of the enzyme, and provide interesting information about the fluorescence dynamics of the individual emitting contributions. Our deconvolution method results in an excellent fitting of all the spectra obtained with GDH in a number of experimental conditions (various conformational states of the protein) and describes very well the dynamics of a variety of phenomena, such as the dependence of hexamers association on protein concentration, the dynamics of thermal denaturation, and the interaction process between the enzyme and external quenchers. The investigation was carried out by means of different optical experiments, i.e., native enzyme fluorescence, thermal-induced unfolding, and fluorescence quenching studies, utilizing both the analysis of the “average” behavior of the enzyme and the proposed deconvolution approach.

Method of Characteristics Calculations and Computer Code for Materials with Arbitrary Equations of State and Using Orthogonal Polynomial Least Square Surface Fits

NASA Technical Reports Server (NTRS)

Chang, T. S.

1974-01-01

A numerical scheme using the method of characteristics to calculate the flow properties and pressures behind decaying shock waves for materials under hypervelocity impact is developed. Time-consuming double interpolation subroutines are replaced by a technique based on orthogonal polynomial least square surface fits. Typical calculated results are given and compared with the double interpolation results. The complete computer program is included.

A new least-squares transport equation compatible with voids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hansen, J. B.; Morel, J. E.

2013-07-01

We define a new least-squares transport equation that is applicable in voids, can be solved using source iteration with diffusion-synthetic acceleration, and requires only the solution of an independent set of second-order self-adjoint equations for each direction during each source iteration. We derive the equation, discretize it using the S{sub n} method in conjunction with a linear-continuous finite-element method in space, and computationally demonstrate various of its properties. (authors)

Vehicle Sprung Mass Estimation for Rough Terrain

DTIC Science & Technology

2011-03-01

distributions are greater than zero. The multivariate polynomials are functions of the Legendre polynomials (Poularikas (1999...developed methods based on polynomial chaos theory and on the maximum likelihood approach to estimate the most likely value of the vehicle sprung...mass. The polynomial chaos estimator is compared to benchmark algorithms including recursive least squares, recursive total least squares, extended

Foundations for estimation by the method of least squares

NASA Technical Reports Server (NTRS)

Hauck, W. W., Jr.

1971-01-01

Least squares estimation is discussed from the point of view of a statistician. Much of the emphasis is on problems encountered in application and, more specifically, on questions involving assumptions: what assumptions are needed, when are they needed, what happens if they are not valid, and if they are invalid, how that fact can be detected.

An Extension of Least Squares Estimation of IRT Linking Coefficients for the Graded Response Model

ERIC Educational Resources Information Center

Kim, Seonghoon

2010-01-01

The three types (generalized, unweighted, and weighted) of least squares methods, proposed by Ogasawara, for estimating item response theory (IRT) linking coefficients under dichotomous models are extended to the graded response model. A simulation study was conducted to confirm the accuracy of the extended formulas, and a real data study was…

Optimal Least-Squares Unidimensional Scaling: Improved Branch-and-Bound Procedures and Comparison to Dynamic Programming

ERIC Educational Resources Information Center

Brusco, Michael J.; Stahl, Stephanie

2005-01-01

There are two well-known methods for obtaining a guaranteed globally optimal solution to the problem of least-squares unidimensional scaling of a symmetric dissimilarity matrix: (a) dynamic programming, and (b) branch-and-bound. Dynamic programming is generally more efficient than branch-and-bound, but the former is limited to matrices with…

Fast and accurate fitting and filtering of noisy exponentials in Legendre space.

PubMed

Bao, Guobin; Schild, Detlev

2014-01-01

The parameters of experimentally obtained exponentials are usually found by least-squares fitting methods. Essentially, this is done by minimizing the mean squares sum of the differences between the data, most often a function of time, and a parameter-defined model function. Here we delineate a novel method where the noisy data are represented and analyzed in the space of Legendre polynomials. This is advantageous in several respects. First, parameter retrieval in the Legendre domain is typically two orders of magnitude faster than direct fitting in the time domain. Second, data fitting in a low-dimensional Legendre space yields estimates for amplitudes and time constants which are, on the average, more precise compared to least-squares-fitting with equal weights in the time domain. Third, the Legendre analysis of two exponentials gives satisfactory estimates in parameter ranges where least-squares-fitting in the time domain typically fails. Finally, filtering exponentials in the domain of Legendre polynomials leads to marked noise removal without the phase shift characteristic for conventional lowpass filters.

An improved partial least-squares regression method for Raman spectroscopy

NASA Astrophysics Data System (ADS)

Momenpour Tehran Monfared, Ali; Anis, Hanan

2017-10-01

It is known that the performance of partial least-squares (PLS) regression analysis can be improved using the backward variable selection method (BVSPLS). In this paper, we further improve the BVSPLS based on a novel selection mechanism. The proposed method is based on sorting the weighted regression coefficients, and then the importance of each variable of the sorted list is evaluated using root mean square errors of prediction (RMSEP) criterion in each iteration step. Our Improved BVSPLS (IBVSPLS) method has been applied to leukemia and heparin data sets and led to an improvement in limit of detection of Raman biosensing ranged from 10% to 43% compared to PLS. Our IBVSPLS was also compared to the jack-knifing (simpler) and Genetic Algorithm (more complex) methods. Our method was consistently better than the jack-knifing method and showed either a similar or a better performance compared to the genetic algorithm.

Least squares reverse time migration of controlled order multiples

NASA Astrophysics Data System (ADS)

Liu, Y.

2016-12-01

Imaging using the reverse time migration of multiples generates inherent crosstalk artifacts due to the interference among different order multiples. Traditionally, least-square fitting has been used to address this issue by seeking the best objective function to measure the amplitude differences between the predicted and observed data. We have developed an alternative objective function by decomposing multiples into different orders to minimize the difference between Born modeling predicted multiples and specific-order multiples from observational data in order to attenuate the crosstalk. This method is denoted as the least-squares reverse time migration of controlled order multiples (LSRTM-CM). Our numerical examples demonstrated that the LSRTM-CM can significantly improve image quality compared with reverse time migration of multiples and least-square reverse time migration of multiples. Acknowledgments This research was funded by the National Nature Science Foundation of China (Grant Nos. 41430321 and 41374138).

High quality image-pair-based deblurring method using edge mask and improved residual deconvolution

NASA Astrophysics Data System (ADS)

Cui, Guangmang; Zhao, Jufeng; Gao, Xiumin; Feng, Huajun; Chen, Yueting

2017-04-01

Image deconvolution problem is a challenging task in the field of image process. Using image pairs could be helpful to provide a better restored image compared with the deblurring method from a single blurred image. In this paper, a high quality image-pair-based deblurring method is presented using the improved RL algorithm and the gain-controlled residual deconvolution technique. The input image pair includes a non-blurred noisy image and a blurred image captured for the same scene. With the estimated blur kernel, an improved RL deblurring method based on edge mask is introduced to obtain the preliminary deblurring result with effective ringing suppression and detail preservation. Then the preliminary deblurring result is served as the basic latent image and the gain-controlled residual deconvolution is utilized to recover the residual image. A saliency weight map is computed as the gain map to further control the ringing effects around the edge areas in the residual deconvolution process. The final deblurring result is obtained by adding the preliminary deblurring result with the recovered residual image. An optical experimental vibration platform is set up to verify the applicability and performance of the proposed algorithm. Experimental results demonstrate that the proposed deblurring framework obtains a superior performance in both subjective and objective assessments and has a wide application in many image deblurring fields.

Nonnegative least-squares image deblurring: improved gradient projection approaches

NASA Astrophysics Data System (ADS)

Benvenuto, F.; Zanella, R.; Zanni, L.; Bertero, M.

2010-02-01

The least-squares approach to image deblurring leads to an ill-posed problem. The addition of the nonnegativity constraint, when appropriate, does not provide regularization, even if, as far as we know, a thorough investigation of the ill-posedness of the resulting constrained least-squares problem has still to be done. Iterative methods, converging to nonnegative least-squares solutions, have been proposed. Some of them have the 'semi-convergence' property, i.e. early stopping of the iteration provides 'regularized' solutions. In this paper we consider two of these methods: the projected Landweber (PL) method and the iterative image space reconstruction algorithm (ISRA). Even if they work well in many instances, they are not frequently used in practice because, in general, they require a large number of iterations before providing a sensible solution. Therefore, the main purpose of this paper is to refresh these methods by increasing their efficiency. Starting from the remark that PL and ISRA require only the computation of the gradient of the functional, we propose the application to these algorithms of special acceleration techniques that have been recently developed in the area of the gradient methods. In particular, we propose the application of efficient step-length selection rules and line-search strategies. Moreover, remarking that ISRA is a scaled gradient algorithm, we evaluate its behaviour in comparison with a recent scaled gradient projection (SGP) method for image deblurring. Numerical experiments demonstrate that the accelerated methods still exhibit the semi-convergence property, with a considerable gain both in the number of iterations and in the computational time; in particular, SGP appears definitely the most efficient one.

First discovery of a magnetic field in a main-sequence δ Scuti star: the Kepler star HD 188774

NASA Astrophysics Data System (ADS)

Neiner, C.; Lampens, P.

2015-11-01

The Kepler space mission provided a wealth of δ Sct-γ Dor hybrid candidates. While some may be genuine hybrids, others might be misclassified due to the presence of a binary companion or to rotational modulation caused by magnetism and related surface inhomogeneities. In particular, the Kepler δ Sct-γ Dor hybrid candidate HD 188774 shows a few low frequencies in its light and radial velocity curves, whose origin is unclear. In this work, we check for the presence of a magnetic field in HD 188774. We obtained two spectropolarimetric measurements with an Echelle SpectroPolarimetric Device for the Observation of Stars (ESPaDOnS) at Canada-France-Hawaii Telescope. The data were analysed with the least-squares deconvolution (LSD) method. We detected a clear magnetic signature in the Stokes V LSD profiles. The origin of the low frequencies detected in HD 188774 is therefore most probably the rotational modulation of surface spots possibly related to the presence of a magnetic field. Consequently, HD 188774 is not a genuine hybrid δ Sct-γ Dor star, but the first known magnetic main-sequence δ Sct star. This makes it a prime target for future asteroseismic and spot modelling. This result casts new light on the interpretation of the Kepler results for other δ Sct-γ Dor hybrid candidates.

Reply to Comment: 'A novel method for fast and robust estimation of fluorescence decay dynamics using constrained least-square deconvolution with Laguerre expansion'.

PubMed

Ma, Dinglong; Liu, Jing; Qi, Jinyi; Marcu, Laura

2017-02-21

In this response we underscore that the instrumentation described in the original publication (Liu et al 2012 Phys. Med. Biol. 57 843-65) was based on pulse-sampling technique, while the comment by Zhang et al is based on the assumption that a time-correlated single photon counting (TCSPC) instrumentation was used. Therefore the arguments made in the comment are not applicable to the noise model reported by Liu et al. As reported in the literature (Lakowicz 2006 Principles of Fluorescence Spectroscopy (New York: Springer)), while in the TCSPC the experimental noise can be estimated from Poisson statistics, such an assumption is not valid for pulse-sampling (transient recording) techniques. To further clarify this aspect, we present here a comprehensive noise model describing the signal and noise propagation of the pulse sampling time-resolved fluorescence detection. Experimental data recorded in various conditions are analyzed as a case study to demonstrate the noise model of our instrumental system. In addition, regarding the statement of correcting equation (3) in Liu et al (2012 Phys. Med. Biol. 57 843-65), the notation of discrete time Laguerre function in the original publication was clear and consistent with literature conventions (Marmarelis 1993 Ann. Biomed. Eng. 21 573-89, Westwick and Kearney 2003 Identification of Nonlinear Physiological Systems (Hoboken, NJ: Wiley)). Thus, it does not require revision.

Reply to Comment: ‘A novel method for fast and robust estimation of fluorescence decay dynamics using constrained least-square deconvolution with Laguerre expansion’

NASA Astrophysics Data System (ADS)

Ma, Dinglong; Liu, Jing; Qi, Jinyi; Marcu, Laura

2017-02-01

In this response we underscore that the instrumentation described in the original publication (Liu et al 2012 Phys. Med. Biol. 57 843-65) was based on pulse-sampling technique, while the comment by Zhang et al is based on the assumption that a time-correlated single photon counting (TCSPC) instrumentation was used. Therefore the arguments made in the comment are not applicable to the noise model reported by Liu et al. As reported in the literature (Lakowicz 2006 Principles of Fluorescence Spectroscopy (New York: Springer)), while in the TCSPC the experimental noise can be estimated from Poisson statistics, such an assumption is not valid for pulse-sampling (transient recording) techniques. To further clarify this aspect, we present here a comprehensive noise model describing the signal and noise propagation of the pulse sampling time-resolved fluorescence detection. Experimental data recorded in various conditions are analyzed as a case study to demonstrate the noise model of our instrumental system. In addition, regarding the statement of correcting equation (3) in Liu et al (2012 Phys. Med. Biol. 57 843-65), the notation of discrete time Laguerre function in the original publication was clear and consistent with literature conventions (Marmarelis 1993 Ann. Biomed. Eng. 21 573-89, Westwick and Kearney 2003 Identification of Nonlinear Physiological Systems (Hoboken, NJ: Wiley)). Thus, it does not require revision.

Deconvolution of continuous paleomagnetic data from pass-through magnetometer: A new algorithm to restore geomagnetic and environmental information based on realistic optimization

NASA Astrophysics Data System (ADS)

Oda, Hirokuni; Xuan, Chuang

2014-10-01

development of pass-through superconducting rock magnetometers (SRM) has greatly promoted collection of paleomagnetic data from continuous long-core samples. The output of pass-through measurement is smoothed and distorted due to convolution of magnetization with the magnetometer sensor response. Although several studies could restore high-resolution paleomagnetic signal through deconvolution of pass-through measurement, difficulties in accurately measuring the magnetometer sensor response have hindered the application of deconvolution. We acquired reliable sensor response of an SRM at the Oregon State University based on repeated measurements of a precisely fabricated magnetic point source. In addition, we present an improved deconvolution algorithm based on Akaike's Bayesian Information Criterion (ABIC) minimization, incorporating new parameters to account for errors in sample measurement position and length. The new algorithm was tested using synthetic data constructed by convolving "true" paleomagnetic signal containing an "excursion" with the sensor response. Realistic noise was added to the synthetic measurement using Monte Carlo method based on measurement noise distribution acquired from 200 repeated measurements of a u-channel sample. Deconvolution of 1000 synthetic measurements with realistic noise closely resembles the "true" magnetization, and successfully restored fine-scale magnetization variations including the "excursion." Our analyses show that inaccuracy in sample measurement position and length significantly affects deconvolution estimation, and can be resolved using the new deconvolution algorithm. Optimized deconvolution of 20 repeated measurements of a u-channel sample yielded highly consistent deconvolution results and estimates of error in sample measurement position and length, demonstrating the reliability of the new deconvolution algorithm for real pass-through measurements.

UDECON: deconvolution optimization software for restoring high-resolution records from pass-through paleomagnetic measurements

NASA Astrophysics Data System (ADS)

Xuan, Chuang; Oda, Hirokuni

2015-11-01

The rapid accumulation of continuous paleomagnetic and rock magnetic records acquired from pass-through measurements on superconducting rock magnetometers (SRM) has greatly contributed to our understanding of the paleomagnetic field and paleo-environment. Pass-through measurements are inevitably smoothed and altered by the convolution effect of SRM sensor response, and deconvolution is needed to restore high-resolution paleomagnetic and environmental signals. Although various deconvolution algorithms have been developed, the lack of easy-to-use software has hindered the practical application of deconvolution. Here, we present standalone graphical software UDECON as a convenient tool to perform optimized deconvolution for pass-through paleomagnetic measurements using the algorithm recently developed by Oda and Xuan (Geochem Geophys Geosyst 15:3907-3924, 2014). With the preparation of a format file, UDECON can directly read pass-through paleomagnetic measurement files collected at different laboratories. After the SRM sensor response is determined and loaded to the software, optimized deconvolution can be conducted using two different approaches (i.e., "Grid search" and "Simplex method") with adjustable initial values or ranges for smoothness, corrections of sample length, and shifts in measurement position. UDECON provides a suite of tools to view conveniently and check various types of original measurement and deconvolution data. Multiple steps of measurement and/or deconvolution data can be compared simultaneously to check the consistency and to guide further deconvolution optimization. Deconvolved data together with the loaded original measurement and SRM sensor response data can be saved and reloaded for further treatment in UDECON. Users can also export the optimized deconvolution data to a text file for analysis in other software.

Evaluation of multivariate calibration models with different pre-processing and processing algorithms for a novel resolution and quantitation of spectrally overlapped quaternary mixture in syrup

NASA Astrophysics Data System (ADS)

Moustafa, Azza A.; Hegazy, Maha A.; Mohamed, Dalia; Ali, Omnia

2016-02-01

A novel approach for the resolution and quantitation of severely overlapped quaternary mixture of carbinoxamine maleate (CAR), pholcodine (PHL), ephedrine hydrochloride (EPH) and sunset yellow (SUN) in syrup was demonstrated utilizing different spectrophotometric assisted multivariate calibration methods. The applied methods have used different processing and pre-processing algorithms. The proposed methods were partial least squares (PLS), concentration residuals augmented classical least squares (CRACLS), and a novel method; continuous wavelet transforms coupled with partial least squares (CWT-PLS). These methods were applied to a training set in the concentration ranges of 40-100 μg/mL, 40-160 μg/mL, 100-500 μg/mL and 8-24 μg/mL for the four components, respectively. The utilized methods have not required any preliminary separation step or chemical pretreatment. The validity of the methods was evaluated by an external validation set. The selectivity of the developed methods was demonstrated by analyzing the drugs in their combined pharmaceutical formulation without any interference from additives. The obtained results were statistically compared with the official and reported methods where no significant difference was observed regarding both accuracy and precision.

Insights into aquifer vulnerability and potential recharge zones from the borehole response to barometric pressure changes

NASA Astrophysics Data System (ADS)

El Araby, Mahmoud; Odling, Noelle; Clark, Roger; West, Jared

2010-05-01

Borehole water levels fluctuate in response to deformation of the surrounding aquifer caused by surface loading due to barometric pressure or strain caused by Earth and ocean tides. The magnitude and nature of this response mainly depend on the hydraulic properties of the aquifer and overlying units and borehole design. Thus water level responses reflect the effectiveness of a confining unit as a protective layer against aquifer contamination (and therefore groundwater vulnerability) and to potential aquifer recharge/discharge zones. In this study, time series of borehole water levels and barometric pressure are being investigated using time series analysis and signal processing techniques with the aim of developing a methodology for assessing recharge/discharge distribution and groundwater vulnerability in the confined/semi-confined part of the Chalk aquifer in East Yorkshire, UK. The chalk aquifer in East Yorkshire is an important source for industrial and domestic water supply. The aquifer water quality is threatened by surface pollution particularly by nitrates from agricultural fertilizers. The confined/semi-confined part of this aquifer is covered by various types of superficial deposits resulting in a wide range of the aquifer's degree of confinement. A number of boreholes have been selected for monitoring to cover all these various types of confining units. Automatic pressure transducers are installed to record water levels and barometric pressure measurements at each borehole on 15 minutes recording intervals. In strictly confined aquifers, borehole water level response to barometric pressure is an un-drained instantaneous response and is a constant fraction of the barometric pressure changes. This static confined constant is called the barometric efficiency which can be estimated simply by the slope of a regression plot of water levels versus barometric pressure. However, in the semi confined aquifer case this response is lagged due to water movement between the aquifer and the confining layer. In this case the static constant barometric efficiency is not applicable and the response is represented by a barometric response function which reflects the timing and frequency of the barometric pressure loading. In this study, the barometric response function is estimated using de-convolution techniques both in the time domain (least squares regression de-convolution) and in the frequency domain (discrete Fourier transform de-convolution). In order to estimate the barometric response function, borehole water level fluctuations due to factors other than barometric pressure should be removed (de-trended) as otherwise they will mask the response relation of interest. It is shown from the collected borehole data records that the main four factors other than barometric pressure contribute to borehole water level fluctuations. These are the rainfall recharge, Earth tides, sea tides and pumping activities close to the borehole location. Due to the highly variable nature of the UK weather, rainfall recharge shows a wide variation throughout the winter and summer seasons. This gives a complicated recharge signal over a wide range of frequencies which must be de-trended from the borehole water level data in order to estimate the barometric response function. Methods for removing this recharge signal are developed and discussed. Earth tides are calculated theoretically at each borehole location taking into account oceanic loading effects. Ocean tide effects on water levels fluctuations are clear for the boreholes located close to the coast. A Matlab code has been designed to calculate and de-trend the periodic fluctuations in borehole water levels due to Earth and ocean tides using the least squares regression technique based on a sum of sine and cosine fitting model functions. The program results have been confirmed using spectral analysis techniques.

Quantized kernel least mean square algorithm.

PubMed

Chen, Badong; Zhao, Songlin; Zhu, Pingping; Príncipe, José C

2012-01-01

In this paper, we propose a quantization approach, as an alternative of sparsification, to curb the growth of the radial basis function structure in kernel adaptive filtering. The basic idea behind this method is to quantize and hence compress the input (or feature) space. Different from sparsification, the new approach uses the "redundant" data to update the coefficient of the closest center. In particular, a quantized kernel least mean square (QKLMS) algorithm is developed, which is based on a simple online vector quantization method. The analytical study of the mean square convergence has been carried out. The energy conservation relation for QKLMS is established, and on this basis we arrive at a sufficient condition for mean square convergence, and a lower and upper bound on the theoretical value of the steady-state excess mean square error. Static function estimation and short-term chaotic time-series prediction examples are presented to demonstrate the excellent performance.

Correction Factor for Gaussian Deconvolution of Optically Thick Linewidths in Homogeneous Sources

NASA Technical Reports Server (NTRS)

Kastner, S. O.; Bhatia, A. K.

1999-01-01

Profiles of optically thick, non-Gaussian emission line profiles convoluted with Gaussian instrumental profiles are constructed, and are deconvoluted on the usual Gaussian basis to examine the departure from accuracy thereby caused in "measured" linewidths. It is found that "measured" linewidths underestimate the true linewidths of optically thick lines, by a factor which depends on the resolution factor r congruent to Doppler width/instrumental width and on the optical thickness tau(sub 0). An approximating expression is obtained for this factor, applicable in the range of at least 0 <= tau(sub 0) <= 10, which can provide estimates of the true linewidth and optical thickness.

Kennard-Stone combined with least square support vector machine method for noncontact discriminating human blood species

NASA Astrophysics Data System (ADS)

Zhang, Linna; Li, Gang; Sun, Meixiu; Li, Hongxiao; Wang, Zhennan; Li, Yingxin; Lin, Ling

2017-11-01

Identifying whole bloods to be either human or nonhuman is an important responsibility for import-export ports and inspection and quarantine departments. Analytical methods and DNA testing methods are usually destructive. Previous studies demonstrated that visible diffuse reflectance spectroscopy method can realize noncontact human and nonhuman blood discrimination. An appropriate method for calibration set selection was very important for a robust quantitative model. In this paper, Random Selection (RS) method and Kennard-Stone (KS) method was applied in selecting samples for calibration set. Moreover, proper stoichiometry method can be greatly beneficial for improving the performance of classification model or quantification model. Partial Least Square Discrimination Analysis (PLSDA) method was commonly used in identification of blood species with spectroscopy methods. Least Square Support Vector Machine (LSSVM) was proved to be perfect for discrimination analysis. In this research, PLSDA method and LSSVM method was used for human blood discrimination. Compared with the results of PLSDA method, this method could enhance the performance of identified models. The overall results convinced that LSSVM method was more feasible for identifying human and animal blood species, and sufficiently demonstrated LSSVM method was a reliable and robust method for human blood identification, and can be more effective and accurate.

Accurate phase extraction algorithm based on Gram–Schmidt orthonormalization and least square ellipse fitting method

NASA Astrophysics Data System (ADS)

Lei, Hebing; Yao, Yong; Liu, Haopeng; Tian, Yiting; Yang, Yanfu; Gu, Yinglong

2018-06-01

An accurate algorithm by combing Gram-Schmidt orthonormalization and least square ellipse fitting technology is proposed, which could be used for phase extraction from two or three interferograms. The DC term of background intensity is suppressed by subtraction operation on three interferograms or by high-pass filter on two interferograms. Performing Gram-Schmidt orthonormalization on pre-processing interferograms, the phase shift error is corrected and a general ellipse form is derived. Then the background intensity error and the corrected error could be compensated by least square ellipse fitting method. Finally, the phase could be extracted rapidly. The algorithm could cope with the two or three interferograms with environmental disturbance, low fringe number or small phase shifts. The accuracy and effectiveness of the proposed algorithm are verified by both of the numerical simulations and experiments.

A consensus least squares support vector regression (LS-SVR) for analysis of near-infrared spectra of plant samples.

PubMed

Li, Yankun; Shao, Xueguang; Cai, Wensheng

2007-04-15

Consensus modeling of combining the results of multiple independent models to produce a single prediction avoids the instability of single model. Based on the principle of consensus modeling, a consensus least squares support vector regression (LS-SVR) method for calibrating the near-infrared (NIR) spectra was proposed. In the proposed approach, NIR spectra of plant samples were firstly preprocessed using discrete wavelet transform (DWT) for filtering the spectral background and noise, then, consensus LS-SVR technique was used for building the calibration model. With an optimization of the parameters involved in the modeling, a satisfied model was achieved for predicting the content of reducing sugar in plant samples. The predicted results show that consensus LS-SVR model is more robust and reliable than the conventional partial least squares (PLS) and LS-SVR methods.

Determination of uronic acids in isolated hemicelluloses from kenaf using diffuse reflectance infrared fourier transform spectroscopy (DRIFTS) and the curve-fitting deconvolution method.

PubMed

Batsoulis, A N; Nacos, M K; Pappas, C S; Tarantilis, P A; Mavromoustakos, T; Polissiou, M G

2004-02-01

Hemicellulose samples were isolated from kenaf (Hibiscus cannabinus L.). Hemicellulosic fractions usually contain a variable percentage of uronic acids. The uronic acid content (expressed in polygalacturonic acid) of the isolated hemicelluloses was determined by diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) and the curve-fitting deconvolution method. A linear relationship between uronic acids content and the sum of the peak areas at 1745, 1715, and 1600 cm(-1) was established with a high correlation coefficient (0.98). The deconvolution analysis using the curve-fitting method allowed the elimination of spectral interferences from other cell wall components. The above method was compared with an established spectrophotometric method and was found equivalent for accuracy and repeatability (t-test, F-test). This method is applicable in analysis of natural or synthetic mixtures and/or crude substances. The proposed method is simple, rapid, and nondestructive for the samples.

Second-order standard addition for deconvolution and quantification of fatty acids of fish oil using GC-MS.

PubMed

Vosough, Maryam; Salemi, Amir

2007-08-15

In the present work two second-order calibration methods, generalized rank annihilation method (GRAM) and multivariate curve resolution-alternating least square (MCR-ALS) have been applied on standard addition data matrices obtained by gas chromatography-mass spectrometry (GC-MS) to characterize and quantify four unsaturated fatty acids cis-9-hexadecenoic acid (C16:1omega7c), cis-9-octadecenoic acid (C18:1omega9c), cis-11-eicosenoic acid (C20:1omega9) and cis-13-docosenoic acid (C22:1omega9) in fish oil considering matrix interferences. With these methods, the area does not need to be directly measured and predictions are more accurate. Because of non-trilinear conditions of GC-MS data matrices, at first MCR-ALS and GRAM have been used on uncorrected data matrices. In comparison to MCR-ALS, biased and imprecise concentrations (%R.S.D.=27.3) were obtained using GRAM without correcting the retention time-shift. As trilinearity is the essential requirement for implementing GRAM, the data need to be corrected. Multivariate rank alignment objectively corrects the run-to-run retention time variations between sample GC-MS data matrix and a standard addition GC-MS data matrix. Then, two second-order algorithms have been compared with each other. The above algorithms provided similar mean predictions, pure concentrations and spectral profiles. The results validated using standard mass spectra of target compounds. In addition, some of the quantification results were compared with the concentration values obtained using the selected mass chromatograms. As in the case of strong peak-overlap and the matrix effect, the classical univariate method of determination of the area of the peaks of the analytes will fail, the "second-order advantage" has solved this problem successfully.

Spectrophotometric Analysis of Pigments: A Critical Assessment of a High-Throughput Method for Analysis of Algal Pigment Mixtures by Spectral Deconvolution

PubMed Central

Thrane, Jan-Erik; Kyle, Marcia; Striebel, Maren; Haande, Sigrid; Grung, Merete; Rohrlack, Thomas; Andersen, Tom

2015-01-01

The Gauss-peak spectra (GPS) method represents individual pigment spectra as weighted sums of Gaussian functions, and uses these to model absorbance spectra of phytoplankton pigment mixtures. We here present several improvements for this type of methodology, including adaptation to plate reader technology and efficient model fitting by open source software. We use a one-step modeling of both pigment absorption and background attenuation with non-negative least squares, following a one-time instrument-specific calibration. The fitted background is shown to be higher than a solvent blank, with features reflecting contributions from both scatter and non-pigment absorption. We assessed pigment aliasing due to absorption spectra similarity by Monte Carlo simulation, and used this information to select a robust set of identifiable pigments that are also expected to be common in natural samples. To test the method’s performance, we analyzed absorbance spectra of pigment extracts from sediment cores, 75 natural lake samples, and four phytoplankton cultures, and compared the estimated pigment concentrations with concentrations obtained using high performance liquid chromatography (HPLC). The deviance between observed and fitted spectra was generally very low, indicating that measured spectra could successfully be reconstructed as weighted sums of pigment and background components. Concentrations of total chlorophylls and total carotenoids could accurately be estimated for both sediment and lake samples, but individual pigment concentrations (especially carotenoids) proved difficult to resolve due to similarity between their absorbance spectra. In general, our modified-GPS method provides an improvement of the GPS method that is a fast, inexpensive, and high-throughput alternative for screening of pigment composition in samples of phytoplankton material. PMID:26359659

Faraday rotation data analysis with least-squares elliptical fitting

DOE Office of Scientific and Technical Information (OSTI.GOV)

White, Adam D.; McHale, G. Brent; Goerz, David A.

2010-10-15

A method of analyzing Faraday rotation data from pulsed magnetic field measurements is described. The method uses direct least-squares elliptical fitting to measured data. The least-squares fit conic parameters are used to rotate, translate, and rescale the measured data. Interpretation of the transformed data provides improved accuracy and time-resolution characteristics compared with many existing methods of analyzing Faraday rotation data. The method is especially useful when linear birefringence is present at the input or output of the sensing medium, or when the relative angle of the polarizers used in analysis is not aligned with precision; under these circumstances the methodmore » is shown to return the analytically correct input signal. The method may be pertinent to other applications where analysis of Lissajous figures is required, such as the velocity interferometer system for any reflector (VISAR) diagnostics. The entire algorithm is fully automated and requires no user interaction. An example of algorithm execution is shown, using data from a fiber-based Faraday rotation sensor on a capacitive discharge experiment.« less

Magnetic fields in single late-type giants in the Solar vicinity: How common is magnetic activity on the giant branches?

NASA Astrophysics Data System (ADS)

Konstantinova-Antova, Renada; Aurière, Michel; Charbonnel, Corinne; Drake, Natalia; Wade, Gregg; Tsvetkova, Svetla; Petit, Pascal; Schröder, Klaus-Peter; Lèbre, Agnes

2014-08-01

We present our first results on a new sample containing all single G, K and M giants down to V = 4 mag in the Solar vicinity, suitable for spectropolarimetric (Stokes V) observations with Narval at TBL, France. For detection and measurement of the magnetic field (MF), the Least Squares Deconvolution (LSD) method was applied (Donati et al. 1997) that in the present case enables detection of large-scale MFs even weaker than the solar one (the typical precision of our longitudinal MF measurements is 0.1-0.2 G). The evolutionary status of the stars is determined on the basis of the evolutionary models with rotation (Lagarde et al. 2012; Charbonnel et al., in prep.) and fundamental parameters given by Massarotti et al. (1998). The stars appear to be in the mass range 1-4 M ⊙, situated at different evolutionary stages after the Main Sequence (MS), up to the Asymptotic Giant Branch (AGB). The sample contains 45 stars. Up to now, 29 stars are observed (that is about 64% of the sample), each observed at least twice. For 2 stars in the Hertzsprung gap, one is definitely Zeeman detected. Only 5 G and K giants, situated mainly at the base of the Red Giant Branch (RGB) and in the He-burning phase are detected. Surprisingly, a lot of stars ascending towards the RGB tip and in early AGB phase are detected (8 of 13 observed stars). For all Zeeman detected stars v sin i is redetermined and appears in the interval 2-3 km/s, but few giants with MF possess larger v sin i.

Stochastic Least-Squares Petrov--Galerkin Method for Parameterized Linear Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Kookjin; Carlberg, Kevin; Elman, Howard C.

Here, we consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input parameters. We explore spectral methods in which the solutions are approximated in a chosen finite-dimensional subspace. It has been shown that the stochastic Galerkin projection technique fails to minimize any measure of the solution error. As a remedy for this, we propose a novel stochatic least-squares Petrov--Galerkin (LSPG) method. The proposed method is optimal in the sense that it produces the solution that minimizes a weightedmore » $$\\ell^2$$-norm of the residual over all solutions in a given finite-dimensional subspace. Moreover, the method can be adapted to minimize the solution error in different weighted $$\\ell^2$$-norms by simply applying a weighting function within the least-squares formulation. In addition, a goal-oriented seminorm induced by an output quantity of interest can be minimized by defining a weighting function as a linear functional of the solution. We establish optimality and error bounds for the proposed method, and extensive numerical experiments show that the weighted LSPG method outperforms other spectral methods in minimizing corresponding target weighted norms.« less

Weibull Modulus Estimated by the Non-linear Least Squares Method: A Solution to Deviation Occurring in Traditional Weibull Estimation

NASA Astrophysics Data System (ADS)

Li, T.; Griffiths, W. D.; Chen, J.

2017-11-01

The Maximum Likelihood method and the Linear Least Squares (LLS) method have been widely used to estimate Weibull parameters for reliability of brittle and metal materials. In the last 30 years, many researchers focused on the bias of Weibull modulus estimation, and some improvements have been achieved, especially in the case of the LLS method. However, there is a shortcoming in these methods for a specific type of data, where the lower tail deviates dramatically from the well-known linear fit in a classic LLS Weibull analysis. This deviation can be commonly found from the measured properties of materials, and previous applications of the LLS method on this kind of dataset present an unreliable linear regression. This deviation was previously thought to be due to physical flaws ( i.e., defects) contained in materials. However, this paper demonstrates that this deviation can also be caused by the linear transformation of the Weibull function, occurring in the traditional LLS method. Accordingly, it may not be appropriate to carry out a Weibull analysis according to the linearized Weibull function, and the Non-linear Least Squares method (Non-LS) is instead recommended for the Weibull modulus estimation of casting properties.

Least Squares Best Fit Method for the Three Parameter Weibull Distribution: Analysis of Tensile and Bend Specimens with Volume or Surface Flaw Failure

NASA Technical Reports Server (NTRS)

Gross, Bernard

1996-01-01

Material characterization parameters obtained from naturally flawed specimens are necessary for reliability evaluation of non-deterministic advanced ceramic structural components. The least squares best fit method is applied to the three parameter uniaxial Weibull model to obtain the material parameters from experimental tests on volume or surface flawed specimens subjected to pure tension, pure bending, four point or three point loading. Several illustrative example problems are provided.

Corruption costs lives: evidence from a cross-country study.

PubMed

Li, Qiang; An, Lian; Xu, Jing; Baliamoune-Lutz, Mina

2018-01-01

This paper investigates the effect of corruption on health outcomes by using cross-country panel data covering about 150 countries for the period of 1995 to 2012. We employ ordinary least squares (OLS), fixed-effects and two-stage least squares (2SLS) estimation methods, and find that corruption significantly increases mortality rates, and reduces life expectancy and immunization rates. The results are consistent across different regions, gender, and measures of corruption. The findings suggest that reducing corruption can be an effective method to improve health outcomes.

Fast and nondestructive determination of protein content in rapeseeds (Brassica napus L.) using Fourier transform infrared photoacoustic spectroscopy (FTIR-PAS).

PubMed

Lu, Yuzhen; Du, Changwen; Yu, Changbing; Zhou, Jianmin

2014-08-01

Fast and non-destructive determination of rapeseed protein content carries significant implications in rapeseed production. This study presented the first attempt of using Fourier transform mid-infrared photoacoustic spectroscopy (FTIR-PAS) to quantify protein content of rapeseed. The full-spectrum model was first built using partial least squares (PLS). Interval selection methods including interval partial least squares (iPLS), synergy interval partial least squares (siPLS), backward elimination interval partial least squares (biPLS) and dynamic backward elimination interval partial least squares (dyn-biPLS) were then employed to select the relevant band or band combination for PLS modeling. The full-spectrum PLS model achieved an ratio of prediction to deviation (RPD) of 2.047. In comparison, all interval selection methods produced better results than full-spectrum modeling. siPLS achieved the best predictive accuracy with an RPD of 3.215 when the spectrum was sectioned into 25 intervals, and two intervals (1198-1335 and 1614-1753 cm(-1) ) were selected. iPLS excelled biPLS and dyn-biPLS, and dyn-biPLS performed slightly better than biPLS. FTIR-PAS was verified as a promising analytical tool to quantify rapeseed protein content. Interval selection could extract the relevant individual band or synergy band associated with the sample constituent of interest, and then improve the prediction accuracy of the full-spectrum model. © 2013 Society of Chemical Industry.

Using Technology to Optimize and Generalize: The Least-Squares Line

ERIC Educational Resources Information Center

Burke, Maurice J.; Hodgson, Ted R.

2007-01-01

With the help of technology and a basic high school algebra method for finding the vertex of a quadratic polynomial, students can develop and prove the formula for least-squares lines. Students are exposed to the power of a computer algebra system to generalize processes they understand and to see deeper patterns in those processes. (Contains 4…

Ejecta distribution patterns at Meteor Crater, Arizona: On the applicability of lithologic end-member deconvolution for spaceborne thermal infrared data of Earth and Mars

NASA Astrophysics Data System (ADS)

Ramsey, Michael S.

2002-08-01

A spectral deconvolution using a constrained least squares approach was applied to airborne thermal infrared multispectral scanner (TIMS) data of Meteor Crater, Arizona. The three principal sedimentary units sampled by the impact were chosen as end-members, and their spectra were derived from the emissivity images. To validate previous estimates of the erosion of the near-rim ejecta, the model was used to identify the areal extent of the reworked material. The outputs of the algorithm reveal subtle mixing patterns in the ejecta, identified larger ejecta blocks, and were used to further constrain the volume of Coconino Sandstone present in the vicinity of the crater. The availability of the multialtitude data set also provided a means to examine the effects of resolution degradation and quantify the subsequent errors on the model. These data served as a test case for the use of image-derived lithologic end-members at various scales, which is critical for examining thermal infrared data of planetary surfaces. The model results indicate that the Coconino Ss. reworked ejecta is detectable over 3 km from the crater. This was confirmed by field sampling within the primary ejecta field and wind streak. The areal distribution patterns of this unit imply past erosion and subsequent sediment transport that was low to moderate compared with early studies and therefore places further constraints on the ejecta degradation of Meteor Crater. It also provides an important example of the analysis that can be performed on thermal infrared data currently being returned from Earth orbit and expected from Mars in 2002.

Assessment of parametric uncertainty for groundwater reactive transport modeling,

USGS Publications Warehouse

Shi, Xiaoqing; Ye, Ming; Curtis, Gary P.; Miller, Geoffery L.; Meyer, Philip D.; Kohler, Matthias; Yabusaki, Steve; Wu, Jichun

2014-01-01

The validity of using Gaussian assumptions for model residuals in uncertainty quantification of a groundwater reactive transport model was evaluated in this study. Least squares regression methods explicitly assume Gaussian residuals, and the assumption leads to Gaussian likelihood functions, model parameters, and model predictions. While the Bayesian methods do not explicitly require the Gaussian assumption, Gaussian residuals are widely used. This paper shows that the residuals of the reactive transport model are non-Gaussian, heteroscedastic, and correlated in time; characterizing them requires using a generalized likelihood function such as the formal generalized likelihood function developed by Schoups and Vrugt (2010). For the surface complexation model considered in this study for simulating uranium reactive transport in groundwater, parametric uncertainty is quantified using the least squares regression methods and Bayesian methods with both Gaussian and formal generalized likelihood functions. While the least squares methods and Bayesian methods with Gaussian likelihood function produce similar Gaussian parameter distributions, the parameter distributions of Bayesian uncertainty quantification using the formal generalized likelihood function are non-Gaussian. In addition, predictive performance of formal generalized likelihood function is superior to that of least squares regression and Bayesian methods with Gaussian likelihood function. The Bayesian uncertainty quantification is conducted using the differential evolution adaptive metropolis (DREAM(zs)) algorithm; as a Markov chain Monte Carlo (MCMC) method, it is a robust tool for quantifying uncertainty in groundwater reactive transport models. For the surface complexation model, the regression-based local sensitivity analysis and Morris- and DREAM(ZS)-based global sensitivity analysis yield almost identical ranking of parameter importance. The uncertainty analysis may help select appropriate likelihood functions, improve model calibration, and reduce predictive uncertainty in other groundwater reactive transport and environmental modeling.

[Locally weighted least squares estimation of DPOAE evoked by continuously sweeping primaries].

PubMed

Han, Xiaoli; Fu, Xinxing; Cui, Jie; Xiao, Ling

2013-12-01

Distortion product otoacoustic emission (DPOAE) signal can be used for diagnosis of hearing loss so that it has an important clinical value. Continuously using sweeping primaries to measure DPOAE provides an efficient tool to record DPOAE data rapidly when DPOAE is measured in a large frequency range. In this paper, locally weighted least squares estimation (LWLSE) of 2f1-f2 DPOAE is presented based on least-squares-fit (LSF) algorithm, in which DPOAE is evoked by continuously sweeping tones. In our study, we used a weighted error function as the loss function and the weighting matrixes in the local sense to obtain a smaller estimated variance. Firstly, ordinary least squares estimation of the DPOAE parameters was obtained. Then the error vectors were grouped and the different local weighting matrixes were calculated in each group. And finally, the parameters of the DPOAE signal were estimated based on least squares estimation principle using the local weighting matrixes. The simulation results showed that the estimate variance and fluctuation errors were reduced, so the method estimates DPOAE and stimuli more accurately and stably, which facilitates extraction of clearer DPOAE fine structure.

Advantages of soft versus hard constraints in self-modeling curve resolution problems. Penalty alternating least squares (P-ALS) extension to multi-way problems.

PubMed

Richards, Selena; Miller, Robert; Gemperline, Paul

2008-02-01

An extension to the penalty alternating least squares (P-ALS) method, called multi-way penalty alternating least squares (NWAY P-ALS), is presented. Optionally, hard constraints (no deviation from predefined constraints) or soft constraints (small deviations from predefined constraints) were applied through the application of a row-wise penalty least squares function. NWAY P-ALS was applied to the multi-batch near-infrared (NIR) data acquired from the base catalyzed esterification reaction of acetic anhydride in order to resolve the concentration and spectral profiles of l-butanol with the reaction constituents. Application of the NWAY P-ALS approach resulted in the reduction of the number of active constraints at the solution point, while the batch column-wise augmentation allowed hard constraints in the spectral profiles and resolved rank deficiency problems of the measurement matrix. The results were compared with the multi-way multivariate curve resolution (MCR)-ALS results using hard and soft constraints to determine whether any advantages had been gained through using the weighted least squares function of NWAY P-ALS over the MCR-ALS resolution.

Respiratory mechanics by least squares fitting in mechanically ventilated patients: application on flow-limited COPD patients.

PubMed

Volta, Carlo A; Marangoni, Elisabetta; Alvisi, Valentina; Capuzzo, Maurizia; Ragazzi, Riccardo; Pavanelli, Lina; Alvisi, Raffaele

2002-01-01

Although computerized methods of analyzing respiratory system mechanics such as the least squares fitting method have been used in various patient populations, no conclusive data are available in patients with chronic obstructive pulmonary disease (COPD), probably because they may develop expiratory flow limitation (EFL). This suggests that respiratory mechanics be determined only during inspiration. Eight-bed multidisciplinary ICU of a teaching hospital. Eight non-flow-limited postvascular surgery patients and eight flow-limited COPD patients. Patients were sedated, paralyzed for diagnostic purposes, and ventilated in volume control ventilation with constant inspiratory flow rate. Data on resistance, compliance, and dynamic intrinsic positive end-expiratory pressure (PEEPi,dyn) obtained by applying the least squares fitting method during inspiration, expiration, and the overall breathing cycle were compared with those obtained by the traditional method (constant flow, end-inspiratory occlusion method). Our results indicate that (a) the presence of EFL markedly decreases the precision of resistance and compliance values measured by the LSF method, (b) the determination of respiratory variables during inspiration allows the calculation of respiratory mechanics in flow limited COPD patients, and (c) the LSF method is able to detect the presence of PEEPi,dyn if only inspiratory data are used.

A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gerritsma, Marc; Bochev, Pavel

Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity–vorticity–pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximatedmore » by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. Here, we also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.« less

Exploring the limits of cryospectroscopy: Least-squares based approaches for analyzing the self-association of HCl.

PubMed

De Beuckeleer, Liene I; Herrebout, Wouter A

2016-02-05

To rationalize the concentration dependent behavior observed for a large spectral data set of HCl recorded in liquid argon, least-squares based numerical methods are developed and validated. In these methods, for each wavenumber a polynomial is used to mimic the relation between monomer concentrations and measured absorbances. Least-squares fitting of higher degree polynomials tends to overfit and thus leads to compensation effects where a contribution due to one species is compensated for by a negative contribution of another. The compensation effects are corrected for by carefully analyzing, using AIC and BIC information criteria, the differences observed between consecutive fittings when the degree of the polynomial model is systematically increased, and by introducing constraints prohibiting negative absorbances to occur for the monomer or for one of the oligomers. The method developed should allow other, more complicated self-associating systems to be analyzed with a much higher accuracy than before. Copyright © 2015 Elsevier B.V. All rights reserved.

A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition

DOE PAGES

Gerritsma, Marc; Bochev, Pavel

2016-03-22

Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity–vorticity–pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximatedmore » by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. Here, we also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.« less

Application of recursive approaches to differential orbit correction of near Earth asteroids

NASA Astrophysics Data System (ADS)

Dmitriev, Vasily; Lupovka, Valery; Gritsevich, Maria

2016-10-01

Comparison of three approaches to the differential orbit correction of celestial bodies was performed: batch least squares fitting, Kalman filter, and recursive least squares filter. The first two techniques are well known and widely used (Montenbruck, O. & Gill, E., 2000). The most attention is paid to the algorithm and details of program realization of recursive least squares filter. The filter's algorithm was derived based on recursive least squares technique that are widely used in data processing applications (Simon, D, 2006). Usage recursive least squares filter, makes possible to process a new set of observational data, without reprocessing data, which has been processed before. Specific feature of such approach is that number of observation in data set may be variable. This feature makes recursive least squares filter more flexible approach compare to batch least squares (process complete set of observations in each iteration) and Kalman filtering (suppose updating state vector on each epoch with measurements).Advantages of proposed approach are demonstrated by processing of real astrometric observations of near Earth asteroids. The case of 2008 TC3 was studied. 2008 TC3 was discovered just before its impact with Earth. There are a many closely spaced observations of 2008 TC3 on the interval between discovering and impact, which creates favorable conditions for usage of recursive approaches. Each of approaches has very similar precision in case of 2008 TC3. At the same time, recursive least squares approaches have much higher performance. Thus, this approach more favorable for orbit fitting of a celestial body, which was detected shortly before the collision or close approach to the Earth.This work was carried out at MIIGAiK and supported by the Russian Science Foundation, Project no. 14-22-00197.References:O. Montenbruck and E. Gill, "Satellite Orbits, Models, Methods and Applications," Springer-Verlag, 2000, pp. 1-369.D. Simon, "Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches",1 edition. Hoboken, N.J.: Wiley-Interscience, 2006.

Interactive Visual Least Absolutes Method: Comparison with the Least Squares and the Median Methods

ERIC Educational Resources Information Center

Kim, Myung-Hoon; Kim, Michelle S.

2016-01-01

A visual regression analysis using the least absolutes method (LAB) was developed, utilizing an interactive approach of visually minimizing the sum of the absolute deviations (SAB) using a bar graph in Excel; the results agree very well with those obtained from nonvisual LAB using a numerical Solver in Excel. These LAB results were compared with…

Chemometrics resolution and quantification power evaluation: Application on pharmaceutical quaternary mixture of Paracetamol, Guaifenesin, Phenylephrine and p-aminophenol

NASA Astrophysics Data System (ADS)

Yehia, Ali M.; Mohamed, Heba M.

2016-01-01

Three advanced chemmometric-assisted spectrophotometric methods namely; Concentration Residuals Augmented Classical Least Squares (CRACLS), Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) and Principal Component Analysis-Artificial Neural Networks (PCA-ANN) were developed, validated and benchmarked to PLS calibration; to resolve the severely overlapped spectra and simultaneously determine; Paracetamol (PAR), Guaifenesin (GUA) and Phenylephrine (PHE) in their ternary mixture and in presence of p-aminophenol (AP) the main degradation product and synthesis impurity of Paracetamol. The analytical performance of the proposed methods was described by percentage recoveries, root mean square error of calibration and standard error of prediction. The four multivariate calibration methods could be directly used without any preliminary separation step and successfully applied for pharmaceutical formulation analysis, showing no excipients' interference.

Prediction of pH of cola beverage using Vis/NIR spectroscopy and least squares-support vector machine

NASA Astrophysics Data System (ADS)

Liu, Fei; He, Yong

2008-02-01

Visible and near infrared (Vis/NIR) transmission spectroscopy and chemometric methods were utilized to predict the pH values of cola beverages. Five varieties of cola were prepared and 225 samples (45 samples for each variety) were selected for the calibration set, while 75 samples (15 samples for each variety) for the validation set. The smoothing way of Savitzky-Golay and standard normal variate (SNV) followed by first-derivative were used as the pre-processing methods. Partial least squares (PLS) analysis was employed to extract the principal components (PCs) which were used as the inputs of least squares-support vector machine (LS-SVM) model according to their accumulative reliabilities. Then LS-SVM with radial basis function (RBF) kernel function and a two-step grid search technique were applied to build the regression model with a comparison of PLS regression. The correlation coefficient (r), root mean square error of prediction (RMSEP) and bias were 0.961, 0.040 and 0.012 for PLS, while 0.975, 0.031 and 4.697x10 -3 for LS-SVM, respectively. Both methods obtained a satisfying precision. The results indicated that Vis/NIR spectroscopy combined with chemometric methods could be applied as an alternative way for the prediction of pH of cola beverages.

Cross-correlation least-squares reverse time migration in the pseudo-time domain

NASA Astrophysics Data System (ADS)

Li, Qingyang; Huang, Jianping; Li, Zhenchun

2017-08-01

The least-squares reverse time migration (LSRTM) method with higher image resolution and amplitude is becoming increasingly popular. However, the LSRTM is not widely used in field land data processing because of its sensitivity to the initial migration velocity model, large computational cost and mismatch of amplitudes between the synthetic and observed data. To overcome the shortcomings of the conventional LSRTM, we propose a cross-correlation least-squares reverse time migration algorithm in pseudo-time domain (PTCLSRTM). Our algorithm not only reduces the depth/velocity ambiguities, but also reduces the effect of velocity error on the imaging results. It relieves the accuracy requirements on the migration velocity model of least-squares migration (LSM). The pseudo-time domain algorithm eliminates the irregular wavelength sampling in the vertical direction, thus it can reduce the vertical grid points and memory requirements used during computation, which makes our method more computationally efficient than the standard implementation. Besides, for field data applications, matching the recorded amplitudes is a very difficult task because of the viscoelastic nature of the Earth and inaccuracies in the estimation of the source wavelet. To relax the requirement for strong amplitude matching of LSM, we extend the normalized cross-correlation objective function to the pseudo-time domain. Our method is only sensitive to the similarity between the predicted and the observed data. Numerical tests on synthetic and land field data confirm the effectiveness of our method and its adaptability for complex models.

Least-squares Minimization Approaches to Interpret Total Magnetic Anomalies Due to Spheres

NASA Astrophysics Data System (ADS)

Abdelrahman, E. M.; El-Araby, T. M.; Soliman, K. S.; Essa, K. S.; Abo-Ezz, E. R.

2007-05-01

We have developed three different least-squares approaches to determine successively: the depth, magnetic angle, and amplitude coefficient of a buried sphere from a total magnetic anomaly. By defining the anomaly value at the origin and the nearest zero-anomaly distance from the origin on the profile, the problem of depth determination is transformed into the problem of finding a solution of a nonlinear equation of the form f(z)=0. Knowing the depth and applying the least-squares method, the magnetic angle and amplitude coefficient are determined using two simple linear equations. In this way, the depth, magnetic angle, and amplitude coefficient are determined individually from all observed total magnetic data. The method is applied to synthetic examples with and without random errors and tested on a field example from Senegal, West Africa. In all cases, the depth solutions are in good agreement with the actual ones.

Multiple concurrent recursive least squares identification with application to on-line spacecraft mass-property identification

NASA Technical Reports Server (NTRS)

Wilson, Edward (Inventor)

2006-01-01

The present invention is a method for identifying unknown parameters in a system having a set of governing equations describing its behavior that cannot be put into regression form with the unknown parameters linearly represented. In this method, the vector of unknown parameters is segmented into a plurality of groups where each individual group of unknown parameters may be isolated linearly by manipulation of said equations. Multiple concurrent and independent recursive least squares identification of each said group run, treating other unknown parameters appearing in their regression equation as if they were known perfectly, with said values provided by recursive least squares estimation from the other groups, thereby enabling the use of fast, compact, efficient linear algorithms to solve problems that would otherwise require nonlinear solution approaches. This invention is presented with application to identification of mass and thruster properties for a thruster-controlled spacecraft.

Enhancing Least-Squares Finite Element Methods Through a Quantity-of-Interest

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chaudhry, Jehanzeb Hameed; Cyr, Eric C.; Liu, Kuo

2014-12-18

Here, we introduce an approach that augments least-squares finite element formulations with user-specified quantities-of-interest. The method incorporates the quantity-of-interest into the least-squares functional and inherits the global approximation properties of the standard formulation as well as increased resolution of the quantity-of-interest. We establish theoretical properties such as optimality and enhanced convergence under a set of general assumptions. Central to the approach is that it offers an element-level estimate of the error in the quantity-of-interest. As a result, we introduce an adaptive approach that yields efficient, adaptively refined approximations. Several numerical experiments for a range of situations are presented to supportmore » the theory and highlight the effectiveness of our methodology. Notably, the results show that the new approach is effective at improving the accuracy per total computational cost.« less

Robust analysis of trends in noisy tokamak confinement data using geodesic least squares regression

DOE Office of Scientific and Technical Information (OSTI.GOV)

Verdoolaege, G., E-mail: geert.verdoolaege@ugent.be; Laboratory for Plasma Physics, Royal Military Academy, B-1000 Brussels; Shabbir, A.

Regression analysis is a very common activity in fusion science for unveiling trends and parametric dependencies, but it can be a difficult matter. We have recently developed the method of geodesic least squares (GLS) regression that is able to handle errors in all variables, is robust against data outliers and uncertainty in the regression model, and can be used with arbitrary distribution models and regression functions. We here report on first results of application of GLS to estimation of the multi-machine scaling law for the energy confinement time in tokamaks, demonstrating improved consistency of the GLS results compared to standardmore » least squares.« less

Prediction model of sinoatrial node field potential using high order partial least squares.

PubMed

Feng, Yu; Cao, Hui; Zhang, Yanbin

2015-01-01

High order partial least squares (HOPLS) is a novel data processing method. It is highly suitable for building prediction model which has tensor input and output. The objective of this study is to build a prediction model of the relationship between sinoatrial node field potential and high glucose using HOPLS. The three sub-signals of the sinoatrial node field potential made up the model's input. The concentration and the actuation duration of high glucose made up the model's output. The results showed that on the premise of predicting two dimensional variables, HOPLS had the same predictive ability and a lower dispersion degree compared with partial least squares (PLS).

Non-oscillatory and non-diffusive solution of convection problems by the iteratively reweighted least-squares finite element method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1993-01-01

A comparative description is presented for the least-squares FEM (LSFEM) for 2D steady-state pure convection problems. In addition to exhibiting better control of the streamline derivative than the streamline upwinding Petrov-Galerkin method, numerical convergence rates are obtained which show the LSFEM to be virtually optimal. The LSFEM is used as a framework for an iteratively reweighted LSFEM yielding nonoscillatory and nondiffusive solutions for problems with contact discontinuities; this method is shown to convect contact discontinuities without error when using triangular and bilinear elements.

Partial least squares density modeling (PLS-DM) - a new class-modeling strategy applied to the authentication of olives in brine by near-infrared spectroscopy.

PubMed

Oliveri, Paolo; López, M Isabel; Casolino, M Chiara; Ruisánchez, Itziar; Callao, M Pilar; Medini, Luca; Lanteri, Silvia

2014-12-03

A new class-modeling method, referred to as partial least squares density modeling (PLS-DM), is presented. The method is based on partial least squares (PLS), using a distance-based sample density measurement as the response variable. Potential function probability density is subsequently calculated on PLS scores and used, jointly with residual Q statistics, to develop efficient class models. The influence of adjustable model parameters on the resulting performances has been critically studied by means of cross-validation and application of the Pareto optimality criterion. The method has been applied to verify the authenticity of olives in brine from cultivar Taggiasca, based on near-infrared (NIR) spectra recorded on homogenized solid samples. Two independent test sets were used for model validation. The final optimal model was characterized by high efficiency and equilibrate balance between sensitivity and specificity values, if compared with those obtained by application of well-established class-modeling methods, such as soft independent modeling of class analogy (SIMCA) and unequal dispersed classes (UNEQ). Copyright © 2014 Elsevier B.V. All rights reserved.

Determination of thiamine HCl and pyridoxine HCl in pharmaceutical preparations using UV-visible spectrophotometry and genetic algorithm based multivariate calibration methods.

PubMed

Ozdemir, Durmus; Dinc, Erdal

2004-07-01

Simultaneous determination of binary mixtures pyridoxine hydrochloride and thiamine hydrochloride in a vitamin combination using UV-visible spectrophotometry and classical least squares (CLS) and three newly developed genetic algorithm (GA) based multivariate calibration methods was demonstrated. The three genetic multivariate calibration methods are Genetic Classical Least Squares (GCLS), Genetic Inverse Least Squares (GILS) and Genetic Regression (GR). The sample data set contains the UV-visible spectra of 30 synthetic mixtures (8 to 40 microg/ml) of these vitamins and 10 tablets containing 250 mg from each vitamin. The spectra cover the range from 200 to 330 nm in 0.1 nm intervals. Several calibration models were built with the four methods for the two components. Overall, the standard error of calibration (SEC) and the standard error of prediction (SEP) for the synthetic data were in the range of <0.01 and 0.43 microg/ml for all the four methods. The SEP values for the tablets were in the range of 2.91 and 11.51 mg/tablets. A comparison of genetic algorithm selected wavelengths for each component using GR method was also included.

Least squares deconvolution for leak detection with a pseudo random binary sequence excitation

NASA Astrophysics Data System (ADS)

Nguyen, Si Tran Nguyen; Gong, Jinzhe; Lambert, Martin F.; Zecchin, Aaron C.; Simpson, Angus R.

2018-01-01

Leak detection and localisation is critical for water distribution system pipelines. This paper examines the use of the time-domain impulse response function (IRF) for leak detection and localisation in a pressurised water pipeline with a pseudo random binary sequence (PRBS) signal excitation. Compared to the conventional step wave generated using a single fast operation of a valve closure, a PRBS signal offers advantageous correlation properties, in that the signal has very low autocorrelation for lags different from zero and low cross correlation with other signals including noise and other interference. These properties result in a significant improvement in the IRF signal to noise ratio (SNR), leading to more accurate leak localisation. In this paper, the estimation of the system IRF is formulated as an optimisation problem in which the l2 norm of the IRF is minimised to suppress the impact of noise and interference sources. Both numerical and experimental data are used to verify the proposed technique. The resultant estimated IRF provides not only accurate leak location estimation, but also good sensitivity to small leak sizes due to the improved SNR.

Rupture directivity and slip distribution of the M 4.3 foreshock to the 1992 Joshua Tree earthquake, Southern California

USGS Publications Warehouse

Mori, J.

1996-01-01

Details of the M 4.3 foreshock to the Joshua Tree earthquake were studied using P waves recorded on the Southern California Seismic Network and the Anza network. Deconvolution, using an M 2.4 event as an empirical Green's function, corrected for complicated path and site effects in the seismograms and produced simple far-field displacement pulses that were inverted for a slip distribution. Both possible fault planes, north-south and east-west, for the focal mechanism were tested by a least-squares inversion procedure with a range of rupture velocities. The results showed that the foreshock ruptured the north-south plane, similar to the mainshock. The foreshock initiated a few hundred meters south of the mainshock and ruptured to the north, toward the mainshock hypocenter. The mainshock (M 6.1) initiated near the northern edge of the foreshock rupture 2 hr later. The foreshock had a high stress drop (320 to 800 bars) and broke a small portion of the fault adjacent to the mainshock but was not able to immediately initiate the mainshock rupture.

Non-destructive and rapid prediction of moisture content in red pepper (Capsicum annuum L.) powder using near-infrared spectroscopy and a partial least squares regression model

USDA-ARS?s Scientific Manuscript database

Purpose: The aim of this study was to develop a technique for the non-destructive and rapid prediction of the moisture content in red pepper powder using near-infrared (NIR) spectroscopy and a partial least squares regression (PLSR) model. Methods: Three red pepper powder products were separated in...

Estimation of the ARNO model baseflow parameters using daily streamflow data

NASA Astrophysics Data System (ADS)

Abdulla, F. A.; Lettenmaier, D. P.; Liang, Xu

1999-09-01

An approach is described for estimation of baseflow parameters of the ARNO model, using historical baseflow recession sequences extracted from daily streamflow records. This approach allows four of the model parameters to be estimated without rainfall data, and effectively facilitates partitioning of the parameter estimation procedure so that parsimonious search procedures can be used to estimate the remaining storm response parameters separately. Three methods of optimization are evaluated for estimation of four baseflow parameters. These methods are the downhill Simplex (S), Simulated Annealing combined with the Simplex method (SA) and Shuffled Complex Evolution (SCE). These estimation procedures are explored in conjunction with four objective functions: (1) ordinary least squares; (2) ordinary least squares with Box-Cox transformation; (3) ordinary least squares on prewhitened residuals; (4) ordinary least squares applied to prewhitened with Box-Cox transformation of residuals. The effects of changing the seed random generator for both SA and SCE methods are also explored, as are the effects of the bounds of the parameters. Although all schemes converge to the same values of the objective function, SCE method was found to be less sensitive to these issues than both the SA and the Simplex schemes. Parameter uncertainty and interactions are investigated through estimation of the variance-covariance matrix and confidence intervals. As expected the parameters were found to be correlated and the covariance matrix was found to be not diagonal. Furthermore, the linearized confidence interval theory failed for about one-fourth of the catchments while the maximum likelihood theory did not fail for any of the catchments.

Studing Regional Wave Source Time Functions Using A Massive Automated EGF Deconvolution Procedure

NASA Astrophysics Data System (ADS)

Xie, J. "; Schaff, D. P.

2010-12-01

Reliably estimated source time functions (STF) from high-frequency regional waveforms, such as Lg, Pn and Pg, provide important input for seismic source studies, explosion detection, and minimization of parameter trade-off in attenuation studies. The empirical Green’s function (EGF) method can be used for estimating STF, but it requires a strict recording condition. Waveforms from pairs of events that are similar in focal mechanism, but different in magnitude must be on-scale recorded on the same stations for the method to work. Searching for such waveforms can be very time consuming, particularly for regional waves that contain complex path effects and have reduced S/N ratios due to attenuation. We have developed a massive, automated procedure to conduct inter-event waveform deconvolution calculations from many candidate event pairs. The procedure automatically evaluates the “spikiness” of the deconvolutions by calculating their “sdc”, which is defined as the peak divided by the background value. The background value is calculated as the mean absolute value of the deconvolution, excluding 10 s around the source time function. When the sdc values are about 10 or higher, the deconvolutions are found to be sufficiently spiky (pulse-like), indicating similar path Green’s functions and good estimates of the STF. We have applied this automated procedure to Lg waves and full regional wavetrains from 989 M ≥ 5 events in and around China, calculating about a million deconvolutions. Of these we found about 2700 deconvolutions with sdc greater than 9, which, if having a sufficiently broad frequency band, can be used to estimate the STF of the larger events. We are currently refining our procedure, as well as the estimated STFs. We will infer the source scaling using the STFs. We will also explore the possibility that the deconvolution procedure could complement cross-correlation in a real time event-screening process.

Fast and Accurate Fitting and Filtering of Noisy Exponentials in Legendre Space

PubMed Central

Bao, Guobin; Schild, Detlev

2014-01-01

The parameters of experimentally obtained exponentials are usually found by least-squares fitting methods. Essentially, this is done by minimizing the mean squares sum of the differences between the data, most often a function of time, and a parameter-defined model function. Here we delineate a novel method where the noisy data are represented and analyzed in the space of Legendre polynomials. This is advantageous in several respects. First, parameter retrieval in the Legendre domain is typically two orders of magnitude faster than direct fitting in the time domain. Second, data fitting in a low-dimensional Legendre space yields estimates for amplitudes and time constants which are, on the average, more precise compared to least-squares-fitting with equal weights in the time domain. Third, the Legendre analysis of two exponentials gives satisfactory estimates in parameter ranges where least-squares-fitting in the time domain typically fails. Finally, filtering exponentials in the domain of Legendre polynomials leads to marked noise removal without the phase shift characteristic for conventional lowpass filters. PMID:24603904

New model for prediction binary mixture of antihistamine decongestant using artificial neural networks and least squares support vector machine by spectrophotometry method

NASA Astrophysics Data System (ADS)

Mofavvaz, Shirin; Sohrabi, Mahmoud Reza; Nezamzadeh-Ejhieh, Alireza

2017-07-01

In the present study, artificial neural networks (ANNs) and least squares support vector machines (LS-SVM) as intelligent methods based on absorption spectra in the range of 230-300 nm have been used for determination of antihistamine decongestant contents. In the first step, one type of network (feed-forward back-propagation) from the artificial neural network with two different training algorithms, Levenberg-Marquardt (LM) and gradient descent with momentum and adaptive learning rate back-propagation (GDX) algorithm, were employed and their performance was evaluated. The performance of the LM algorithm was better than the GDX algorithm. In the second one, the radial basis network was utilized and results compared with the previous network. In the last one, the other intelligent method named least squares support vector machine was proposed to construct the antihistamine decongestant prediction model and the results were compared with two of the aforementioned networks. The values of the statistical parameters mean square error (MSE), Regression coefficient (R2), correlation coefficient (r) and also mean recovery (%), relative standard deviation (RSD) used for selecting the best model between these methods. Moreover, the proposed methods were compared to the high- performance liquid chromatography (HPLC) as a reference method. One way analysis of variance (ANOVA) test at the 95% confidence level applied to the comparison results of suggested and reference methods that there were no significant differences between them.

Growth kinetics of borided layers: Artificial neural network and least square approaches

NASA Astrophysics Data System (ADS)

Campos, I.; Islas, M.; Ramírez, G.; VillaVelázquez, C.; Mota, C.

2007-05-01

The present study evaluates the growth kinetics of the boride layer Fe 2B in AISI 1045 steel, by means of neural networks and the least square techniques. The Fe 2B phase was formed at the material surface using the paste boriding process. The surface boron potential was modified considering different boron paste thicknesses, with exposure times of 2, 4 and 6 h, and treatment temperatures of 1193, 1223 and 1273 K. The neural network and the least square models were set by the layer thickness of Fe 2B phase, and assuming that the growth of the boride layer follows a parabolic law. The reliability of the techniques used is compared with a set of experiments at a temperature of 1223 K with 5 h of treatment time and boron potentials of 2, 3, 4 and 5 mm. The results of the Fe 2B layer thicknesses show a mean error of 5.31% for the neural network and 3.42% for the least square method.

Accurate human limb angle measurement: sensor fusion through Kalman, least mean squares and recursive least-squares adaptive filtering

NASA Astrophysics Data System (ADS)

Olivares, A.; Górriz, J. M.; Ramírez, J.; Olivares, G.

2011-02-01

Inertial sensors are widely used in human body motion monitoring systems since they permit us to determine the position of the subject's limbs. Limb angle measurement is carried out through the integration of the angular velocity measured by a rate sensor and the decomposition of the components of static gravity acceleration measured by an accelerometer. Different factors derived from the sensors' nature, such as the angle random walk and dynamic bias, lead to erroneous measurements. Dynamic bias effects can be reduced through the use of adaptive filtering based on sensor fusion concepts. Most existing published works use a Kalman filtering sensor fusion approach. Our aim is to perform a comparative study among different adaptive filters. Several least mean squares (LMS), recursive least squares (RLS) and Kalman filtering variations are tested for the purpose of finding the best method leading to a more accurate and robust limb angle measurement. A new angle wander compensation sensor fusion approach based on LMS and RLS filters has been developed.

A CLASS OF RECONSTRUCTED DISCONTINUOUS GALERKIN METHODS IN COMPUTATIONAL FLUID DYNAMICS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hong Luo; Yidong Xia; Robert Nourgaliev

2011-05-01

A class of reconstructed discontinuous Galerkin (DG) methods is presented to solve compressible flow problems on arbitrary grids. The idea is to combine the efficiency of the reconstruction methods in finite volume methods and the accuracy of the DG methods to obtain a better numerical algorithm in computational fluid dynamics. The beauty of the resulting reconstructed discontinuous Galerkin (RDG) methods is that they provide a unified formulation for both finite volume and DG methods, and contain both classical finite volume and standard DG methods as two special cases of the RDG methods, and thus allow for a direct efficiency comparison.more » Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are presented to obtain a quadratic polynomial representation of the underlying linear discontinuous Galerkin solution on each cell via a so-called in-cell reconstruction process. The devised in-cell reconstruction is aimed to augment the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. These three reconstructed discontinuous Galerkin methods are used to compute a variety of compressible flow problems on arbitrary meshes to assess their accuracy. The numerical experiments demonstrate that all three reconstructed discontinuous Galerkin methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstructed DG method provides the best performance in terms of both accuracy, efficiency, and robustness.« less

Efficient Levenberg-Marquardt minimization of the maximum likelihood estimator for Poisson deviates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Laurence, T; Chromy, B

2009-11-10

Histograms of counted events are Poisson distributed, but are typically fitted without justification using nonlinear least squares fitting. The more appropriate maximum likelihood estimator (MLE) for Poisson distributed data is seldom used. We extend the use of the Levenberg-Marquardt algorithm commonly used for nonlinear least squares minimization for use with the MLE for Poisson distributed data. In so doing, we remove any excuse for not using this more appropriate MLE. We demonstrate the use of the algorithm and the superior performance of the MLE using simulations and experiments in the context of fluorescence lifetime imaging. Scientists commonly form histograms ofmore » counted events from their data, and extract parameters by fitting to a specified model. Assuming that the probability of occurrence for each bin is small, event counts in the histogram bins will be distributed according to the Poisson distribution. We develop here an efficient algorithm for fitting event counting histograms using the maximum likelihood estimator (MLE) for Poisson distributed data, rather than the non-linear least squares measure. This algorithm is a simple extension of the common Levenberg-Marquardt (L-M) algorithm, is simple to implement, quick and robust. Fitting using a least squares measure is most common, but it is the maximum likelihood estimator only for Gaussian-distributed data. Non-linear least squares methods may be applied to event counting histograms in cases where the number of events is very large, so that the Poisson distribution is well approximated by a Gaussian. However, it is not easy to satisfy this criterion in practice - which requires a large number of events. It has been well-known for years that least squares procedures lead to biased results when applied to Poisson-distributed data; a recent paper providing extensive characterization of these biases in exponential fitting is given. The more appropriate measure based on the maximum likelihood estimator (MLE) for the Poisson distribution is also well known, but has not become generally used. This is primarily because, in contrast to non-linear least squares fitting, there has been no quick, robust, and general fitting method. In the field of fluorescence lifetime spectroscopy and imaging, there have been some efforts to use this estimator through minimization routines such as Nelder-Mead optimization, exhaustive line searches, and Gauss-Newton minimization. Minimization based on specific one- or multi-exponential models has been used to obtain quick results, but this procedure does not allow the incorporation of the instrument response, and is not generally applicable to models found in other fields. Methods for using the MLE for Poisson-distributed data have been published by the wider spectroscopic community, including iterative minimization schemes based on Gauss-Newton minimization. The slow acceptance of these procedures for fitting event counting histograms may also be explained by the use of the ubiquitous, fast Levenberg-Marquardt (L-M) fitting procedure for fitting non-linear models using least squares fitting (simple searches obtain {approx}10000 references - this doesn't include those who use it, but don't know they are using it). The benefits of L-M include a seamless transition between Gauss-Newton minimization and downward gradient minimization through the use of a regularization parameter. This transition is desirable because Gauss-Newton methods converge quickly, but only within a limited domain of convergence; on the other hand the downward gradient methods have a much wider domain of convergence, but converge extremely slowly nearer the minimum. L-M has the advantages of both procedures: relative insensitivity to initial parameters and rapid convergence. Scientists, when wanting an answer quickly, will fit data using L-M, get an answer, and move on. Only those that are aware of the bias issues will bother to fit using the more appropriate MLE for Poisson deviates. However, since there is a simple, analytical formula for the appropriate MLE measure for Poisson deviates, it is inexcusable that least squares estimators are used almost exclusively when fitting event counting histograms. There have been ways found to use successive non-linear least squares fitting to obtain similarly unbiased results, but this procedure is justified by simulation, must be re-tested when conditions change significantly, and requires two successive fits. There is a great need for a fitting routine for the MLE estimator for Poisson deviates that has convergence domains and rates comparable to the non-linear least squares L-M fitting. We show in this report that a simple way to achieve that goal is to use the L-M fitting procedure not to minimize the least squares measure, but the MLE for Poisson deviates.« less

Data Dependent Peak Model Based Spectrum Deconvolution for Analysis of High Resolution LC-MS Data

PubMed Central

2015-01-01

A data dependent peak model (DDPM) based spectrum deconvolution method was developed for analysis of high resolution LC-MS data. To construct the selected ion chromatogram (XIC), a clustering method, the density based spatial clustering of applications with noise (DBSCAN), is applied to all m/z values of an LC-MS data set to group the m/z values into each XIC. The DBSCAN constructs XICs without the need for a user defined m/z variation window. After the XIC construction, the peaks of molecular ions in each XIC are detected using both the first and the second derivative tests, followed by an optimized chromatographic peak model selection method for peak deconvolution. A total of six chromatographic peak models are considered, including Gaussian, log-normal, Poisson, gamma, exponentially modified Gaussian, and hybrid of exponential and Gaussian models. The abundant nonoverlapping peaks are chosen to find the optimal peak models that are both data- and retention-time-dependent. Analysis of 18 spiked-in LC-MS data demonstrates that the proposed DDPM spectrum deconvolution method outperforms the traditional method. On average, the DDPM approach not only detected 58 more chromatographic peaks from each of the testing LC-MS data but also improved the retention time and peak area 3% and 6%, respectively. PMID:24533635

Convex blind image deconvolution with inverse filtering

NASA Astrophysics Data System (ADS)

Lv, Xiao-Guang; Li, Fang; Zeng, Tieyong

2018-03-01

Blind image deconvolution is the process of estimating both the original image and the blur kernel from the degraded image with only partial or no information about degradation and the imaging system. It is a bilinear ill-posed inverse problem corresponding to the direct problem of convolution. Regularization methods are used to handle the ill-posedness of blind deconvolution and get meaningful solutions. In this paper, we investigate a convex regularized inverse filtering method for blind deconvolution of images. We assume that the support region of the blur object is known, as has been done in a few existing works. By studying the inverse filters of signal and image restoration problems, we observe the oscillation structure of the inverse filters. Inspired by the oscillation structure of the inverse filters, we propose to use the star norm to regularize the inverse filter. Meanwhile, we use the total variation to regularize the resulting image obtained by convolving the inverse filter with the degraded image. The proposed minimization model is shown to be convex. We employ the first-order primal-dual method for the solution of the proposed minimization model. Numerical examples for blind image restoration are given to show that the proposed method outperforms some existing methods in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), visual quality and time consumption.

Methods for estimating annual exceedance probability discharges for streams in Arkansas, based on data through water year 2013

USGS Publications Warehouse

Wagner, Daniel M.; Krieger, Joshua D.; Veilleux, Andrea G.

2016-08-04

In 2013, the U.S. Geological Survey initiated a study to update regional skew, annual exceedance probability discharges, and regional regression equations used to estimate annual exceedance probability discharges for ungaged locations on streams in the study area with the use of recent geospatial data, new analytical methods, and available annual peak-discharge data through the 2013 water year. An analysis of regional skew using Bayesian weighted least-squares/Bayesian generalized-least squares regression was performed for Arkansas, Louisiana, and parts of Missouri and Oklahoma. The newly developed constant regional skew of -0.17 was used in the computation of annual exceedance probability discharges for 281 streamgages used in the regional regression analysis. Based on analysis of covariance, four flood regions were identified for use in the generation of regional regression models. Thirty-nine basin characteristics were considered as potential explanatory variables, and ordinary least-squares regression techniques were used to determine the optimum combinations of basin characteristics for each of the four regions. Basin characteristics in candidate models were evaluated based on multicollinearity with other basin characteristics (variance inflation factor < 2.5) and statistical significance at the 95-percent confidence level (p ≤ 0.05). Generalized least-squares regression was used to develop the final regression models for each flood region. Average standard errors of prediction of the generalized least-squares models ranged from 32.76 to 59.53 percent, with the largest range in flood region D. Pseudo coefficients of determination of the generalized least-squares models ranged from 90.29 to 97.28 percent, with the largest range also in flood region D. The regional regression equations apply only to locations on streams in Arkansas where annual peak discharges are not substantially affected by regulation, diversion, channelization, backwater, or urbanization. The applicability and accuracy of the regional regression equations depend on the basin characteristics measured for an ungaged location on a stream being within range of those used to develop the equations.

Approximating a retarded-advanced differential equation that models human phonation

NASA Astrophysics Data System (ADS)

Teodoro, M. Filomena

2017-11-01

In [1, 2, 3] we have got the numerical solution of a linear mixed type functional differential equation (MTFDE) introduced initially in [4], considering the autonomous and non-autonomous case by collocation, least squares and finite element methods considering B-splines basis set. The present work introduces a numerical scheme using least squares method (LSM) and Gaussian basis functions to solve numerically a nonlinear mixed type equation with symmetric delay and advance which models human phonation. The preliminary results are promising. We obtain an accuracy comparable with the previous results.

Fourier Deconvolution Methods for Resolution Enhancement in Continuous-Wave EPR Spectroscopy.

PubMed

Reed, George H; Poyner, Russell R

2015-01-01

An overview of resolution enhancement of conventional, field-swept, continuous-wave electron paramagnetic resonance spectra using Fourier transform-based deconvolution methods is presented. Basic steps that are involved in resolution enhancement of calculated spectra using an implementation based on complex discrete Fourier transform algorithms are illustrated. Advantages and limitations of the method are discussed. An application to an experimentally obtained spectrum is provided to illustrate the power of the method for resolving overlapped transitions. © 2015 Elsevier Inc. All rights reserved.

Blind source deconvolution for deep Earth seismology

NASA Astrophysics Data System (ADS)

Stefan, W.; Renaut, R.; Garnero, E. J.; Lay, T.

2007-12-01

We present an approach to automatically estimate an empirical source characterization of deep earthquakes recorded teleseismically and subsequently remove the source from the recordings by applying regularized deconvolution. A principle goal in this work is to effectively deblur the seismograms, resulting in more impulsive and narrower pulses, permitting better constraints in high resolution waveform analyses. Our method consists of two stages: (1) we first estimate the empirical source by automatically registering traces to their 1st principal component with a weighting scheme based on their deviation from this shape, we then use this shape as an estimation of the earthquake source. (2) We compare different deconvolution techniques to remove the source characteristic from the trace. In particular Total Variation (TV) regularized deconvolution is used which utilizes the fact that most natural signals have an underlying spareness in an appropriate basis, in this case, impulsive onsets of seismic arrivals. We show several examples of deep focus Fiji-Tonga region earthquakes for the phases S and ScS, comparing source responses for the separate phases. TV deconvolution is compared to the water level deconvolution, Tikenov deconvolution, and L1 norm deconvolution, for both data and synthetics. This approach significantly improves our ability to study subtle waveform features that are commonly masked by either noise or the earthquake source. Eliminating source complexities improves our ability to resolve deep mantle triplications, waveform complexities associated with possible double crossings of the post-perovskite phase transition, as well as increasing stability in waveform analyses used for deep mantle anisotropy measurements.

Monitoring of Time-Dependent System Profiles by Multiplex Gas Chromatography with Maximum Entropy Demodulation

NASA Technical Reports Server (NTRS)

Becker, Joseph F.; Valentin, Jose

1996-01-01

The maximum entropy technique was successfully applied to the deconvolution of overlapped chromatographic peaks. An algorithm was written in which the chromatogram was represented as a vector of sample concentrations multiplied by a peak shape matrix. Simulation results demonstrated that there is a trade off between the detector noise and peak resolution in the sense that an increase of the noise level reduced the peak separation that could be recovered by the maximum entropy method. Real data originated from a sample storage column was also deconvoluted using maximum entropy. Deconvolution is useful in this type of system because the conservation of time dependent profiles depends on the band spreading processes in the chromatographic column, which might smooth out the finer details in the concentration profile. The method was also applied to the deconvolution of previously interpretted Pioneer Venus chromatograms. It was found in this case that the correct choice of peak shape function was critical to the sensitivity of maximum entropy in the reconstruction of these chromatograms.

Least-squares model-based halftoning

NASA Astrophysics Data System (ADS)

Pappas, Thrasyvoulos N.; Neuhoff, David L.

1992-08-01

A least-squares model-based approach to digital halftoning is proposed. It exploits both a printer model and a model for visual perception. It attempts to produce an 'optimal' halftoned reproduction, by minimizing the squared error between the response of the cascade of the printer and visual models to the binary image and the response of the visual model to the original gray-scale image. Conventional methods, such as clustered ordered dither, use the properties of the eye only implicitly, and resist printer distortions at the expense of spatial and gray-scale resolution. In previous work we showed that our printer model can be used to modify error diffusion to account for printer distortions. The modified error diffusion algorithm has better spatial and gray-scale resolution than conventional techniques, but produces some well known artifacts and asymmetries because it does not make use of an explicit eye model. Least-squares model-based halftoning uses explicit eye models and relies on printer models that predict distortions and exploit them to increase, rather than decrease, both spatial and gray-scale resolution. We have shown that the one-dimensional least-squares problem, in which each row or column of the image is halftoned independently, can be implemented with the Viterbi's algorithm. Unfortunately, no closed form solution can be found in two dimensions. The two-dimensional least squares solution is obtained by iterative techniques. Experiments show that least-squares model-based halftoning produces more gray levels and better spatial resolution than conventional techniques. We also show that the least- squares approach eliminates the problems associated with error diffusion. Model-based halftoning can be especially useful in transmission of high quality documents using high fidelity gray-scale image encoders. As we have shown, in such cases halftoning can be performed at the receiver, just before printing. Apart from coding efficiency, this approach permits the halftoner to be tuned to the individual printer, whose characteristics may vary considerably from those of other printers, for example, write-black vs. write-white laser printers.

Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography.

PubMed

Yalavarthy, Phaneendra K; Pogue, Brian W; Dehghani, Hamid; Paulsen, Keith D

2007-06-01

Diffuse optical tomography (DOT) involves estimation of tissue optical properties using noninvasive boundary measurements. The image reconstruction procedure is a nonlinear, ill-posed, and ill-determined problem, so overcoming these difficulties requires regularization of the solution. While the methods developed for solving the DOT image reconstruction procedure have a long history, there is less direct evidence on the optimal regularization methods, or exploring a common theoretical framework for techniques which uses least-squares (LS) minimization. A generalized least-squares (GLS) method is discussed here, which takes into account the variances and covariances among the individual data points and optical properties in the image into a structured weight matrix. It is shown that most of the least-squares techniques applied in DOT can be considered as special cases of this more generalized LS approach. The performance of three minimization techniques using the same implementation scheme is compared using test problems with increasing noise level and increasing complexity within the imaging field. Techniques that use spatial-prior information as constraints can be also incorporated into the GLS formalism. It is also illustrated that inclusion of spatial priors reduces the image error by at least a factor of 2. The improvement of GLS minimization is even more apparent when the noise level in the data is high (as high as 10%), indicating that the benefits of this approach are important for reconstruction of data in a routine setting where the data variance can be known based upon the signal to noise properties of the instruments.

Toward Overcoming the Local Minimum Trap in MFBD

DTIC Science & Technology

2015-07-14

the first two years of this grant: • A. Cornelio, E. Loli -Piccolomini, and J. G. Nagy. Constrained Variable Projection Method for Blind Deconvolution...Cornelio, E. Loli -Piccolomini, and J. G. Nagy. Constrained Numerical Optimization Meth- ods for Blind Deconvolution, Numerical Algorithms, volume 65, issue 1...Publications (published) during reporting period: A. Cornelio, E. Loli Piccolomini, and J. G. Nagy. Constrained Variable Projection Method for Blind

Chemometrics resolution and quantification power evaluation: Application on pharmaceutical quaternary mixture of Paracetamol, Guaifenesin, Phenylephrine and p-aminophenol.

PubMed

Yehia, Ali M; Mohamed, Heba M

2016-01-05

Three advanced chemmometric-assisted spectrophotometric methods namely; Concentration Residuals Augmented Classical Least Squares (CRACLS), Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) and Principal Component Analysis-Artificial Neural Networks (PCA-ANN) were developed, validated and benchmarked to PLS calibration; to resolve the severely overlapped spectra and simultaneously determine; Paracetamol (PAR), Guaifenesin (GUA) and Phenylephrine (PHE) in their ternary mixture and in presence of p-aminophenol (AP) the main degradation product and synthesis impurity of Paracetamol. The analytical performance of the proposed methods was described by percentage recoveries, root mean square error of calibration and standard error of prediction. The four multivariate calibration methods could be directly used without any preliminary separation step and successfully applied for pharmaceutical formulation analysis, showing no excipients' interference. Copyright © 2015 Elsevier B.V. All rights reserved.

Application of the Galerkin/least-squares formulation to the analysis of hypersonic flows. II - Flow past a double ellipse

NASA Technical Reports Server (NTRS)

Chalot, F.; Hughes, T. J. R.; Johan, Z.; Shakib, F.

1991-01-01

A finite element method for the compressible Navier-Stokes equations is introduced. The discretization is based on entropy variables. The methodology is developed within the framework of a Galerkin/least-squares formulation to which a discontinuity-capturing operator is added. Results for four test cases selected among those of the Workshop on Hypersonic Flows for Reentry Problems are presented.

Solving matrix effects exploiting the second-order advantage in the resolution and determination of eight tetracycline antibiotics in effluent wastewater by modelling liquid chromatography data with multivariate curve resolution-alternating least squares and unfolded-partial least squares followed by residual bilinearization algorithms II. Prediction and figures of merit.

PubMed

García, M D Gil; Culzoni, M J; De Zan, M M; Valverde, R Santiago; Galera, M Martínez; Goicoechea, H C

2008-02-01

A new powerful algorithm (unfolded-partial least squares followed by residual bilinearization (U-PLS/RBL)) was applied for first time on second-order liquid chromatography with diode array detection (LC-DAD) data and compared with a well-known established method (multivariate curve resolution-alternating least squares (MCR-ALS)) for the simultaneous determination of eight tetracyclines (tetracycline, oxytetracycline, meclocycline, minocycline, metacycline, chlortetracycline, demeclocycline and doxycycline) in wastewaters. Tetracyclines were pre-concentrated using Oasis Max C18 cartridges and then separated on a Thermo Aquasil C18 (150 mm x 4.6mm, 5 microm) column. The whole method was validated using Milli-Q water samples and both univariate and multivariate analytical figures of merit were obtained. Additionally, two data pre-treatment were applied (baseline correction and piecewise direct standardization), which allowed to correct the effect of breakthrough and to reduce the total interferences retained after pre-concentration of wastewaters. The results showed that the eight tetracycline antibiotics can be successfully determined in wastewaters, the drawbacks due to matrix interferences being adequately handled and overcome by using U-PSL/RBL.

Forward Looking Radar Imaging by Truncated Singular Value Decomposition and Its Application for Adverse Weather Aircraft Landing.

PubMed

Huang, Yulin; Zha, Yuebo; Wang, Yue; Yang, Jianyu

2015-06-18

The forward looking radar imaging task is a practical and challenging problem for adverse weather aircraft landing industry. Deconvolution method can realize the forward looking imaging but it often leads to the noise amplification in the radar image. In this paper, a forward looking radar imaging based on deconvolution method is presented for adverse weather aircraft landing. We first present the theoretical background of forward looking radar imaging task and its application for aircraft landing. Then, we convert the forward looking radar imaging task into a corresponding deconvolution problem, which is solved in the framework of algebraic theory using truncated singular decomposition method. The key issue regarding the selecting of the truncated parameter is addressed using generalized cross validation approach. Simulation and experimental results demonstrate that the proposed method is effective in achieving angular resolution enhancement with suppressing the noise amplification in forward looking radar imaging.

Algorithms for Nonlinear Least-Squares Problems

DTIC Science & Technology

1988-09-01

O -,i(x) 2 , where each -,(x) is a smooth function mapping Rn to R. J - The m x n Jacobian matrix of f. ... x g - The gradient of the nonlinear least...V211f(X*)I112~ l~ l) J(xk)T J(xk) 2 + O(k - X*) For more convergence results and detailed convergence analysis for the Gauss-Newton method, see, e. g ...for a class of nonlinear least-squares problems that includes zero-residual prob- lems. The function Jt is the pseudo-inverse of Jk (see, e. g

An efficient variable projection formulation for separable nonlinear least squares problems.

PubMed

Gan, Min; Li, Han-Xiong

2014-05-01

We consider in this paper a class of nonlinear least squares problems in which the model can be represented as a linear combination of nonlinear functions. The variable projection algorithm projects the linear parameters out of the problem, leaving the nonlinear least squares problems involving only the nonlinear parameters. To implement the variable projection algorithm more efficiently, we propose a new variable projection functional based on matrix decomposition. The advantage of the proposed formulation is that the size of the decomposed matrix may be much smaller than those of previous ones. The Levenberg-Marquardt algorithm using finite difference method is then applied to minimize the new criterion. Numerical results show that the proposed approach achieves significant reduction in computing time.

Correcting bias in the rational polynomial coefficients of satellite imagery using thin-plate smoothing splines

NASA Astrophysics Data System (ADS)

Shen, Xiang; Liu, Bin; Li, Qing-Quan

2017-03-01

The Rational Function Model (RFM) has proven to be a viable alternative to the rigorous sensor models used for geo-processing of high-resolution satellite imagery. Because of various errors in the satellite ephemeris and instrument calibration, the Rational Polynomial Coefficients (RPCs) supplied by image vendors are often not sufficiently accurate, and there is therefore a clear need to correct the systematic biases in order to meet the requirements of high-precision topographic mapping. In this paper, we propose a new RPC bias-correction method using the thin-plate spline modeling technique. Benefiting from its excellent performance and high flexibility in data fitting, the thin-plate spline model has the potential to remove complex distortions in vendor-provided RPCs, such as the errors caused by short-period orbital perturbations. The performance of the new method was evaluated by using Ziyuan-3 satellite images and was compared against the recently developed least-squares collocation approach, as well as the classical affine-transformation and quadratic-polynomial based methods. The results show that the accuracies of the thin-plate spline and the least-squares collocation approaches were better than the other two methods, which indicates that strong non-rigid deformations exist in the test data because they cannot be adequately modeled by simple polynomial-based methods. The performance of the thin-plate spline method was close to that of the least-squares collocation approach when only a few Ground Control Points (GCPs) were used, and it improved more rapidly with an increase in the number of redundant observations. In the test scenario using 21 GCPs (some of them located at the four corners of the scene), the correction residuals of the thin-plate spline method were about 36%, 37%, and 19% smaller than those of the affine transformation method, the quadratic polynomial method, and the least-squares collocation algorithm, respectively, which demonstrates that the new method can be more effective at removing systematic biases in vendor-supplied RPCs.

Augmented classical least squares multivariate spectral analysis

DOEpatents

Haaland, David M.; Melgaard, David K.

2004-02-03

A method of multivariate spectral analysis, termed augmented classical least squares (ACLS), provides an improved CLS calibration model when unmodeled sources of spectral variation are contained in a calibration sample set. The ACLS methods use information derived from component or spectral residuals during the CLS calibration to provide an improved calibration-augmented CLS model. The ACLS methods are based on CLS so that they retain the qualitative benefits of CLS, yet they have the flexibility of PLS and other hybrid techniques in that they can define a prediction model even with unmodeled sources of spectral variation that are not explicitly included in the calibration model. The unmodeled sources of spectral variation may be unknown constituents, constituents with unknown concentrations, nonlinear responses, non-uniform and correlated errors, or other sources of spectral variation that are present in the calibration sample spectra. Also, since the various ACLS methods are based on CLS, they can incorporate the new prediction-augmented CLS (PACLS) method of updating the prediction model for new sources of spectral variation contained in the prediction sample set without having to return to the calibration process. The ACLS methods can also be applied to alternating least squares models. The ACLS methods can be applied to all types of multivariate data.

Augmented Classical Least Squares Multivariate Spectral Analysis

DOEpatents

Haaland, David M.; Melgaard, David K.

2005-07-26

A method of multivariate spectral analysis, termed augmented classical least squares (ACLS), provides an improved CLS calibration model when unmodeled sources of spectral variation are contained in a calibration sample set. The ACLS methods use information derived from component or spectral residuals during the CLS calibration to provide an improved calibration-augmented CLS model. The ACLS methods are based on CLS so that they retain the qualitative benefits of CLS, yet they have the flexibility of PLS and other hybrid techniques in that they can define a prediction model even with unmodeled sources of spectral variation that are not explicitly included in the calibration model. The unmodeled sources of spectral variation may be unknown constituents, constituents with unknown concentrations, nonlinear responses, non-uniform and correlated errors, or other sources of spectral variation that are present in the calibration sample spectra. Also, since the various ACLS methods are based on CLS, they can incorporate the new prediction-augmented CLS (PACLS) method of updating the prediction model for new sources of spectral variation contained in the prediction sample set without having to return to the calibration process. The ACLS methods can also be applied to alternating least squares models. The ACLS methods can be applied to all types of multivariate data.

Augmented Classical Least Squares Multivariate Spectral Analysis

DOEpatents

Haaland, David M.; Melgaard, David K.

2005-01-11

A method of multivariate spectral analysis, termed augmented classical least squares (ACLS), provides an improved CLS calibration model when unmodeled sources of spectral variation are contained in a calibration sample set. The ACLS methods use information derived from component or spectral residuals during the CLS calibration to provide an improved calibration-augmented CLS model. The ACLS methods are based on CLS so that they retain the qualitative benefits of CLS, yet they have the flexibility of PLS and other hybrid techniques in that they can define a prediction model even with unmodeled sources of spectral variation that are not explicitly included in the calibration model. The unmodeled sources of spectral variation may be unknown constituents, constituents with unknown concentrations, nonlinear responses, non-uniform and correlated errors, or other sources of spectral variation that are present in the calibration sample spectra. Also, since the various ACLS methods are based on CLS, they can incorporate the new prediction-augmented CLS (PACLS) method of updating the prediction model for new sources of spectral variation contained in the prediction sample set without having to return to the calibration process. The ACLS methods can also be applied to alternating least squares models. The ACLS methods can be applied to all types of multivariate data.

Strong variable linear polarization in the cool active star II Peg

NASA Astrophysics Data System (ADS)

Rosén, Lisa; Kochukhov, Oleg; Wade, Gregg A.

2014-08-01

Magnetic fields of cool active stars are currently studied polarimetrically using only circular polarization observations. This provides limited information about the magnetic field geometry since circular polarization is only sensitive to the line-of-sight component of the magnetic field. Reconstructions of the magnetic field topology will therefore not be completely trustworthy when only circular polarization is used. On the other hand, linear polarization is sensitive to the transverse component of the magnetic field. By including linear polarization in the reconstruction the quality of the reconstructed magnetic map is dramatically improved. For that reason, we wanted to identify cool stars for which linear polarization could be detected at a level sufficient for magnetic imaging. Four active RS CVn binaries, II Peg, HR 1099, IM Peg, and σ Gem were observed with the ESPaDOnS spectropolarimeter at the Canada-France-Hawaii Telescope. Mean polarization profiles in all four Stokes parameters were derived using the multi-line technique of least-squares deconvolution (LSD). Not only was linear polarization successfully detected in all four stars in at least one observation, but also, II Peg showed an extraordinarily strong linear polarization signature throughout all observations. This qualifies II Peg as the first promising target for magnetic Doppler imaging in all four Stokes parameters and, at the same time, suggests that other such targets can possibly be identified.

Deconvolution of gas chromatographic data

NASA Technical Reports Server (NTRS)

Howard, S.; Rayborn, G. H.

1980-01-01

The use of deconvolution methods on gas chromatographic data to obtain an accurate determination of the relative amounts of each material present by mathematically separating the merged peaks is discussed. Data were obtained on a gas chromatograph with a flame ionization detector. Chromatograms of five xylenes with differing degrees of separation were generated by varying the column temperature at selected rates. The merged peaks were then successfully separated by deconvolution. The concept of function continuation in the frequency domain was introduced in striving to reach the theoretical limit of accuracy, but proved to be only partially successful.

A new family of stable elements for the Stokes problem based on a mixed Galerkin/least-squares finite element formulation

NASA Technical Reports Server (NTRS)

Franca, Leopoldo P.; Loula, Abimael F. D.; Hughes, Thomas J. R.; Miranda, Isidoro

1989-01-01

Adding to the classical Hellinger-Reissner formulation, a residual form of the equilibrium equation, a new Galerkin/least-squares finite element method is derived. It fits within the framework of a mixed finite element method and is stable for rather general combinations of stress and velocity interpolations, including equal-order discontinuous stress and continuous velocity interpolations which are unstable within the Galerkin approach. Error estimates are presented based on a generalization of the Babuska-Brezzi theory. Numerical results (not presented herein) have confirmed these estimates as well as the good accuracy and stability of the method.

SU-F-T-478: Effect of Deconvolution in Analysis of Mega Voltage Photon Beam Profiles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Muthukumaran, M; Manigandan, D; Murali, V

2016-06-15

Purpose: To study and compare the penumbra of 6 MV and 15 MV photon beam profiles after deconvoluting different volume ionization chambers. Methods: 0.125cc Semi-Flex chamber, Markus Chamber and PTW Farmer chamber were used to measure the in-plane and cross-plane profiles at 5 cm depth for 6 MV and 15 MV photons. The profiles were measured for various field sizes starting from 2×2 cm till 30×30 cm. PTW TBA scan software was used for the measurements and the “deconvolution” functionality in the software was used to remove the volume averaging effect due to finite volume of the chamber along lateralmore » and longitudinal directions for all the ionization chambers. The predicted true profile was compared and the change in penumbra before and after deconvolution was studied. Results: After deconvoluting the penumbra decreased by 1 mm for field sizes ranging from 2 × 2 cm till 20 x20 cm. This is observed for along both lateral and longitudinal directions. However for field sizes from 20 × 20 till 30 ×30 cm the difference in penumbra was around 1.2 till 1.8 mm. This was observed for both 6 MV and 15 MV photon beams. The penumbra was always lesser in the deconvoluted profiles for all the ionization chambers involved in the study. The variation in difference in penumbral values were in the order of 0.1 till 0.3 mm between the deconvoluted profile along lateral and longitudinal directions for all the chambers under study. Deconvolution of the profiles along longitudinal direction for Farmer chamber was not good and is not comparable with other deconvoluted profiles. Conclusion: The results of the deconvoluted profiles for 0.125cc and Markus chamber was comparable and the deconvolution functionality can be used to overcome the volume averaging effect.« less

An optimized algorithm for multiscale wideband deconvolution of radio astronomical images

NASA Astrophysics Data System (ADS)

Offringa, A. R.; Smirnov, O.

2017-10-01

We describe a new multiscale deconvolution algorithm that can also be used in a multifrequency mode. The algorithm only affects the minor clean loop. In single-frequency mode, the minor loop of our improved multiscale algorithm is over an order of magnitude faster than the casa multiscale algorithm, and produces results of similar quality. For multifrequency deconvolution, a technique named joined-channel cleaning is used. In this mode, the minor loop of our algorithm is two to three orders of magnitude faster than casa msmfs. We extend the multiscale mode with automated scale-dependent masking, which allows structures to be cleaned below the noise. We describe a new scale-bias function for use in multiscale cleaning. We test a second deconvolution method that is a variant of the moresane deconvolution technique, and uses a convex optimization technique with isotropic undecimated wavelets as dictionary. On simple well-calibrated data, the convex optimization algorithm produces visually more representative models. On complex or imperfect data, the convex optimization algorithm has stability issues.

New regularization scheme for blind color image deconvolution

NASA Astrophysics Data System (ADS)

Chen, Li; He, Yu; Yap, Kim-Hui

2011-01-01

This paper proposes a new regularization scheme to address blind color image deconvolution. Color images generally have a significant correlation among the red, green, and blue channels. Conventional blind monochromatic deconvolution algorithms handle each color image channels independently, thereby ignoring the interchannel correlation present in the color images. In view of this, a unified regularization scheme for image is developed to recover edges of color images and reduce color artifacts. In addition, by using the color image properties, a spectral-based regularization operator is adopted to impose constraints on the blurs. Further, this paper proposes a reinforcement regularization framework that integrates a soft parametric learning term in addressing blind color image deconvolution. A blur modeling scheme is developed to evaluate the relevance of manifold parametric blur structures, and the information is integrated into the deconvolution scheme. An optimization procedure called alternating minimization is then employed to iteratively minimize the image- and blur-domain cost functions. Experimental results show that the method is able to achieve satisfactory restored color images under different blurring conditions.

Petroleomics by electrospray ionization FT-ICR mass spectrometry coupled to partial least squares with variable selection methods: prediction of the total acid number of crude oils.

PubMed

Terra, Luciana A; Filgueiras, Paulo R; Tose, Lílian V; Romão, Wanderson; de Souza, Douglas D; de Castro, Eustáquio V R; de Oliveira, Mirela S L; Dias, Júlio C M; Poppi, Ronei J

2014-10-07

Negative-ion mode electrospray ionization, ESI(-), with Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) was coupled to a Partial Least Squares (PLS) regression and variable selection methods to estimate the total acid number (TAN) of Brazilian crude oil samples. Generally, ESI(-)-FT-ICR mass spectra present a power of resolution of ca. 500,000 and a mass accuracy less than 1 ppm, producing a data matrix containing over 5700 variables per sample. These variables correspond to heteroatom-containing species detected as deprotonated molecules, [M - H](-) ions, which are identified primarily as naphthenic acids, phenols and carbazole analog species. The TAN values for all samples ranged from 0.06 to 3.61 mg of KOH g(-1). To facilitate the spectral interpretation, three methods of variable selection were studied: variable importance in the projection (VIP), interval partial least squares (iPLS) and elimination of uninformative variables (UVE). The UVE method seems to be more appropriate for selecting important variables, reducing the dimension of the variables to 183 and producing a root mean square error of prediction of 0.32 mg of KOH g(-1). By reducing the size of the data, it was possible to relate the selected variables with their corresponding molecular formulas, thus identifying the main chemical species responsible for the TAN values.

Time-domain least-squares migration using the Gaussian beam summation method

NASA Astrophysics Data System (ADS)

Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo

2018-04-01

With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modeling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modeling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a preconditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.

Time-domain least-squares migration using the Gaussian beam summation method

NASA Astrophysics Data System (ADS)

Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo

2018-07-01

With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modelling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modelling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a pre-conditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.

XDGMM: eXtreme Deconvolution Gaussian Mixture Modeling

NASA Astrophysics Data System (ADS)

Holoien, Thomas W.-S.; Marshall, Philip J.; Wechsler, Risa H.

2017-08-01

XDGMM uses Gaussian mixtures to do density estimation of noisy, heterogenous, and incomplete data using extreme deconvolution (XD) algorithms which is compatible with the scikit-learn machine learning methods. It implements both the astroML and Bovy et al. (2011) algorithms, and extends the BaseEstimator class from scikit-learn so that cross-validation methods work. It allows the user to produce a conditioned model if values of some parameters are known.

Sparse deconvolution for the large-scale ill-posed inverse problem of impact force reconstruction

NASA Astrophysics Data System (ADS)

Qiao, Baijie; Zhang, Xingwu; Gao, Jiawei; Liu, Ruonan; Chen, Xuefeng

2017-01-01

Most previous regularization methods for solving the inverse problem of force reconstruction are to minimize the l2-norm of the desired force. However, these traditional regularization methods such as Tikhonov regularization and truncated singular value decomposition, commonly fail to solve the large-scale ill-posed inverse problem in moderate computational cost. In this paper, taking into account the sparse characteristic of impact force, the idea of sparse deconvolution is first introduced to the field of impact force reconstruction and a general sparse deconvolution model of impact force is constructed. Second, a novel impact force reconstruction method based on the primal-dual interior point method (PDIPM) is proposed to solve such a large-scale sparse deconvolution model, where minimizing the l2-norm is replaced by minimizing the l1-norm. Meanwhile, the preconditioned conjugate gradient algorithm is used to compute the search direction of PDIPM with high computational efficiency. Finally, two experiments including the small-scale or medium-scale single impact force reconstruction and the relatively large-scale consecutive impact force reconstruction are conducted on a composite wind turbine blade and a shell structure to illustrate the advantage of PDIPM. Compared with Tikhonov regularization, PDIPM is more efficient, accurate and robust whether in the single impact force reconstruction or in the consecutive impact force reconstruction.

Evaluation of uncertainty for regularized deconvolution: A case study in hydrophone measurements.

PubMed

Eichstädt, S; Wilkens, V

2017-06-01

An estimation of the measurand in dynamic metrology usually requires a deconvolution based on a dynamic calibration of the measuring system. Since deconvolution is, mathematically speaking, an ill-posed inverse problem, some kind of regularization is required to render the problem stable and obtain usable results. Many approaches to regularized deconvolution exist in the literature, but the corresponding evaluation of measurement uncertainties is, in general, an unsolved issue. In particular, the uncertainty contribution of the regularization itself is a topic of great importance, because it has a significant impact on the estimation result. Here, a versatile approach is proposed to express prior knowledge about the measurand based on a flexible, low-dimensional modeling of an upper bound on the magnitude spectrum of the measurand. This upper bound allows the derivation of an uncertainty associated with the regularization method in line with the guidelines in metrology. As a case study for the proposed method, hydrophone measurements in medical ultrasound with an acoustic working frequency of up to 7.5 MHz are considered, but the approach is applicable for all kinds of estimation methods in dynamic metrology, where regularization is required and which can be expressed as a multiplication in the frequency domain.

4Pi microscopy deconvolution with a variable point-spread function.

PubMed

Baddeley, David; Carl, Christian; Cremer, Christoph

2006-09-20

To remove the axial sidelobes from 4Pi images, deconvolution forms an integral part of 4Pi microscopy. As a result of its high axial resolution, the 4Pi point spread function (PSF) is particularly susceptible to imperfect optical conditions within the sample. This is typically observed as a shift in the position of the maxima under the PSF envelope. A significantly varying phase shift renders deconvolution procedures based on a spatially invariant PSF essentially useless. We present a technique for computing the forward transformation in the case of a varying phase at a computational expense of the same order of magnitude as that of the shift invariant case, a method for the estimation of PSF phase from an acquired image, and a deconvolution procedure built on these techniques.

Comparison of three newton-like nonlinear least-squares methods for estimating parameters of ground-water flow models

USGS Publications Warehouse

Cooley, R.L.; Hill, M.C.

1992-01-01

Three methods of solving nonlinear least-squares problems were compared for robustness and efficiency using a series of hypothetical and field problems. A modified Gauss-Newton/full Newton hybrid method (MGN/FN) and an analogous method for which part of the Hessian matrix was replaced by a quasi-Newton approximation (MGN/QN) solved some of the problems with appreciably fewer iterations than required using only a modified Gauss-Newton (MGN) method. In these problems, model nonlinearity and a large variance for the observed data apparently caused MGN to converge more slowly than MGN/FN or MGN/QN after the sum of squared errors had almost stabilized. Other problems were solved as efficiently with MGN as with MGN/FN or MGN/QN. Because MGN/FN can require significantly more computer time per iteration and more computer storage for transient problems, it is less attractive for a general purpose algorithm than MGN/QN.

Quantitative methods for structural characterization of proteins based on deep UV resonance Raman spectroscopy.

PubMed

Shashilov, Victor A; Sikirzhytski, Vitali; Popova, Ludmila A; Lednev, Igor K

2010-09-01

Here we report on novel quantitative approaches for protein structural characterization using deep UV resonance Raman (DUVRR) spectroscopy. Specifically, we propose a new method combining hydrogen-deuterium (HD) exchange and Bayesian source separation for extracting the DUVRR signatures of various structural elements of aggregated proteins including the cross-beta core and unordered parts of amyloid fibrils. The proposed method is demonstrated using the set of DUVRR spectra of hen egg white lysozyme acquired at various stages of HD exchange. Prior information about the concentration matrix and the spectral features of the individual components was incorporated into the Bayesian equation to eliminate the ill-conditioning of the problem caused by 100% correlation of the concentration profiles of protonated and deuterated species. Secondary structure fractions obtained by partial least squares (PLS) and least squares support vector machines (LS-SVMs) were used as the initial guess for the Bayessian source separation. Advantages of the PLS and LS-SVMs methods over the classical least squares calibration (CLSC) are discussed and illustrated using the DUVRR data of the prion protein in its native and aggregated forms. Copyright (c) 2010 Elsevier Inc. All rights reserved.

The Inverse Problem for Confined Aquifer Flow: Identification and Estimation With Extensions

NASA Astrophysics Data System (ADS)

Loaiciga, Hugo A.; MariñO, Miguel A.

1987-01-01

The contributions of this work are twofold. First, a methodology for estimating the elements of parameter matrices in the governing equation of flow in a confined aquifer is developed. The estimation techniques for the distributed-parameter inverse problem pertain to linear least squares and generalized least squares methods. The linear relationship among the known heads and unknown parameters of the flow equation provides the background for developing criteria for determining the identifiability status of unknown parameters. Under conditions of exact or overidentification it is possible to develop statistically consistent parameter estimators and their asymptotic distributions. The estimation techniques, namely, two-stage least squares and three stage least squares, are applied to a specific groundwater inverse problem and compared between themselves and with an ordinary least squares estimator. The three-stage estimator provides the closer approximation to the actual parameter values, but it also shows relatively large standard errors as compared to the ordinary and two-stage estimators. The estimation techniques provide the parameter matrices required to simulate the unsteady groundwater flow equation. Second, a nonlinear maximum likelihood estimation approach to the inverse problem is presented. The statistical properties of maximum likelihood estimators are derived, and a procedure to construct confidence intervals and do hypothesis testing is given. The relative merits of the linear and maximum likelihood estimators are analyzed. Other topics relevant to the identification and estimation methodologies, i.e., a continuous-time solution to the flow equation, coping with noise-corrupted head measurements, and extension of the developed theory to nonlinear cases are also discussed. A simulation study is used to evaluate the methods developed in this study.

Least-Squares Curve-Fitting Program

NASA Technical Reports Server (NTRS)

Kantak, Anil V.

1990-01-01

Least Squares Curve Fitting program, AKLSQF, easily and efficiently computes polynomial providing least-squares best fit to uniformly spaced data. Enables user to specify tolerable least-squares error in fit or degree of polynomial. AKLSQF returns polynomial and actual least-squares-fit error incurred in operation. Data supplied to routine either by direct keyboard entry or via file. Written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler.

Inline Measurement of Particle Concentrations in Multicomponent Suspensions using Ultrasonic Sensor and Least Squares Support Vector Machines.

PubMed

Zhan, Xiaobin; Jiang, Shulan; Yang, Yili; Liang, Jian; Shi, Tielin; Li, Xiwen

2015-09-18

This paper proposes an ultrasonic measurement system based on least squares support vector machines (LS-SVM) for inline measurement of particle concentrations in multicomponent suspensions. Firstly, the ultrasonic signals are analyzed and processed, and the optimal feature subset that contributes to the best model performance is selected based on the importance of features. Secondly, the LS-SVM model is tuned, trained and tested with different feature subsets to obtain the optimal model. In addition, a comparison is made between the partial least square (PLS) model and the LS-SVM model. Finally, the optimal LS-SVM model with the optimal feature subset is applied to inline measurement of particle concentrations in the mixing process. The results show that the proposed method is reliable and accurate for inline measuring the particle concentrations in multicomponent suspensions and the measurement accuracy is sufficiently high for industrial application. Furthermore, the proposed method is applicable to the modeling of the nonlinear system dynamically and provides a feasible way to monitor industrial processes.

Development of Jet Noise Power Spectral Laws Using SHJAR Data

NASA Technical Reports Server (NTRS)

Khavaran, Abbas; Bridges, James

2009-01-01

High quality jet noise spectral data measured at the Aeroacoustic Propulsion Laboratory at the NASA Glenn Research Center is used to examine a number of jet noise scaling laws. Configurations considered in the present study consist of convergent and convergent-divergent axisymmetric nozzles. Following the work of Viswanathan, velocity power factors are estimated using a least squares fit on spectral power density as a function of jet temperature and observer angle. The regression parameters are scrutinized for their uncertainty within the desired confidence margins. As an immediate application of the velocity power laws, spectral density in supersonic jets are decomposed into their respective components attributed to the jet mixing noise and broadband shock associated noise. Subsequent application of the least squares method on the shock power intensity shows that the latter also scales with some power of the shock parameter. A modified shock parameter is defined in order to reduce the dependency of the regression factors on the nozzle design point within the uncertainty margins of the least squares method.

Least Square Fast Learning Network for modeling the combustion efficiency of a 300WM coal-fired boiler.

PubMed

Li, Guoqiang; Niu, Peifeng; Wang, Huaibao; Liu, Yongchao

2014-03-01

This paper presents a novel artificial neural network with a very fast learning speed, all of whose weights and biases are determined by the twice Least Square method, so it is called Least Square Fast Learning Network (LSFLN). In addition, there is another difference from conventional neural networks, which is that the output neurons of LSFLN not only receive the information from the hidden layer neurons, but also receive the external information itself directly from the input neurons. In order to test the validity of LSFLN, it is applied to 6 classical regression applications, and also employed to build the functional relation between the combustion efficiency and operating parameters of a 300WM coal-fired boiler. Experimental results show that, compared with other methods, LSFLN with very less hidden neurons could achieve much better regression precision and generalization ability at a much faster learning speed. Copyright © 2013 Elsevier Ltd. All rights reserved.

Asymptotic Analysis Of The Total Least Squares ESPRIT Algorithm'

NASA Astrophysics Data System (ADS)

Ottersten, B. E.; Viberg, M.; Kailath, T.

1989-11-01

This paper considers the problem of estimating the parameters of multiple narrowband signals arriving at an array of sensors. Modern approaches to this problem often involve costly procedures for calculating the estimates. The ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) algorithm was recently proposed as a means for obtaining accurate estimates without requiring a costly search of the parameter space. This method utilizes an array invariance to arrive at a computationally efficient multidimensional estimation procedure. Herein, the asymptotic distribution of the estimation error is derived for the Total Least Squares (TLS) version of ESPRIT. The Cramer-Rao Bound (CRB) for the ESPRIT problem formulation is also derived and found to coincide with the variance of the asymptotic distribution through numerical examples. The method is also compared to least squares ESPRIT and MUSIC as well as to the CRB for a calibrated array. Simulations indicate that the theoretic expressions can be used to accurately predict the performance of the algorithm.

Distance-Based Phylogenetic Methods Around a Polytomy.

PubMed

Davidson, Ruth; Sullivant, Seth

2014-01-01

Distance-based phylogenetic algorithms attempt to solve the NP-hard least-squares phylogeny problem by mapping an arbitrary dissimilarity map representing biological data to a tree metric. The set of all dissimilarity maps is a Euclidean space properly containing the space of all tree metrics as a polyhedral fan. Outputs of distance-based tree reconstruction algorithms such as UPGMA and neighbor-joining are points in the maximal cones in the fan. Tree metrics with polytomies lie at the intersections of maximal cones. A phylogenetic algorithm divides the space of all dissimilarity maps into regions based upon which combinatorial tree is reconstructed by the algorithm. Comparison of phylogenetic methods can be done by comparing the geometry of these regions. We use polyhedral geometry to compare the local nature of the subdivisions induced by least-squares phylogeny, UPGMA, and neighbor-joining when the true tree has a single polytomy with exactly four neighbors. Our results suggest that in some circumstances, UPGMA and neighbor-joining poorly match least-squares phylogeny.

An improved conjugate gradient scheme to the solution of least squares SVM.

PubMed

Chu, Wei; Ong, Chong Jin; Keerthi, S Sathiya

2005-03-01

The least square support vector machines (LS-SVM) formulation corresponds to the solution of a linear system of equations. Several approaches to its numerical solutions have been proposed in the literature. In this letter, we propose an improved method to the numerical solution of LS-SVM and show that the problem can be solved using one reduced system of linear equations. Compared with the existing algorithm for LS-SVM, the approach used in this letter is about twice as efficient. Numerical results using the proposed method are provided for comparisons with other existing algorithms.

Quantitative Modelling of Trace Elements in Hard Coal.

PubMed

Smoliński, Adam; Howaniec, Natalia

2016-01-01

The significance of coal in the world economy remains unquestionable for decades. It is also expected to be the dominant fossil fuel in the foreseeable future. The increased awareness of sustainable development reflected in the relevant regulations implies, however, the need for the development and implementation of clean coal technologies on the one hand, and adequate analytical tools on the other. The paper presents the application of the quantitative Partial Least Squares method in modeling the concentrations of trace elements (As, Ba, Cd, Co, Cr, Cu, Mn, Ni, Pb, Rb, Sr, V and Zn) in hard coal based on the physical and chemical parameters of coal, and coal ash components. The study was focused on trace elements potentially hazardous to the environment when emitted from coal processing systems. The studied data included 24 parameters determined for 132 coal samples provided by 17 coal mines of the Upper Silesian Coal Basin, Poland. Since the data set contained outliers, the construction of robust Partial Least Squares models for contaminated data set and the correct identification of outlying objects based on the robust scales were required. These enabled the development of the correct Partial Least Squares models, characterized by good fit and prediction abilities. The root mean square error was below 10% for all except for one the final Partial Least Squares models constructed, and the prediction error (root mean square error of cross-validation) exceeded 10% only for three models constructed. The study is of both cognitive and applicative importance. It presents the unique application of the chemometric methods of data exploration in modeling the content of trace elements in coal. In this way it contributes to the development of useful tools of coal quality assessment.

Quantitative Modelling of Trace Elements in Hard Coal

PubMed Central

Smoliński, Adam; Howaniec, Natalia

2016-01-01

The significance of coal in the world economy remains unquestionable for decades. It is also expected to be the dominant fossil fuel in the foreseeable future. The increased awareness of sustainable development reflected in the relevant regulations implies, however, the need for the development and implementation of clean coal technologies on the one hand, and adequate analytical tools on the other. The paper presents the application of the quantitative Partial Least Squares method in modeling the concentrations of trace elements (As, Ba, Cd, Co, Cr, Cu, Mn, Ni, Pb, Rb, Sr, V and Zn) in hard coal based on the physical and chemical parameters of coal, and coal ash components. The study was focused on trace elements potentially hazardous to the environment when emitted from coal processing systems. The studied data included 24 parameters determined for 132 coal samples provided by 17 coal mines of the Upper Silesian Coal Basin, Poland. Since the data set contained outliers, the construction of robust Partial Least Squares models for contaminated data set and the correct identification of outlying objects based on the robust scales were required. These enabled the development of the correct Partial Least Squares models, characterized by good fit and prediction abilities. The root mean square error was below 10% for all except for one the final Partial Least Squares models constructed, and the prediction error (root mean square error of cross–validation) exceeded 10% only for three models constructed. The study is of both cognitive and applicative importance. It presents the unique application of the chemometric methods of data exploration in modeling the content of trace elements in coal. In this way it contributes to the development of useful tools of coal quality assessment. PMID:27438794

First-Order System Least Squares for Velocity-Vorticity-Pressure Form of the Stokes Equations, with Application to Linear Elasticity

NASA Technical Reports Server (NTRS)

Cai, Zhiqiang; Manteuffel, Thomas A.; McCormick, Stephen F.

1996-01-01

In this paper, we study the least-squares method for the generalized Stokes equations (including linear elasticity) based on the velocity-vorticity-pressure formulation in d = 2 or 3 dimensions. The least squares functional is defined in terms of the sum of the L(exp 2)- and H(exp -1)-norms of the residual equations, which is weighted appropriately by by the Reynolds number. Our approach for establishing ellipticity of the functional does not use ADN theory, but is founded more on basic principles. We also analyze the case where the H(exp -1)-norm in the functional is replaced by a discrete functional to make the computation feasible. We show that the resulting algebraic equations can be uniformly preconditioned by well-known techniques.

Least Square Regression Method for Estimating Gas Concentration in an Electronic Nose System

PubMed Central

Khalaf, Walaa; Pace, Calogero; Gaudioso, Manlio

2009-01-01

We describe an Electronic Nose (ENose) system which is able to identify the type of analyte and to estimate its concentration. The system consists of seven sensors, five of them being gas sensors (supplied with different heater voltage values), the remainder being a temperature and a humidity sensor, respectively. To identify a new analyte sample and then to estimate its concentration, we use both some machine learning techniques and the least square regression principle. In fact, we apply two different training models; the first one is based on the Support Vector Machine (SVM) approach and is aimed at teaching the system how to discriminate among different gases, while the second one uses the least squares regression approach to predict the concentration of each type of analyte. PMID:22573980

Sound reproduction in personal audio systems using the least-squares approach with acoustic contrast control constraint.

PubMed

Cai, Yefeng; Wu, Ming; Yang, Jun

2014-02-01

This paper describes a method for focusing the reproduced sound in the bright zone without disturbing other people in the dark zone in personal audio systems. The proposed method combines the least-squares and acoustic contrast criteria. A constrained parameter is introduced to tune the balance between two performance indices, namely, the acoustic contrast and the spatial average error. An efficient implementation of this method using convex optimization is presented. Offline simulations and real-time experiments using a linear loudspeaker array are conducted to evaluate the performance of the presented method. Results show that compared with the traditional acoustic contrast control method, the proposed method can improve the flatness of response in the bright zone by sacrificing the level of acoustic contrast.

Deconvolution of Voltage Sensor Time Series and Electro-diffusion Modeling Reveal the Role of Spine Geometry in Controlling Synaptic Strength.

PubMed

Cartailler, Jerome; Kwon, Taekyung; Yuste, Rafael; Holcman, David

2018-03-07

Most synaptic excitatory connections are made on dendritic spines. But how the voltage in spines is modulated by its geometry remains unclear. To investigate the electrical properties of spines, we combine voltage imaging data with electro-diffusion modeling. We first present a temporal deconvolution procedure for the genetically encoded voltage sensor expressed in hippocampal cultured neurons and then use electro-diffusion theory to compute the electric field and the current-voltage conversion. We extract a range for the neck resistances of 〈R〉=100±35MΩ. When a significant current is injected in a spine, the neck resistance can be inversely proportional to its radius, but not to the radius square, as predicted by Ohm's law. We conclude that the postsynaptic voltage cannot only be modulated by changing the number of receptors, but also by the spine geometry. Thus, spine morphology could be a key component in determining synaptic transduction and plasticity. Copyright © 2018 Elsevier Inc. All rights reserved.

Adaptive Optics Image Restoration Based on Frame Selection and Multi-frame Blind Deconvolution

NASA Astrophysics Data System (ADS)

Tian, Yu; Rao, Chang-hui; Wei, Kai

Restricted by the observational condition and the hardware, adaptive optics can only make a partial correction of the optical images blurred by atmospheric turbulence. A postprocessing method based on frame selection and multi-frame blind deconvolution is proposed for the restoration of high-resolution adaptive optics images. By frame selection we mean we first make a selection of the degraded (blurred) images for participation in the iterative blind deconvolution calculation, with no need of any a priori knowledge, and with only a positivity constraint. This method has been applied to the restoration of some stellar images observed by the 61-element adaptive optics system installed on the Yunnan Observatory 1.2m telescope. The experimental results indicate that this method can effectively compensate for the residual errors of the adaptive optics system on the image, and the restored image can reach the diffraction-limited quality.

Selective Weighted Least Squares Method for Fourier Transform Infrared Quantitative Analysis.

PubMed

Wang, Xin; Li, Yan; Wei, Haoyun; Chen, Xia

2017-06-01

Classical least squares (CLS) regression is a popular multivariate statistical method used frequently for quantitative analysis using Fourier transform infrared (FT-IR) spectrometry. Classical least squares provides the best unbiased estimator for uncorrelated residual errors with zero mean and equal variance. However, the noise in FT-IR spectra, which accounts for a large portion of the residual errors, is heteroscedastic. Thus, if this noise with zero mean dominates in the residual errors, the weighted least squares (WLS) regression method described in this paper is a better estimator than CLS. However, if bias errors, such as the residual baseline error, are significant, WLS may perform worse than CLS. In this paper, we compare the effect of noise and bias error in using CLS and WLS in quantitative analysis. Results indicated that for wavenumbers with low absorbance, the bias error significantly affected the error, such that the performance of CLS is better than that of WLS. However, for wavenumbers with high absorbance, the noise significantly affected the error, and WLS proves to be better than CLS. Thus, we propose a selective weighted least squares (SWLS) regression that processes data with different wavenumbers using either CLS or WLS based on a selection criterion, i.e., lower or higher than an absorbance threshold. The effects of various factors on the optimal threshold value (OTV) for SWLS have been studied through numerical simulations. These studies reported that: (1) the concentration and the analyte type had minimal effect on OTV; and (2) the major factor that influences OTV is the ratio between the bias error and the standard deviation of the noise. The last part of this paper is dedicated to quantitative analysis of methane gas spectra, and methane/toluene mixtures gas spectra as measured using FT-IR spectrometry and CLS, WLS, and SWLS. The standard error of prediction (SEP), bias of prediction (bias), and the residual sum of squares of the errors (RSS) from the three quantitative analyses were compared. In methane gas analysis, SWLS yielded the lowest SEP and RSS among the three methods. In methane/toluene mixture gas analysis, a modification of the SWLS has been presented to tackle the bias error from other components. The SWLS without modification presents the lowest SEP in all cases but not bias and RSS. The modification of SWLS reduced the bias, which showed a lower RSS than CLS, especially for small components.

Sparse partial least squares regression for simultaneous dimension reduction and variable selection

PubMed Central

Chun, Hyonho; Keleş, Sündüz

2010-01-01

Partial least squares regression has been an alternative to ordinary least squares for handling multicollinearity in several areas of scientific research since the 1960s. It has recently gained much attention in the analysis of high dimensional genomic data. We show that known asymptotic consistency of the partial least squares estimator for a univariate response does not hold with the very large p and small n paradigm. We derive a similar result for a multivariate response regression with partial least squares. We then propose a sparse partial least squares formulation which aims simultaneously to achieve good predictive performance and variable selection by producing sparse linear combinations of the original predictors. We provide an efficient implementation of sparse partial least squares regression and compare it with well-known variable selection and dimension reduction approaches via simulation experiments. We illustrate the practical utility of sparse partial least squares regression in a joint analysis of gene expression and genomewide binding data. PMID:20107611

WE-AB-207A-03: A CBCT Head Scanner for Point-Of-Care Imaging of Intracranial Hemorrhage

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, J; Sisniega, A; Zbijewski, W

Purpose: This work reports the design, development, and first technical assessment of a cone-beam CT (CBCT) scanner developed specifically for imaging of acute intracranial hemorrhage (ICH) at the point of care, with target applications in diagnosis and monitoring of traumatic brain injury, stroke, and postsurgical hemorrhage. Methods: System design employed a task-based image quality model to quantify the influence of factors such as additive noise and high-gain (HG) detector readout on ICH detectability. Three bowtie filters with varying bare-beam attenuation strength and curvature were designed to enable HG readout without detector saturation, and a polyenergetic gain correction was developed tomore » minimize artifacts from bowtie flood-field calibration. Image reconstruction used an iterative penalized weighted least squares (PWLS) method with artifact correction including Monte Carlo scatter estimation, Joseph-Spital beam hardening correction, and spatiotemporal deconvolution of detector glare and lag. Radiation dose was characterized for half-scan and full-scan protocols at various kV, and imaging performance was assessed in a head phantom presenting simulated ICH with diameter ranging 2–12 mm. Results: The image quality model guided system design and was validated by measurements on a CBCT imaging bench. Compared to low-gain readout without a bowtie filter, the combination of HG readout and a modest bowtie improved the contrast-to-noise ratio (CNR per unit square-root dose) by 20% in the center of the image but degraded noise performance near the periphery (20% reduction in CNR). Low-frequency bowtie artifacts (∼100 HU magnitude) were corrected by the polyenergetic gain correction. Image reconstructions on the prototype scanner demonstrate clear visibility of the smallest ICH insert (2 mm diameter) in both HG readout (with a bowtie) and dual-gain readout (without bowtie). Conclusion: Technical assessment of the prototype scanner suggests the capability for reliable visualization of small (2 mm), low-contrast (50 HU) ICH at <20 mGy dose and motivates translation to clinical studies, now underway. Xiaohui Wang and David Foos (co-authors) are employees of Carestream Health. Research funding support from Carestream Health.« less

Histogram deconvolution - An aid to automated classifiers

NASA Technical Reports Server (NTRS)

Lorre, J. J.

1983-01-01

It is shown that N-dimensional histograms are convolved by the addition of noise in the picture domain. Three methods are described which provide the ability to deconvolve such noise-affected histograms. The purpose of the deconvolution is to provide automated classifiers with a higher quality N-dimensional histogram from which to obtain classification statistics.

A feasibility and optimization study to determine cooling time and burnup of advanced test reactor fuels using a nondestructive technique

NASA Astrophysics Data System (ADS)

Navarro, Jorge

The goal of this study presented is to determine the best available nondestructive technique necessary to collect validation data as well as to determine burnup and cooling time of the fuel elements on-site at the Advanced Test Reactor (ATR) canal. This study makes a recommendation of the viability of implementing a permanent fuel scanning system at the ATR canal and leads to the full design of a permanent fuel scan system. The study consisted at first in determining if it was possible and which equipment was necessary to collect useful spectra from ATR fuel elements at the canal adjacent to the reactor. Once it was establish that useful spectra can be obtained at the ATR canal, the next step was to determine which detector and which configuration was better suited to predict burnup and cooling time of fuel elements nondestructively. Three different detectors of High Purity Germanium (HPGe), Lanthanum Bromide (LaBr3), and High Pressure Xenon (HPXe) in two system configurations of above and below the water pool were used during the study. The data collected and analyzed were used to create burnup and cooling time calibration prediction curves for ATR fuel. The next stage of the study was to determine which of the three detectors tested was better suited for the permanent system. From spectra taken and the calibration curves obtained, it was determined that although the HPGe detector yielded better results, a detector that could better withstand the harsh environment of the ATR canal was needed. The in-situ nature of the measurements required a rugged fuel scanning system, low in maintenance and easy to control system. Based on the ATR canal feasibility measurements and calibration results, it was determined that the LaBr3 detector was the best alternative for canal in-situ measurements; however, in order to enhance the quality of the spectra collected using this scintillator, a deconvolution method was developed. Following the development of the deconvolution method for ATR applications, the technique was tested using one-isotope, multi-isotope, and fuel simulated sources. Burnup calibrations were perfomed using convoluted and deconvoluted data. The calibrations results showed burnup prediction by this method improves using deconvolution. The final stage of the deconvolution method development was to perform an irradiation experiment in order to create a surrogate fuel source to test the deconvolution method using experimental data. A conceptual design of the fuel scan system is path forward using the rugged LaBr 3 detector in an above the water configuration and deconvolution algorithms.

The Multivariate Regression Statistics Strategy to Investigate Content-Effect Correlation of Multiple Components in Traditional Chinese Medicine Based on a Partial Least Squares Method.

PubMed

Peng, Ying; Li, Su-Ning; Pei, Xuexue; Hao, Kun

2018-03-01

Amultivariate regression statisticstrategy was developed to clarify multi-components content-effect correlation ofpanaxginseng saponins extract and predict the pharmacological effect by components content. In example 1, firstly, we compared pharmacological effects between panax ginseng saponins extract and individual saponin combinations. Secondly, we examined the anti-platelet aggregation effect in seven different saponin combinations of ginsenoside Rb1, Rg1, Rh, Rd, Ra3 and notoginsenoside R1. Finally, the correlation between anti-platelet aggregation and the content of multiple components was analyzed by a partial least squares algorithm. In example 2, firstly, 18 common peaks were identified in ten different batches of panax ginseng saponins extracts from different origins. Then, we investigated the anti-myocardial ischemia reperfusion injury effects of the ten different panax ginseng saponins extracts. Finally, the correlation between the fingerprints and the cardioprotective effects was analyzed by a partial least squares algorithm. Both in example 1 and 2, the relationship between the components content and pharmacological effect was modeled well by the partial least squares regression equations. Importantly, the predicted effect curve was close to the observed data of dot marked on the partial least squares regression model. This study has given evidences that themulti-component content is a promising information for predicting the pharmacological effects of traditional Chinese medicine.

Exact least squares adaptive beamforming using an orthogonalization network

NASA Astrophysics Data System (ADS)

Yuen, Stanley M.

1991-03-01

The pros and cons of various classical and state-of-the-art methods in adaptive array processing are discussed, and the relevant concepts and historical developments are pointed out. A set of easy-to-understand equations for facilitating derivation of any least-squares-based algorithm is derived. Using this set of equations and incorporating all of the useful properties associated with various techniques, an efficient solution to the real-time adaptive beamforming problem is developed.

Investigation into the Use of Normal and Half-Normal Plots for Interpreting Results from Screening Experiments.

DTIC Science & Technology

1987-03-25

by Lloyd (1952) using generalized least squares instead of ordinary least squares, and by Wilk, % 20 Gnanadesikan , and Freeny (1963) using a maximum...plot. The half-normal distribution is a special case of the gamma distribution proposed by Wilk, Gnanadesikan , and Huyett (1962). VARIATIONS ON THE... Gnanadesikan , R. Probability plotting methods for the analysis of data. Biometrika, 1968, 55, 1-17. This paper describes and discusses graphical techniques

Probability distribution functions for unit hydrographs with optimization using genetic algorithm

NASA Astrophysics Data System (ADS)

Ghorbani, Mohammad Ali; Singh, Vijay P.; Sivakumar, Bellie; H. Kashani, Mahsa; Atre, Atul Arvind; Asadi, Hakimeh

2017-05-01

A unit hydrograph (UH) of a watershed may be viewed as the unit pulse response function of a linear system. In recent years, the use of probability distribution functions (pdfs) for determining a UH has received much attention. In this study, a nonlinear optimization model is developed to transmute a UH into a pdf. The potential of six popular pdfs, namely two-parameter gamma, two-parameter Gumbel, two-parameter log-normal, two-parameter normal, three-parameter Pearson distribution, and two-parameter Weibull is tested on data from the Lighvan catchment in Iran. The probability distribution parameters are determined using the nonlinear least squares optimization method in two ways: (1) optimization by programming in Mathematica; and (2) optimization by applying genetic algorithm. The results are compared with those obtained by the traditional linear least squares method. The results show comparable capability and performance of two nonlinear methods. The gamma and Pearson distributions are the most successful models in preserving the rising and recession limbs of the unit hydographs. The log-normal distribution has a high ability in predicting both the peak flow and time to peak of the unit hydrograph. The nonlinear optimization method does not outperform the linear least squares method in determining the UH (especially for excess rainfall of one pulse), but is comparable.

Limited-memory BFGS based least-squares pre-stack Kirchhoff depth migration

NASA Astrophysics Data System (ADS)

Wu, Shaojiang; Wang, Yibo; Zheng, Yikang; Chang, Xu

2015-08-01

Least-squares migration (LSM) is a linearized inversion technique for subsurface reflectivity estimation. Compared to conventional migration algorithms, it can improve spatial resolution significantly with a few iterative calculations. There are three key steps in LSM, (1) calculate data residuals between observed data and demigrated data using the inverted reflectivity model; (2) migrate data residuals to form reflectivity gradient and (3) update reflectivity model using optimization methods. In order to obtain an accurate and high-resolution inversion result, the good estimation of inverse Hessian matrix plays a crucial role. However, due to the large size of Hessian matrix, the inverse matrix calculation is always a tough task. The limited-memory BFGS (L-BFGS) method can evaluate the Hessian matrix indirectly using a limited amount of computer memory which only maintains a history of the past m gradients (often m < 10). We combine the L-BFGS method with least-squares pre-stack Kirchhoff depth migration. Then, we validate the introduced approach by the 2-D Marmousi synthetic data set and a 2-D marine data set. The results show that the introduced method can effectively obtain reflectivity model and has a faster convergence rate with two comparison gradient methods. It might be significant for general complex subsurface imaging.

Identification of Reliable Components in Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS): a Data-Driven Approach across Metabolic Processes.

PubMed

Motegi, Hiromi; Tsuboi, Yuuri; Saga, Ayako; Kagami, Tomoko; Inoue, Maki; Toki, Hideaki; Minowa, Osamu; Noda, Tetsuo; Kikuchi, Jun

2015-11-04

There is an increasing need to use multivariate statistical methods for understanding biological functions, identifying the mechanisms of diseases, and exploring biomarkers. In addition to classical analyses such as hierarchical cluster analysis, principal component analysis, and partial least squares discriminant analysis, various multivariate strategies, including independent component analysis, non-negative matrix factorization, and multivariate curve resolution, have recently been proposed. However, determining the number of components is problematic. Despite the proposal of several different methods, no satisfactory approach has yet been reported. To resolve this problem, we implemented a new idea: classifying a component as "reliable" or "unreliable" based on the reproducibility of its appearance, regardless of the number of components in the calculation. Using the clustering method for classification, we applied this idea to multivariate curve resolution-alternating least squares (MCR-ALS). Comparisons between conventional and modified methods applied to proton nuclear magnetic resonance ((1)H-NMR) spectral datasets derived from known standard mixtures and biological mixtures (urine and feces of mice) revealed that more plausible results are obtained by the modified method. In particular, clusters containing little information were detected with reliability. This strategy, named "cluster-aided MCR-ALS," will facilitate the attainment of more reliable results in the metabolomics datasets.

New robust bilinear least squares method for the analysis of spectral-pH matrix data.

PubMed

Goicoechea, Héctor C; Olivieri, Alejandro C

2005-07-01

A new second-order multivariate method has been developed for the analysis of spectral-pH matrix data, based on a bilinear least-squares (BLLS) model achieving the second-order advantage and handling multiple calibration standards. A simulated Monte Carlo study of synthetic absorbance-pH data allowed comparison of the newly proposed BLLS methodology with constrained parallel factor analysis (PARAFAC) and with the combination multivariate curve resolution-alternating least-squares (MCR-ALS) technique under different conditions of sample-to-sample pH mismatch and analyte-background ratio. The results indicate an improved prediction ability for the new method. Experimental data generated by measuring absorption spectra of several calibration standards of ascorbic acid and samples of orange juice were subjected to second-order calibration analysis with PARAFAC, MCR-ALS, and the new BLLS method. The results indicate that the latter method provides the best analytical results in regard to analyte recovery in samples of complex composition requiring strict adherence to the second-order advantage. Linear dependencies appear when multivariate data are produced by using the pH or a reaction time as one of the data dimensions, posing a challenge to classical multivariate calibration models. The presently discussed algorithm is useful for these latter systems.

A comparison of deconvolution and the Rutland-Patlak plot in parenchymal renal uptake rate.

PubMed

Al-Shakhrah, Issa A

2012-07-01

Deconvolution and the Rutland-Patlak (R-P) plot are two of the most commonly used methods for analyzing dynamic radionuclide renography. Both methods allow estimation of absolute and relative renal uptake of radiopharmaceutical and of its rate of transit through the kidney. Seventeen patients (32 kidneys) were referred for further evaluation by renal scanning. All patients were positioned supine with their backs to the scintillation gamma camera, so that the kidneys and the heart are both in the field of view. Approximately 5-7 mCi of (99m)Tc-DTPA (diethylinetriamine penta-acetic acid) in about 0.5 ml of saline is injected intravenously and sequential 20 s frames were acquired, the study on each patient lasts for approximately 20 min. The time-activity curves of the parenchymal region of interest of each kidney, as well as the heart were obtained for analysis. The data were then analyzed with deconvolution and the R-P plot. A strong positive association (n = 32; r = 0.83; R (2) = 0.68) was found between the values that obtained by applying the two methods. Bland-Altman statistical analysis demonstrated that ninety seven percent of the values in the study (31 cases from 32 cases, 97% of the cases) were within limits of agreement (mean ± 1.96 standard deviation). We believe that R-P analysis method is expected to be more reproducible than iterative deconvolution method, because the deconvolution technique (the iterative method) relies heavily on the accuracy of the first point analyzed, as any errors are carried forward into the calculations of all the subsequent points, whereas R-P technique is based on an initial analysis of the data by means of the R-P plot, and it can be considered as an alternative technique to find and calculate the renal uptake rate.

Comparison between the basic least squares and the Bayesian approach for elastic constants identification

NASA Astrophysics Data System (ADS)

Gogu, C.; Haftka, R.; LeRiche, R.; Molimard, J.; Vautrin, A.; Sankar, B.

2008-11-01

The basic formulation of the least squares method, based on the L2 norm of the misfit, is still widely used today for identifying elastic material properties from experimental data. An alternative statistical approach is the Bayesian method. We seek here situations with significant difference between the material properties found by the two methods. For a simple three bar truss example we illustrate three such situations in which the Bayesian approach leads to more accurate results: different magnitude of the measurements, different uncertainty in the measurements and correlation among measurements. When all three effects add up, the Bayesian approach can have a large advantage. We then compared the two methods for identification of elastic constants from plate vibration natural frequencies.

Genetic Algorithm for Initial Orbit Determination with Too Short Arc (Continued)

NASA Astrophysics Data System (ADS)

Li, X. R.; Wang, X.

2016-03-01

When using the genetic algorithm to solve the problem of too-short-arc (TSA) determination, due to the difference of computing processes between the genetic algorithm and classical method, the methods for outliers editing are no longer applicable. In the genetic algorithm, the robust estimation is acquired by means of using different loss functions in the fitness function, then the outlier problem of TSAs is solved. Compared with the classical method, the application of loss functions in the genetic algorithm is greatly simplified. Through the comparison of results of different loss functions, it is clear that the methods of least median square and least trimmed square can greatly improve the robustness of TSAs, and have a high breakdown point.

The derivation of vector magnetic fields from Stokes profiles - Integral versus least squares fitting techniques

NASA Technical Reports Server (NTRS)

Ronan, R. S.; Mickey, D. L.; Orrall, F. Q.

1987-01-01

The results of two methods for deriving photospheric vector magnetic fields from the Zeeman effect, as observed in the Fe I line at 6302.5 A at high spectral resolution (45 mA), are compared. The first method does not take magnetooptical effects into account, but determines the vector magnetic field from the integral properties of the Stokes profiles. The second method is an iterative least-squares fitting technique which fits the observed Stokes profiles to the profiles predicted by the Unno-Rachkovsky solution to the radiative transfer equation. For sunspot fields above about 1500 gauss, the two methods are found to agree in derived azimuthal and inclination angles to within about + or - 20 deg.

Prediction Analysis for Measles Epidemics

NASA Astrophysics Data System (ADS)

Sumi, Ayako; Ohtomo, Norio; Tanaka, Yukio; Sawamura, Sadashi; Olsen, Lars Folke; Kobayashi, Nobumichi

2003-12-01

A newly devised procedure of prediction analysis, which is a linearized version of the nonlinear least squares method combined with the maximum entropy spectral analysis method, was proposed. This method was applied to time series data of measles case notification in several communities in the UK, USA and Denmark. The dominant spectral lines observed in each power spectral density (PSD) can be safely assigned as fundamental periods. The optimum least squares fitting (LSF) curve calculated using these fundamental periods can essentially reproduce the underlying variation of the measles data. An extension of the LSF curve can be used to predict measles case notification quantitatively. Some discussions including a predictability of chaotic time series are presented.

An Efficient Estimator for Moving Target Localization Using Multi-Station Dual-Frequency Radars.

PubMed

Huang, Jiyan; Zhang, Ying; Luo, Shan

2017-12-15

Localization of a moving target in a dual-frequency radars system has now gained considerable attention. The noncoherent localization approach based on a least squares (LS) estimator has been addressed in the literature. Compared with the LS method, a novel localization method based on a two-step weighted least squares estimator is proposed to increase positioning accuracy for a multi-station dual-frequency radars system in this paper. The effects of signal noise ratio and the number of samples on the performance of range estimation are also analyzed in the paper. Furthermore, both the theoretical variance and Cramer-Rao lower bound (CRLB) are derived. The simulation results verified the proposed method.

An Efficient Estimator for Moving Target Localization Using Multi-Station Dual-Frequency Radars

PubMed Central

Zhang, Ying; Luo, Shan

2017-01-01

Localization of a moving target in a dual-frequency radars system has now gained considerable attention. The noncoherent localization approach based on a least squares (LS) estimator has been addressed in the literature. Compared with the LS method, a novel localization method based on a two-step weighted least squares estimator is proposed to increase positioning accuracy for a multi-station dual-frequency radars system in this paper. The effects of signal noise ratio and the number of samples on the performance of range estimation are also analyzed in the paper. Furthermore, both the theoretical variance and Cramer–Rao lower bound (CRLB) are derived. The simulation results verified the proposed method. PMID:29244727

Least-squares dual characterization for ROI assessment in emission tomography

NASA Astrophysics Data System (ADS)

Ben Bouallègue, F.; Crouzet, J. F.; Dubois, A.; Buvat, I.; Mariano-Goulart, D.

2013-06-01

Our aim is to describe an original method for estimating the statistical properties of regions of interest (ROIs) in emission tomography. Drawn upon the works of Louis on the approximate inverse, we propose a dual formulation of the ROI estimation problem to derive the ROI activity and variance directly from the measured data without any image reconstruction. The method requires the definition of an ROI characteristic function that can be extracted from a co-registered morphological image. This characteristic function can be smoothed to optimize the resolution-variance tradeoff. An iterative procedure is detailed for the solution of the dual problem in the least-squares sense (least-squares dual (LSD) characterization), and a linear extrapolation scheme is described to compensate for sampling partial volume effect and reduce the estimation bias (LSD-ex). LSD and LSD-ex are compared with classical ROI estimation using pixel summation after image reconstruction and with Huesman's method. For this comparison, we used Monte Carlo simulations (GATE simulation tool) of 2D PET data of a Hoffman brain phantom containing three small uniform high-contrast ROIs and a large non-uniform low-contrast ROI. Our results show that the performances of LSD characterization are at least as good as those of the classical methods in terms of root mean square (RMS) error. For the three small tumor regions, LSD-ex allows a reduction in the estimation bias by up to 14%, resulting in a reduction in the RMS error of up to 8.5%, compared with the optimal classical estimation. For the large non-specific region, LSD using appropriate smoothing could intuitively and efficiently handle the resolution-variance tradeoff.

Kernel-based least squares policy iteration for reinforcement learning.

PubMed

Xu, Xin; Hu, Dewen; Lu, Xicheng

2007-07-01

In this paper, we present a kernel-based least squares policy iteration (KLSPI) algorithm for reinforcement learning (RL) in large or continuous state spaces, which can be used to realize adaptive feedback control of uncertain dynamic systems. By using KLSPI, near-optimal control policies can be obtained without much a priori knowledge on dynamic models of control plants. In KLSPI, Mercer kernels are used in the policy evaluation of a policy iteration process, where a new kernel-based least squares temporal-difference algorithm called KLSTD-Q is proposed for efficient policy evaluation. To keep the sparsity and improve the generalization ability of KLSTD-Q solutions, a kernel sparsification procedure based on approximate linear dependency (ALD) is performed. Compared to the previous works on approximate RL methods, KLSPI makes two progresses to eliminate the main difficulties of existing results. One is the better convergence and (near) optimality guarantee by using the KLSTD-Q algorithm for policy evaluation with high precision. The other is the automatic feature selection using the ALD-based kernel sparsification. Therefore, the KLSPI algorithm provides a general RL method with generalization performance and convergence guarantee for large-scale Markov decision problems (MDPs). Experimental results on a typical RL task for a stochastic chain problem demonstrate that KLSPI can consistently achieve better learning efficiency and policy quality than the previous least squares policy iteration (LSPI) algorithm. Furthermore, the KLSPI method was also evaluated on two nonlinear feedback control problems, including a ship heading control problem and the swing up control of a double-link underactuated pendulum called acrobot. Simulation results illustrate that the proposed method can optimize controller performance using little a priori information of uncertain dynamic systems. It is also demonstrated that KLSPI can be applied to online learning control by incorporating an initial controller to ensure online performance.

40 CFR 85.2114 - Basis of certification.

Code of Federal Regulations, 2014 CFR

2014-07-01

... calculated using the least squares straight line method, in accordance with § 86.088-28(a). The deterioration... requirements of this paragraph for at least the part's useful life mileage interval. (i) If an original... the aftermarket parts that accumulated at least its useful life mileage during the aging process under...

40 CFR 85.2114 - Basis of certification.

Code of Federal Regulations, 2012 CFR

2012-07-01

... calculated using the least squares straight line method, in accordance with § 86.088-28(a). The deterioration... requirements of this paragraph for at least the part's useful life mileage interval. (i) If an original... the aftermarket parts that accumulated at least its useful life mileage during the aging process under...

40 CFR 85.2114 - Basis of certification.

Code of Federal Regulations, 2011 CFR

2011-07-01

... calculated using the least squares straight line method, in accordance with § 86.088-28(a). The deterioration... requirements of this paragraph for at least the part's useful life mileage interval. (i) If an original... the aftermarket parts that accumulated at least its useful life mileage during the aging process under...

40 CFR 85.2114 - Basis of certification.

Code of Federal Regulations, 2013 CFR

2013-07-01

... calculated using the least squares straight line method, in accordance with § 86.088-28(a). The deterioration... requirements of this paragraph for at least the part's useful life mileage interval. (i) If an original... the aftermarket parts that accumulated at least its useful life mileage during the aging process under...

Efficient volumetric estimation from plenoptic data

NASA Astrophysics Data System (ADS)

Anglin, Paul; Reeves, Stanley J.; Thurow, Brian S.

2013-03-01

The commercial release of the Lytro camera, and greater availability of plenoptic imaging systems in general, have given the image processing community cost-effective tools for light-field imaging. While this data is most commonly used to generate planar images at arbitrary focal depths, reconstruction of volumetric fields is also possible. Similarly, deconvolution is a technique that is conventionally used in planar image reconstruction, or deblurring, algorithms. However, when leveraged with the ability of a light-field camera to quickly reproduce multiple focal planes within an imaged volume, deconvolution offers a computationally efficient method of volumetric reconstruction. Related research has shown than light-field imaging systems in conjunction with tomographic reconstruction techniques are also capable of estimating the imaged volume and have been successfully applied to particle image velocimetry (PIV). However, while tomographic volumetric estimation through algorithms such as multiplicative algebraic reconstruction techniques (MART) have proven to be highly accurate, they are computationally intensive. In this paper, the reconstruction problem is shown to be solvable by deconvolution. Deconvolution offers significant improvement in computational efficiency through the use of fast Fourier transforms (FFTs) when compared to other tomographic methods. This work describes a deconvolution algorithm designed to reconstruct a 3-D particle field from simulated plenoptic data. A 3-D extension of existing 2-D FFT-based refocusing techniques is presented to further improve efficiency when computing object focal stacks and system point spread functions (PSF). Reconstruction artifacts are identified; their underlying source and methods of mitigation are explored where possible, and reconstructions of simulated particle fields are provided.

Automated processing for proton spectroscopic imaging using water reference deconvolution.

PubMed

Maudsley, A A; Wu, Z; Meyerhoff, D J; Weiner, M W

1994-06-01

Automated formation of MR spectroscopic images (MRSI) is necessary before routine application of these methods is possible for in vivo studies; however, this task is complicated by the presence of spatially dependent instrumental distortions and the complex nature of the MR spectrum. A data processing method is presented for completely automated formation of in vivo proton spectroscopic images, and applied for analysis of human brain metabolites. This procedure uses the water reference deconvolution method (G. A. Morris, J. Magn. Reson. 80, 547(1988)) to correct for line shape distortions caused by instrumental and sample characteristics, followed by parametric spectral analysis. Results for automated image formation were found to compare favorably with operator dependent spectral integration methods. While the water reference deconvolution processing was found to provide good correction of spatially dependent resonance frequency shifts, it was found to be susceptible to errors for correction of line shape distortions. These occur due to differences between the water reference and the metabolite distributions.

A Robust Deconvolution Method based on Transdimensional Hierarchical Bayesian Inference

NASA Astrophysics Data System (ADS)

Kolb, J.; Lekic, V.

2012-12-01

Analysis of P-S and S-P conversions allows us to map receiver side crustal and lithospheric structure. This analysis often involves deconvolution of the parent wave field from the scattered wave field as a means of suppressing source-side complexity. A variety of deconvolution techniques exist including damped spectral division, Wiener filtering, iterative time-domain deconvolution, and the multitaper method. All of these techniques require estimates of noise characteristics as input parameters. We present a deconvolution method based on transdimensional Hierarchical Bayesian inference in which both noise magnitude and noise correlation are used as parameters in calculating the likelihood probability distribution. Because the noise for P-S and S-P conversion analysis in terms of receiver functions is a combination of both background noise - which is relatively easy to characterize - and signal-generated noise - which is much more difficult to quantify - we treat measurement errors as an known quantity, characterized by a probability density function whose mean and variance are model parameters. This transdimensional Hierarchical Bayesian approach has been successfully used previously in the inversion of receiver functions in terms of shear and compressional wave speeds of an unknown number of layers [1]. In our method we used a Markov chain Monte Carlo (MCMC) algorithm to find the receiver function that best fits the data while accurately assessing the noise parameters. In order to parameterize the receiver function we model the receiver function as an unknown number of Gaussians of unknown amplitude and width. The algorithm takes multiple steps before calculating the acceptance probability of a new model, in order to avoid getting trapped in local misfit minima. Using both observed and synthetic data, we show that the MCMC deconvolution method can accurately obtain a receiver function as well as an estimate of the noise parameters given the parent and daughter components. Furthermore, we demonstrate that this new approach is far less susceptible to generating spurious features even at high noise levels. Finally, the method yields not only the most-likely receiver function, but also quantifies its full uncertainty. [1] Bodin, T., M. Sambridge, H. Tkalčić, P. Arroucau, K. Gallagher, and N. Rawlinson (2012), Transdimensional inversion of receiver functions and surface wave dispersion, J. Geophys. Res., 117, B02301

Mitigating Errors in External Respiratory Surrogate-Based Models of Tumor Position

DOE Office of Scientific and Technical Information (OSTI.GOV)

Malinowski, Kathleen T.; Fischell Department of Bioengineering, University of Maryland, College Park, MD; McAvoy, Thomas J.

2012-04-01

Purpose: To investigate the effect of tumor site, measurement precision, tumor-surrogate correlation, training data selection, model design, and interpatient and interfraction variations on the accuracy of external marker-based models of tumor position. Methods and Materials: Cyberknife Synchrony system log files comprising synchronously acquired positions of external markers and the tumor from 167 treatment fractions were analyzed. The accuracy of Synchrony, ordinary-least-squares regression, and partial-least-squares regression models for predicting the tumor position from the external markers was evaluated. The quantity and timing of the data used to build the predictive model were varied. The effects of tumor-surrogate correlation and the precisionmore » in both the tumor and the external surrogate position measurements were explored by adding noise to the data. Results: The tumor position prediction errors increased during the duration of a fraction. Increasing the training data quantities did not always lead to more accurate models. Adding uncorrelated noise to the external marker-based inputs degraded the tumor-surrogate correlation models by 16% for partial-least-squares and 57% for ordinary-least-squares. External marker and tumor position measurement errors led to tumor position prediction changes 0.3-3.6 times the magnitude of the measurement errors, varying widely with model algorithm. The tumor position prediction errors were significantly associated with the patient index but not with the fraction index or tumor site. Partial-least-squares was as accurate as Synchrony and more accurate than ordinary-least-squares. Conclusions: The accuracy of surrogate-based inferential models of tumor position was affected by all the investigated factors, except for the tumor site and fraction index.« less

An improved method to estimate reflectance parameters for high dynamic range imaging

NASA Astrophysics Data System (ADS)

Li, Shiying; Deguchi, Koichiro; Li, Renfa; Manabe, Yoshitsugu; Chihara, Kunihiro

2008-01-01

Two methods are described to accurately estimate diffuse and specular reflectance parameters for colors, gloss intensity and surface roughness, over the dynamic range of the camera used to capture input images. Neither method needs to segment color areas on an image, or to reconstruct a high dynamic range (HDR) image. The second method improves on the first, bypassing the requirement for specific separation of diffuse and specular reflection components. For the latter method, diffuse and specular reflectance parameters are estimated separately, using the least squares method. Reflection values are initially assumed to be diffuse-only reflection components, and are subjected to the least squares method to estimate diffuse reflectance parameters. Specular reflection components, obtained by subtracting the computed diffuse reflection components from reflection values, are then subjected to a logarithmically transformed equation of the Torrance-Sparrow reflection model, and specular reflectance parameters for gloss intensity and surface roughness are finally estimated using the least squares method. Experiments were carried out using both methods, with simulation data at different saturation levels, generated according to the Lambert and Torrance-Sparrow reflection models, and the second method, with spectral images captured by an imaging spectrograph and a moving light source. Our results show that the second method can estimate the diffuse and specular reflectance parameters for colors, gloss intensity and surface roughness more accurately and faster than the first one, so that colors and gloss can be reproduced more efficiently for HDR imaging.

Minimum entropy deconvolution optimized sinusoidal synthesis and its application to vibration based fault detection

NASA Astrophysics Data System (ADS)

Li, Gang; Zhao, Qing

2017-03-01

In this paper, a minimum entropy deconvolution based sinusoidal synthesis (MEDSS) filter is proposed to improve the fault detection performance of the regular sinusoidal synthesis (SS) method. The SS filter is an efficient linear predictor that exploits the frequency properties during model construction. The phase information of the harmonic components is not used in the regular SS filter. However, the phase relationships are important in differentiating noise from characteristic impulsive fault signatures. Therefore, in this work, the minimum entropy deconvolution (MED) technique is used to optimize the SS filter during the model construction process. A time-weighted-error Kalman filter is used to estimate the MEDSS model parameters adaptively. Three simulation examples and a practical application case study are provided to illustrate the effectiveness of the proposed method. The regular SS method and the autoregressive MED (ARMED) method are also implemented for comparison. The MEDSS model has demonstrated superior performance compared to the regular SS method and it also shows comparable or better performance with much less computational intensity than the ARMED method.

GSTAR-SUR Modeling With Calendar Variations And Intervention To Forecast Outflow Of Currencies In Java Indonesia

NASA Astrophysics Data System (ADS)

Akbar, M. S.; Setiawan; Suhartono; Ruchjana, B. N.; Riyadi, M. A. A.

2018-03-01

Ordinary Least Squares (OLS) is general method to estimates Generalized Space Time Autoregressive (GSTAR) parameters. But in some cases, the residuals of GSTAR are correlated between location. If OLS is applied to this case, then the estimators are inefficient. Generalized Least Squares (GLS) is a method used in Seemingly Unrelated Regression (SUR) model. This method estimated parameters of some models with residuals between equations are correlated. Simulation study shows that GSTAR with GLS method for estimating parameters (GSTAR-SUR) is more efficient than GSTAR-OLS method. The purpose of this research is to apply GSTAR-SUR with calendar variation and intervention as exogenous variable (GSTARX-SUR) for forecast outflow of currency in Java, Indonesia. As a result, GSTARX-SUR provides better performance than GSTARX-OLS.

Concerning an application of the method of least squares with a variable weight matrix

NASA Technical Reports Server (NTRS)

Sukhanov, A. A.

1979-01-01

An estimate of a state vector for a physical system when the weight matrix in the method of least squares is a function of this vector is considered. An iterative procedure is proposed for calculating the desired estimate. Conditions for the existence and uniqueness of the limit of this procedure are obtained, and a domain is found which contains the limit estimate. A second method for calculating the desired estimate which reduces to the solution of a system of algebraic equations is proposed. The question of applying Newton's method of tangents to solving the given system of algebraic equations is considered and conditions for the convergence of the modified Newton's method are obtained. Certain properties of the estimate obtained are presented together with an example.

Determination of propranolol hydrochloride in pharmaceutical preparations using near infrared spectrometry with fiber optic probe and multivariate calibration methods.

PubMed

Marques Junior, Jucelino Medeiros; Muller, Aline Lima Hermes; Foletto, Edson Luiz; da Costa, Adilson Ben; Bizzi, Cezar Augusto; Irineu Muller, Edson

2015-01-01

A method for determination of propranolol hydrochloride in pharmaceutical preparation using near infrared spectrometry with fiber optic probe (FTNIR/PROBE) and combined with chemometric methods was developed. Calibration models were developed using two variable selection models: interval partial least squares (iPLS) and synergy interval partial least squares (siPLS). The treatments based on the mean centered data and multiplicative scatter correction (MSC) were selected for models construction. A root mean square error of prediction (RMSEP) of 8.2 mg g(-1) was achieved using siPLS (s2i20PLS) algorithm with spectra divided into 20 intervals and combination of 2 intervals (8501 to 8801 and 5201 to 5501 cm(-1)). Results obtained by the proposed method were compared with those using the pharmacopoeia reference method and significant difference was not observed. Therefore, proposed method allowed a fast, precise, and accurate determination of propranolol hydrochloride in pharmaceutical preparations. Furthermore, it is possible to carry out on-line analysis of this active principle in pharmaceutical formulations with use of fiber optic probe.

Local classification: Locally weighted-partial least squares-discriminant analysis (LW-PLS-DA).

PubMed

Bevilacqua, Marta; Marini, Federico

2014-08-01

The possibility of devising a simple, flexible and accurate non-linear classification method, by extending the locally weighted partial least squares (LW-PLS) approach to the cases where the algorithm is used in a discriminant way (partial least squares discriminant analysis, PLS-DA), is presented. In particular, to assess which category an unknown sample belongs to, the proposed algorithm operates by identifying which training objects are most similar to the one to be predicted and building a PLS-DA model using these calibration samples only. Moreover, the influence of the selected training samples on the local model can be further modulated by adopting a not uniform distance-based weighting scheme which allows the farthest calibration objects to have less impact than the closest ones. The performances of the proposed locally weighted-partial least squares-discriminant analysis (LW-PLS-DA) algorithm have been tested on three simulated data sets characterized by a varying degree of non-linearity: in all cases, a classification accuracy higher than 99% on external validation samples was achieved. Moreover, when also applied to a real data set (classification of rice varieties), characterized by a high extent of non-linearity, the proposed method provided an average correct classification rate of about 93% on the test set. By the preliminary results, showed in this paper, the performances of the proposed LW-PLS-DA approach have proved to be comparable and in some cases better than those obtained by other non-linear methods (k nearest neighbors, kernel-PLS-DA and, in the case of rice, counterpropagation neural networks). Copyright © 2014 Elsevier B.V. All rights reserved.

On estimating gravity anomalies: A comparison of least squares collocation with least squares techniques

NASA Technical Reports Server (NTRS)

Argentiero, P.; Lowrey, B.

1976-01-01

The least squares collocation algorithm for estimating gravity anomalies from geodetic data is shown to be an application of the well known regression equations which provide the mean and covariance of a random vector (gravity anomalies) given a realization of a correlated random vector (geodetic data). It is also shown that the collocation solution for gravity anomalies is equivalent to the conventional least-squares-Stokes' function solution when the conventional solution utilizes properly weighted zero a priori estimates. The mathematical and physical assumptions underlying the least squares collocation estimator are described, and its numerical properties are compared with the numerical properties of the conventional least squares estimator.

From least squares to multilevel modeling: A graphical introduction to Bayesian inference

NASA Astrophysics Data System (ADS)

Loredo, Thomas J.

2016-01-01

This tutorial presentation will introduce some of the key ideas and techniques involved in applying Bayesian methods to problems in astrostatistics. The focus will be on the big picture: understanding the foundations (interpreting probability, Bayes's theorem, the law of total probability and marginalization), making connections to traditional methods (propagation of errors, least squares, chi-squared, maximum likelihood, Monte Carlo simulation), and highlighting problems where a Bayesian approach can be particularly powerful (Poisson processes, density estimation and curve fitting with measurement error). The "graphical" component of the title reflects an emphasis on pictorial representations of some of the math, but also on the use of graphical models (multilevel or hierarchical models) for analyzing complex data. Code for some examples from the talk will be available to participants, in Python and in the Stan probabilistic programming language.

Methods for Improving Information from ’Undesigned’ Human Factors Experiments.

DTIC Science & Technology

Human factors engineering, Information processing, Regression analysis , Experimental design, Least squares method, Analysis of variance, Correlation techniques, Matrices(Mathematics), Multiple disciplines, Mathematical prediction

On recursive least-squares filtering algorithms and implementations. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Hsieh, Shih-Fu

1990-01-01

In many real-time signal processing applications, fast and numerically stable algorithms for solving least-squares problems are necessary and important. In particular, under non-stationary conditions, these algorithms must be able to adapt themselves to reflect the changes in the system and take appropriate adjustments to achieve optimum performances. Among existing algorithms, the QR-decomposition (QRD)-based recursive least-squares (RLS) methods have been shown to be useful and effective for adaptive signal processing. In order to increase the speed of processing and achieve high throughput rate, many algorithms are being vectorized and/or pipelined to facilitate high degrees of parallelism. A time-recursive formulation of RLS filtering employing block QRD will be considered first. Several methods, including a new non-continuous windowing scheme based on selectively rejecting contaminated data, were investigated for adaptive processing. Based on systolic triarrays, many other forms of systolic arrays are shown to be capable of implementing different algorithms. Various updating and downdating systolic algorithms and architectures for RLS filtering are examined and compared in details, which include Householder reflector, Gram-Schmidt procedure, and Givens rotation. A unified approach encompassing existing square-root-free algorithms is also proposed. For the sinusoidal spectrum estimation problem, a judicious method of separating the noise from the signal is of great interest. Various truncated QR methods are proposed for this purpose and compared to the truncated SVD method. Computer simulations provided for detailed comparisons show the effectiveness of these methods. This thesis deals with fundamental issues of numerical stability, computational efficiency, adaptivity, and VLSI implementation for the RLS filtering problems. In all, various new and modified algorithms and architectures are proposed and analyzed; the significance of any of the new method depends crucially on specific application.

Weighted Least Squares Fitting Using Ordinary Least Squares Algorithms.

ERIC Educational Resources Information Center

Kiers, Henk A. L.

1997-01-01

A general approach for fitting a model to a data matrix by weighted least squares (WLS) is studied. The approach consists of iteratively performing steps of existing algorithms for ordinary least squares fitting of the same model and is based on maximizing a function that majorizes WLS loss function. (Author/SLD)

Least-Squares Models to Correct for Rater Effects in Performance Assessment.

ERIC Educational Resources Information Center

Raymond, Mark R.; Viswesvaran, Chockalingam

This study illustrates the use of three least-squares models to control for rater effects in performance evaluation: (1) ordinary least squares (OLS); (2) weighted least squares (WLS); and (3) OLS subsequent to applying a logistic transformation to observed ratings (LOG-OLS). The three models were applied to ratings obtained from four…

Comparison of techniques for approximating ocean bottom topography in a wave-refraction computer model

NASA Technical Reports Server (NTRS)

Poole, L. R.

1975-01-01

A study of the effects of using different methods for approximating bottom topography in a wave-refraction computer model was conducted. Approximation techniques involving quadratic least squares, cubic least squares, and constrained bicubic polynomial interpolation were compared for computed wave patterns and parameters in the region of Saco Bay, Maine. Although substantial local differences can be attributed to use of the different approximation techniques, results indicated that overall computed wave patterns and parameter distributions were quite similar.

Matrix-Free Polynomial-Based Nonlinear Least Squares Optimized Preconditioning and its Application to Discontinuous Galerkin Discretizations of the Euler Equations

DTIC Science & Technology

2015-06-01

cient parallel code for applying the operator. Our method constructs a polynomial preconditioner using a nonlinear least squares (NLLS) algorithm. We show...apply the underlying operator. Such a preconditioner can be very attractive in scenarios where one has a highly efficient parallel code for applying...repeatedly solve a large system of linear equations where one has an extremely fast parallel code for applying an underlying fixed linear operator

Least-squares finite element solutions for three-dimensional backward-facing step flow

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Hou, Lin-Jun; Lin, Tsung-Liang

1993-01-01

Comprehensive numerical solutions of the steady state incompressible viscous flow over a three-dimensional backward-facing step up to Re equals 800 are presented. The results are obtained by the least-squares finite element method (LSFEM) which is based on the velocity-pressure-vorticity formulation. The computed model is of the same size as that of Armaly's experiment. Three-dimensional phenomena are observed even at low Reynolds number. The calculated values of the primary reattachment length are in good agreement with experimental results.

A new finite element formulation for computational fluid dynamics. IX - Fourier analysis of space-time Galerkin/least-squares algorithms

NASA Technical Reports Server (NTRS)

Shakib, Farzin; Hughes, Thomas J. R.

1991-01-01

A Fourier stability and accuracy analysis of the space-time Galerkin/least-squares method as applied to a time-dependent advective-diffusive model problem is presented. Two time discretizations are studied: a constant-in-time approximation and a linear-in-time approximation. Corresponding space-time predictor multi-corrector algorithms are also derived and studied. The behavior of the space-time algorithms is compared to algorithms based on semidiscrete formulations.

Weighted least squares phase unwrapping based on the wavelet transform

NASA Astrophysics Data System (ADS)

Chen, Jiafeng; Chen, Haiqin; Yang, Zhengang; Ren, Haixia

2007-01-01

The weighted least squares phase unwrapping algorithm is a robust and accurate method to solve phase unwrapping problem. This method usually leads to a large sparse linear equation system. Gauss-Seidel relaxation iterative method is usually used to solve this large linear equation. However, this method is not practical due to its extremely slow convergence. The multigrid method is an efficient algorithm to improve convergence rate. However, this method needs an additional weight restriction operator which is very complicated. For this reason, the multiresolution analysis method based on the wavelet transform is proposed. By applying the wavelet transform, the original system is decomposed into its coarse and fine resolution levels and an equivalent equation system with better convergence condition can be obtained. Fast convergence in separate coarse resolution levels speeds up the overall system convergence rate. The simulated experiment shows that the proposed method converges faster and provides better result than the multigrid method.

CARS Spectral Fitting with Multiple Resonant Species using Sparse Libraries

NASA Technical Reports Server (NTRS)

Cutler, Andrew D.; Magnotti, Gaetano

2010-01-01

The dual pump CARS technique is often used in the study of turbulent flames. Fast and accurate algorithms are needed for fitting dual-pump CARS spectra for temperature and multiple chemical species. This paper describes the development of such an algorithm. The algorithm employs sparse libraries, whose size grows much more slowly with number of species than a conventional library. The method was demonstrated by fitting synthetic "experimental" spectra containing 4 resonant species (N2, O2, H2 and CO2), both with noise and without it, and by fitting experimental spectra from a H2-air flame produced by a Hencken burner. In both studies, weighted least squares fitting of signal, as opposed to least squares fitting signal or square-root signal, was shown to produce the least random error and minimize bias error in the fitted parameters.

Use of partial least squares regression for the multivariate calibration of hazardous air pollutants in open-path FT-IR spectrometry

NASA Astrophysics Data System (ADS)

Hart, Brian K.; Griffiths, Peter R.

1998-06-01

Partial least squares (PLS) regression has been evaluated as a robust calibration technique for over 100 hazardous air pollutants (HAPs) measured by open path Fourier transform infrared (OP/FT-IR) spectrometry. PLS has the advantage over the current recommended calibration method of classical least squares (CLS), in that it can look at the whole useable spectrum (700-1300 cm-1, 2000-2150 cm-1, and 2400-3000 cm-1), and detect several analytes simultaneously. Up to one hundred HAPs synthetically added to OP/FT-IR backgrounds have been simultaneously calibrated and detected using PLS. PLS also has the advantage in requiring less preprocessing of spectra than that which is required in CLS calibration schemes, allowing PLS to provide user independent real-time analysis of OP/FT-IR spectra.

Least-squares luma-chroma demultiplexing algorithm for Bayer demosaicking.

PubMed

Leung, Brian; Jeon, Gwanggil; Dubois, Eric

2011-07-01

This paper addresses the problem of interpolating missing color components at the output of a Bayer color filter array (CFA), a process known as demosaicking. A luma-chroma demultiplexing algorithm is presented in detail, using a least-squares design methodology for the required bandpass filters. A systematic study of objective demosaicking performance and system complexity is carried out, and several system configurations are recommended. The method is compared with other benchmark algorithms in terms of CPSNR and S-CIELAB ∆E∗ objective quality measures and demosaicking speed. It was found to provide excellent performance and the best quality-speed tradeoff among the methods studied.

A weighted least squares approach to retrieve aerosol layer height over bright surfaces applied to GOME-2 measurements of the oxygen A band for forest fire cases over Europe

NASA Astrophysics Data System (ADS)

Nanda, Swadhin; Pepijn Veefkind, J.; de Graaf, Martin; Sneep, Maarten; Stammes, Piet; de Haan, Johan F.; Sanders, Abram F. J.; Apituley, Arnoud; Tuinder, Olaf; Levelt, Pieternel F.

2018-06-01

This paper presents a weighted least squares approach to retrieve aerosol layer height from top-of-atmosphere reflectance measurements in the oxygen A band (758-770 nm) over bright surfaces. A property of the measurement error covariance matrix is discussed, due to which photons travelling from the surface are given a higher preference over photons that scatter back from the aerosol layer. This is a potential source of biases in the estimation of aerosol properties over land, which can be mitigated by revisiting the design of the measurement error covariance matrix. The alternative proposed in this paper, which we call the dynamic scaling method, introduces a scene-dependent and wavelength-dependent modification in the measurement signal-to-noise ratio in order to influence this matrix. This method is generally applicable to other retrieval algorithms using weighted least squares. To test this method, synthetic experiments are done in addition to application to GOME-2A and GOME-2B measurements of the oxygen A band over the August 2010 Russian wildfires and the October 2017 Portugal wildfire plume over western Europe.

Confidence Region of Least Squares Solution for Single-Arc Observations

NASA Astrophysics Data System (ADS)

Principe, G.; Armellin, R.; Lewis, H.

2016-09-01

The total number of active satellites, rocket bodies, and debris larger than 10 cm is currently about 20,000. Considering all resident space objects larger than 1 cm this rises to an estimated minimum of 500,000 objects. Latest generation sensor networks will be able to detect small-size objects, producing millions of observations per day. Due to observability constraints it is likely that long gaps between observations will occur for small objects. This requires to determine the space object (SO) orbit and to accurately describe the associated uncertainty when observations are acquired on a single arc. The aim of this work is to revisit the classical least squares method taking advantage of the high order Taylor expansions enabled by differential algebra. In particular, the high order expansion of the residuals with respect to the state is used to implement an arbitrary order least squares solver, avoiding the typical approximations of differential correction methods. In addition, the same expansions are used to accurately characterize the confidence region of the solution, going beyond the classical Gaussian distributions. The properties and performances of the proposed method are discussed using optical observations of objects in LEO, HEO, and GEO.

A novel second-order standard addition analytical method based on data processing with multidimensional partial least-squares and residual bilinearization.

PubMed

Lozano, Valeria A; Ibañez, Gabriela A; Olivieri, Alejandro C

2009-10-05

In the presence of analyte-background interactions and a significant background signal, both second-order multivariate calibration and standard addition are required for successful analyte quantitation achieving the second-order advantage. This report discusses a modified second-order standard addition method, in which the test data matrix is subtracted from the standard addition matrices, and quantitation proceeds via the classical external calibration procedure. It is shown that this novel data processing method allows one to apply not only parallel factor analysis (PARAFAC) and multivariate curve resolution-alternating least-squares (MCR-ALS), but also the recently introduced and more flexible partial least-squares (PLS) models coupled to residual bilinearization (RBL). In particular, the multidimensional variant N-PLS/RBL is shown to produce the best analytical results. The comparison is carried out with the aid of a set of simulated data, as well as two experimental data sets: one aimed at the determination of salicylate in human serum in the presence of naproxen as an additional interferent, and the second one devoted to the analysis of danofloxacin in human serum in the presence of salicylate.

Applying ISO 11929:2010 Standard to detection limit calculation in least-squares based multi-nuclide gamma-ray spectrum evaluation

NASA Astrophysics Data System (ADS)

Kanisch, G.

2017-05-01

The concepts of ISO 11929 (2010) are applied to evaluation of radionuclide activities from more complex multi-nuclide gamma-ray spectra. From net peak areas estimated by peak fitting, activities and their standard uncertainties are calculated by weighted linear least-squares method with an additional step, where uncertainties of the design matrix elements are taken into account. A numerical treatment of the standard's uncertainty function, based on ISO 11929 Annex C.5, leads to a procedure for deriving decision threshold and detection limit values. The methods shown allow resolving interferences between radionuclide activities also in case of calculating detection limits where they can improve the latter by including more than one gamma line per radionuclide. The co"mmon single nuclide weighted mean is extended to an interference-corrected (generalized) weighted mean, which, combined with the least-squares method, allows faster detection limit calculations. In addition, a new grouped uncertainty budget was inferred, which for each radionuclide gives uncertainty budgets from seven main variables, such as net count rates, peak efficiencies, gamma emission intensities and others; grouping refers to summation over lists of peaks per radionuclide.

A Temperature Compensation Method for Piezo-Resistive Pressure Sensor Utilizing Chaotic Ions Motion Algorithm Optimized Hybrid Kernel LSSVM.

PubMed

Li, Ji; Hu, Guoqing; Zhou, Yonghong; Zou, Chong; Peng, Wei; Alam Sm, Jahangir

2016-10-14

A piezo-resistive pressure sensor is made of silicon, the nature of which is considerably influenced by ambient temperature. The effect of temperature should be eliminated during the working period in expectation of linear output. To deal with this issue, an approach consists of a hybrid kernel Least Squares Support Vector Machine (LSSVM) optimized by a chaotic ions motion algorithm presented. To achieve the learning and generalization for excellent performance, a hybrid kernel function, constructed by a local kernel as Radial Basis Function (RBF) kernel, and a global kernel as polynomial kernel is incorporated into the Least Squares Support Vector Machine. The chaotic ions motion algorithm is introduced to find the best hyper-parameters of the Least Squares Support Vector Machine. The temperature data from a calibration experiment is conducted to validate the proposed method. With attention on algorithm robustness and engineering applications, the compensation result shows the proposed scheme outperforms other compared methods on several performance measures as maximum absolute relative error, minimum absolute relative error mean and variance of the averaged value on fifty runs. Furthermore, the proposed temperature compensation approach lays a foundation for more extensive research.

Two Enhancements of the Logarithmic Least-Squares Method for Analyzing Subjective Comparisons

DTIC Science & Technology

1989-03-25

error term. 1 For this model, the total sum of squares ( SSTO ), defined as n 2 SSTO = E (yi y) i=1 can be partitioned into error and regression sums...of the regression line around the mean value. Mathematically, for the model given by equation A.4, SSTO = SSE + SSR (A.6) A-4 where SSTO is the total...sum of squares (i.e., the variance of the yi’s), SSE is error sum of squares, and SSR is the regression sum of squares. SSTO , SSE, and SSR are given

Development of New Methods for Predicting the Bistatic Electromagnetic Scattering from Absorbing Shapes

DTIC Science & Technology

1990-01-01

least-squares sense by adding a penalty term proportional to the square of the divergence to the variational principle At the start of this project... principle required for stable solutions of the electromagnetic field: It must be possible to express the basis functions used in the finite element method as... principle to derive several different methods for computing stable solutions to electromagnetic field problems. To understand above principle , notice that

Computerized glow curve deconvolution of thermoluminescent emission from polyminerals of Jamaica Mexican flower

NASA Astrophysics Data System (ADS)

Favalli, A.; Furetta, C.; Zaragoza, E. Cruz; Reyes, A.

The aim of this work is to study the main thermoluminescence (TL) characteristics of the inorganic polyminerals extracted from dehydrated Jamaica flower or roselle (Hibiscus sabdariffa L.) belonging to Malvaceae family of Mexican origin. TL emission properties of the polymineral fraction in powder were studied using the initial rise (IR) method. The complex structure and kinetic parameters of the glow curves have been analysed accurately using the computerized glow curve deconvolution (CGCD) assuming an exponential distribution of trapping levels. The extension of the IR method to the case of a continuous and exponential distribution of traps is reported, such as the derivation of the TL glow curve deconvolution functions for continuous trap distribution. CGCD is performed both in the case of frequency factor, s, temperature independent, and in the case with the s function of temperature.

A novel approach to the experimental study on methane/steam reforming kinetics using the Orthogonal Least Squares method

NASA Astrophysics Data System (ADS)

Sciazko, Anna; Komatsu, Yosuke; Brus, Grzegorz; Kimijima, Shinji; Szmyd, Janusz S.

2014-09-01

For a mathematical model based on the result of physical measurements, it becomes possible to determine their influence on the final solution and its accuracy. However, in classical approaches, the influence of different model simplifications on the reliability of the obtained results are usually not comprehensively discussed. This paper presents a novel approach to the study of methane/steam reforming kinetics based on an advanced methodology called the Orthogonal Least Squares method. The kinetics of the reforming process published earlier are divergent among themselves. To obtain the most probable values of kinetic parameters and enable direct and objective model verification, an appropriate calculation procedure needs to be proposed. The applied Generalized Least Squares (GLS) method includes all the experimental results into the mathematical model which becomes internally contradicted, as the number of equations is greater than number of unknown variables. The GLS method is adopted to select the most probable values of results and simultaneously determine the uncertainty coupled with all the variables in the system. In this paper, the evaluation of the reaction rate after the pre-determination of the reaction rate, which was made by preliminary calculation based on the obtained experimental results over a Nickel/Yttria-stabilized Zirconia catalyst, was performed.

Online Detection of Broken Rotor Bar Fault in Induction Motors by Combining Estimation of Signal Parameters via Min-norm Algorithm and Least Square Method

NASA Astrophysics Data System (ADS)

Wang, Pan-Pan; Yu, Qiang; Hu, Yong-Jun; Miao, Chang-Xin

2017-11-01

Current research in broken rotor bar (BRB) fault detection in induction motors is primarily focused on a high-frequency resolution analysis of the stator current. Compared with a discrete Fourier transformation, the parametric spectrum estimation technique has a higher frequency accuracy and resolution. However, the existing detection methods based on parametric spectrum estimation cannot realize online detection, owing to the large computational cost. To improve the efficiency of BRB fault detection, a new detection method based on the min-norm algorithm and least square estimation is proposed in this paper. First, the stator current is filtered using a band-pass filter and divided into short overlapped data windows. The min-norm algorithm is then applied to determine the frequencies of the fundamental and fault characteristic components with each overlapped data window. Next, based on the frequency values obtained, a model of the fault current signal is constructed. Subsequently, a linear least squares problem solved through singular value decomposition is designed to estimate the amplitudes and phases of the related components. Finally, the proposed method is applied to a simulated current and an actual motor, the results of which indicate that, not only parametric spectrum estimation technique.

[Glossary of terms used by radiologists in image processing].

PubMed

Rolland, Y; Collorec, R; Bruno, A; Ramée, A; Morcet, N; Haigron, P

1995-01-01

We give the definition of 166 words used in image processing. Adaptivity, aliazing, analog-digital converter, analysis, approximation, arc, artifact, artificial intelligence, attribute, autocorrelation, bandwidth, boundary, brightness, calibration, class, classification, classify, centre, cluster, coding, color, compression, contrast, connectivity, convolution, correlation, data base, decision, decomposition, deconvolution, deduction, descriptor, detection, digitization, dilation, discontinuity, discretization, discrimination, disparity, display, distance, distorsion, distribution dynamic, edge, energy, enhancement, entropy, erosion, estimation, event, extrapolation, feature, file, filter, filter floaters, fitting, Fourier transform, frequency, fusion, fuzzy, Gaussian, gradient, graph, gray level, group, growing, histogram, Hough transform, Houndsfield, image, impulse response, inertia, intensity, interpolation, interpretation, invariance, isotropy, iterative, JPEG, knowledge base, label, laplacian, learning, least squares, likelihood, matching, Markov field, mask, matching, mathematical morphology, merge (to), MIP, median, minimization, model, moiré, moment, MPEG, neural network, neuron, node, noise, norm, normal, operator, optical system, optimization, orthogonal, parametric, pattern recognition, periodicity, photometry, pixel, polygon, polynomial, prediction, pulsation, pyramidal, quantization, raster, reconstruction, recursive, region, rendering, representation space, resolution, restoration, robustness, ROC, thinning, transform, sampling, saturation, scene analysis, segmentation, separable function, sequential, smoothing, spline, split (to), shape, threshold, tree, signal, speckle, spectrum, spline, stationarity, statistical, stochastic, structuring element, support, syntaxic, synthesis, texture, truncation, variance, vision, voxel, windowing.

Nonlinear least squares regression for single image scanning electron microscope signal-to-noise ratio estimation.

PubMed

Sim, K S; Norhisham, S

2016-11-01

A new method based on nonlinear least squares regression (NLLSR) is formulated to estimate signal-to-noise ratio (SNR) of scanning electron microscope (SEM) images. The estimation of SNR value based on NLLSR method is compared with the three existing methods of nearest neighbourhood, first-order interpolation and the combination of both nearest neighbourhood and first-order interpolation. Samples of SEM images with different textures, contrasts and edges were used to test the performance of NLLSR method in estimating the SNR values of the SEM images. It is shown that the NLLSR method is able to produce better estimation accuracy as compared to the other three existing methods. According to the SNR results obtained from the experiment, the NLLSR method is able to produce approximately less than 1% of SNR error difference as compared to the other three existing methods. © 2016 The Authors Journal of Microscopy © 2016 Royal Microscopical Society.

Sensitivity test of derivative matrix isopotential synchronous fluorimetry and least squares fitting methods.

PubMed

Makkai, Géza; Buzády, Andrea; Erostyák, János

2010-01-01

Determination of concentrations of spectrally overlapping compounds has special difficulties. Several methods are available to calculate the constituents' concentrations in moderately complex mixtures. A method which can provide information about spectrally hidden components in mixtures is very useful. Two methods powerful in resolving spectral components are compared in this paper. The first method tested is the Derivative Matrix Isopotential Synchronous Fluorimetry (DMISF). It is based on derivative analysis of MISF spectra, which are constructed using isopotential trajectories in the Excitation-Emission Matrix (EEM) of background solution. For DMISF method, a mathematical routine fitting the 3D data of EEMs was developed. The other method tested uses classical Least Squares Fitting (LSF) algorithm, wherein Rayleigh- and Raman-scattering bands may lead to complications. Both methods give excellent sensitivity and have advantages against each other. Detection limits of DMISF and LSF have been determined at very different concentration and noise levels.

Retrieval of the non-depolarizing components of depolarizing Mueller matrices by using symmetry conditions and least squares minimization

NASA Astrophysics Data System (ADS)

Kuntman, Ertan; Canillas, Adolf; Arteaga, Oriol

2017-11-01

Experimental Mueller matrices contain certain amount of uncertainty in their elements and these uncertainties can create difficulties for decomposition methods based on analytic solutions. In an earlier paper [1], we proposed a decomposition method for depolarizing Mueller matrices by using certain symmetry conditions. However, because of the experimental error, that method creates over-determined systems with non-unique solutions. Here we propose to use least squares minimization approach in order to improve the accuracy of our results. In this method, we are taking into account the number of independent parameters of the corresponding symmetry and the rank constraints on the component matrices to decide on our fitting model. This approach is illustrated with experimental Mueller matrices that include material media with different Mueller symmetries.

Hybrid least squares multivariate spectral analysis methods

DOEpatents

Haaland, David M.

2004-03-23

A set of hybrid least squares multivariate spectral analysis methods in which spectral shapes of components or effects not present in the original calibration step are added in a following prediction or calibration step to improve the accuracy of the estimation of the amount of the original components in the sampled mixture. The hybrid method herein means a combination of an initial calibration step with subsequent analysis by an inverse multivariate analysis method. A spectral shape herein means normally the spectral shape of a non-calibrated chemical component in the sample mixture but can also mean the spectral shapes of other sources of spectral variation, including temperature drift, shifts between spectrometers, spectrometer drift, etc. The shape can be continuous, discontinuous, or even discrete points illustrative of the particular effect.

A method for the selection of a functional form for a thermodynamic equation of state using weighted linear least squares stepwise regression

NASA Technical Reports Server (NTRS)

Jacobsen, R. T.; Stewart, R. B.; Crain, R. W., Jr.; Rose, G. L.; Myers, A. F.

1976-01-01

A method was developed for establishing a rational choice of the terms to be included in an equation of state with a large number of adjustable coefficients. The methods presented were developed for use in the determination of an equation of state for oxygen and nitrogen. However, a general application of the methods is possible in studies involving the determination of an optimum polynomial equation for fitting a large number of data points. The data considered in the least squares problem are experimental thermodynamic pressure-density-temperature data. Attention is given to a description of stepwise multiple regression and the use of stepwise regression in the determination of an equation of state for oxygen and nitrogen.

Weighted partial least squares based on the error and variance of the recovery rate in calibration set.

PubMed

Yu, Shaohui; Xiao, Xue; Ding, Hong; Xu, Ge; Li, Haixia; Liu, Jing

2017-08-05

The quantitative analysis is very difficult for the emission-excitation fluorescence spectroscopy of multi-component mixtures whose fluorescence peaks are serious overlapping. As an effective method for the quantitative analysis, partial least squares can extract the latent variables from both the independent variables and the dependent variables, so it can model for multiple correlations between variables. However, there are some factors that usually affect the prediction results of partial least squares, such as the noise, the distribution and amount of the samples in calibration set etc. This work focuses on the problems in the calibration set that are mentioned above. Firstly, the outliers in the calibration set are removed by leave-one-out cross-validation. Then, according to two different prediction requirements, the EWPLS method and the VWPLS method are proposed. The independent variables and dependent variables are weighted in the EWPLS method by the maximum error of the recovery rate and weighted in the VWPLS method by the maximum variance of the recovery rate. Three organic matters with serious overlapping excitation-emission fluorescence spectroscopy are selected for the experiments. The step adjustment parameter, the iteration number and the sample amount in the calibration set are discussed. The results show the EWPLS method and the VWPLS method are superior to the PLS method especially for the case of small samples in the calibration set. Copyright © 2017 Elsevier B.V. All rights reserved.

A localized Richardson-Lucy algorithm for fiber orientation estimation in high angular resolution diffusion imaging.

PubMed

Liu, Xiaozheng; Yuan, Zhenming; Guo, Zhongwei; Xu, Dongrong

2015-05-01

Diffusion tensor imaging is widely used for studying neural fiber trajectories in white matter and for quantifying changes in tissue using diffusion properties at each voxel in the brain. To better model the nature of crossing fibers within complex architectures, rather than using a simplified tensor model that assumes only a single fiber direction at each image voxel, a model mixing multiple diffusion tensors is used to profile diffusion signals from high angular resolution diffusion imaging (HARDI) data. Based on the HARDI signal and a multiple tensors model, spherical deconvolution methods have been developed to overcome the limitations of the diffusion tensor model when resolving crossing fibers. The Richardson-Lucy algorithm is a popular spherical deconvolution method used in previous work. However, it is based on a Gaussian distribution, while HARDI data are always very noisy, and the distribution of HARDI data follows a Rician distribution. This current work aims to present a novel solution to address these issues. By simultaneously considering both the Rician bias and neighbor correlation in HARDI data, the authors propose a localized Richardson-Lucy (LRL) algorithm to estimate fiber orientations for HARDI data. The proposed method can simultaneously reduce noise and correct the Rician bias. Mean angular error (MAE) between the estimated Fiber orientation distribution (FOD) field and the reference FOD field was computed to examine whether the proposed LRL algorithm offered any advantage over the conventional RL algorithm at various levels of noise. Normalized mean squared error (NMSE) was also computed to measure the similarity between the true FOD field and the estimated FOD filed. For MAE comparisons, the proposed LRL approach obtained the best results in most of the cases at different levels of SNR and b-values. For NMSE comparisons, the proposed LRL approach obtained the best results in most of the cases at b-value = 3000 s/mm(2), which is the recommended schema for HARDI data acquisition. In addition, the FOD fields estimated by the proposed LRL approach in regions of fiber crossing regions using real data sets also showed similar fiber structures which agreed with common acknowledge in these regions. The novel spherical deconvolution method for improved accuracy in investigating crossing fibers can simultaneously reduce noise and correct Rician bias. With the noise smoothed and bias corrected, this algorithm is especially suitable for estimation of fiber orientations in HARDI data. Experimental results using both synthetic and real imaging data demonstrated the success and effectiveness of the proposed LRL algorithm.

Studies of superresolution range-Doppler imaging

NASA Astrophysics Data System (ADS)

Zhu, Zhaoda; Ye, Zhenru; Wu, Xiaoqing; Yin, Jun; She, Zhishun

1993-02-01

This paper presents three superresolution imaging methods, including the linear prediction data extrapolation DFT (LPDEDFT), the dynamic optimization linear least squares (DOLLS), and the Hopfield neural network nonlinear least squares (HNNNLS). Live data of a metalized scale model B-52 aircraft, mounted on a rotating platform in a microwave anechoic chamber, have in this way been processed, as has a flying Boeing-727 aircraft. The imaging results indicate that, compared to the conventional Fourier method, either higher resolution for the same effective bandwidth of transmitted signals and total rotation angle in imaging, or equal-quality images from smaller bandwidth and total rotation, angle may be obtained by these superresolution approaches. Moreover, these methods are compared in respect of their resolution capability and computational complexity.

Classical least squares multivariate spectral analysis

DOEpatents

Haaland, David M.

2002-01-01

An improved classical least squares multivariate spectral analysis method that adds spectral shapes describing non-calibrated components and system effects (other than baseline corrections) present in the analyzed mixture to the prediction phase of the method. These improvements decrease or eliminate many of the restrictions to the CLS-type methods and greatly extend their capabilities, accuracy, and precision. One new application of PACLS includes the ability to accurately predict unknown sample concentrations when new unmodeled spectral components are present in the unknown samples. Other applications of PACLS include the incorporation of spectrometer drift into the quantitative multivariate model and the maintenance of a calibration on a drifting spectrometer. Finally, the ability of PACLS to transfer a multivariate model between spectrometers is demonstrated.

Least Squares Shadowing sensitivity analysis of chaotic limit cycle oscillations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Qiqi, E-mail: qiqi@mit.edu; Hu, Rui, E-mail: hurui@mit.edu; Blonigan, Patrick, E-mail: blonigan@mit.edu

2014-06-15

The adjoint method, among other sensitivity analysis methods, can fail in chaotic dynamical systems. The result from these methods can be too large, often by orders of magnitude, when the result is the derivative of a long time averaged quantity. This failure is known to be caused by ill-conditioned initial value problems. This paper overcomes this failure by replacing the initial value problem with the well-conditioned “least squares shadowing (LSS) problem”. The LSS problem is then linearized in our sensitivity analysis algorithm, which computes a derivative that converges to the derivative of the infinitely long time average. We demonstrate ourmore » algorithm in several dynamical systems exhibiting both periodic and chaotic oscillations.« less

Detection of Glutamic Acid in Oilseed Rape Leaves Using Near Infrared Spectroscopy and the Least Squares-Support Vector Machine

PubMed Central

Bao, Yidan; Kong, Wenwen; Liu, Fei; Qiu, Zhengjun; He, Yong

2012-01-01

Amino acids are quite important indices to indicate the growth status of oilseed rape under herbicide stress. Near infrared (NIR) spectroscopy combined with chemometrics was applied for fast determination of glutamic acid in oilseed rape leaves. The optimal spectral preprocessing method was obtained after comparing Savitzky-Golay smoothing, standard normal variate, multiplicative scatter correction, first and second derivatives, detrending and direct orthogonal signal correction. Linear and nonlinear calibration methods were developed, including partial least squares (PLS) and least squares-support vector machine (LS-SVM). The most effective wavelengths (EWs) were determined by the successive projections algorithm (SPA), and these wavelengths were used as the inputs of PLS and LS-SVM model. The best prediction results were achieved by SPA-LS-SVM (Raw) model with correlation coefficient r = 0.9943 and root mean squares error of prediction (RMSEP) = 0.0569 for prediction set. These results indicated that NIR spectroscopy combined with SPA-LS-SVM was feasible for the fast and effective detection of glutamic acid in oilseed rape leaves. The selected EWs could be used to develop spectral sensors, and the important and basic amino acid data were helpful to study the function mechanism of herbicide. PMID:23203052

A KPI-based process monitoring and fault detection framework for large-scale processes.

PubMed

Zhang, Kai; Shardt, Yuri A W; Chen, Zhiwen; Yang, Xu; Ding, Steven X; Peng, Kaixiang

2017-05-01

Large-scale processes, consisting of multiple interconnected subprocesses, are commonly encountered in industrial systems, whose performance needs to be determined. A common approach to this problem is to use a key performance indicator (KPI)-based approach. However, the different KPI-based approaches are not developed with a coherent and consistent framework. Thus, this paper proposes a framework for KPI-based process monitoring and fault detection (PM-FD) for large-scale industrial processes, which considers the static and dynamic relationships between process and KPI variables. For the static case, a least squares-based approach is developed that provides an explicit link with least-squares regression, which gives better performance than partial least squares. For the dynamic case, using the kernel representation of each subprocess, an instrument variable is used to reduce the dynamic case to the static case. This framework is applied to the TE benchmark process and the hot strip mill rolling process. The results show that the proposed method can detect faults better than previous methods. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Identification of multivariable nonlinear systems in the presence of colored noises using iterative hierarchical least squares algorithm.

PubMed

Jafari, Masoumeh; Salimifard, Maryam; Dehghani, Maryam

2014-07-01

This paper presents an efficient method for identification of nonlinear Multi-Input Multi-Output (MIMO) systems in the presence of colored noises. The method studies the multivariable nonlinear Hammerstein and Wiener models, in which, the nonlinear memory-less block is approximated based on arbitrary vector-based basis functions. The linear time-invariant (LTI) block is modeled by an autoregressive moving average with exogenous (ARMAX) model which can effectively describe the moving average noises as well as the autoregressive and the exogenous dynamics. According to the multivariable nature of the system, a pseudo-linear-in-the-parameter model is obtained which includes two different kinds of unknown parameters, a vector and a matrix. Therefore, the standard least squares algorithm cannot be applied directly. To overcome this problem, a Hierarchical Least Squares Iterative (HLSI) algorithm is used to simultaneously estimate the vector and the matrix of unknown parameters as well as the noises. The efficiency of the proposed identification approaches are investigated through three nonlinear MIMO case studies. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Study of the convergence behavior of the complex kernel least mean square algorithm.

PubMed

Paul, Thomas K; Ogunfunmi, Tokunbo

2013-09-01

The complex kernel least mean square (CKLMS) algorithm is recently derived and allows for online kernel adaptive learning for complex data. Kernel adaptive methods can be used in finding solutions for neural network and machine learning applications. The derivation of CKLMS involved the development of a modified Wirtinger calculus for Hilbert spaces to obtain the cost function gradient. We analyze the convergence of the CKLMS with different kernel forms for complex data. The expressions obtained enable us to generate theory-predicted mean-square error curves considering the circularity of the complex input signals and their effect on nonlinear learning. Simulations are used for verifying the analysis results.

Image restoration and superresolution as probes of small scale far-IR structure in star forming regions

NASA Technical Reports Server (NTRS)

Lester, D. F.; Harvey, P. M.; Joy, M.; Ellis, H. B., Jr.

1986-01-01

Far-infrared continuum studies from the Kuiper Airborne Observatory are described that are designed to fully exploit the small-scale spatial information that this facility can provide. This work gives the clearest picture to data on the structure of galactic and extragalactic star forming regions in the far infrared. Work is presently being done with slit scans taken simultaneously at 50 and 100 microns, yielding one-dimensional data. Scans of sources in different directions have been used to get certain information on two dimensional structure. Planned work with linear arrays will allow us to generalize our techniques to two dimensional image restoration. For faint sources, spatial information at the diffraction limit of the telescope is obtained, while for brighter sources, nonlinear deconvolution techniques have allowed us to improve over the diffraction limit by as much as a factor of four. Information on the details of the color temperature distribution is derived as well. This is made possible by the accuracy with which the instrumental point-source profile (PSP) is determined at both wavelengths. While these two PSPs are different, data at different wavelengths can be compared by proper spatial filtering. Considerable effort has been devoted to implementing deconvolution algorithms. Nonlinear deconvolution methods offer the potential of superresolution -- that is, inference of power at spatial frequencies that exceed D lambda. This potential is made possible by the implicit assumption by the algorithm of positivity of the deconvolved data, a universally justifiable constraint for photon processes. We have tested two nonlinear deconvolution algorithms on our data; the Richardson-Lucy (R-L) method and the Maximum Entropy Method (MEM). The limits of image deconvolution techniques for achieving spatial resolution are addressed.

Spline based least squares integration for two-dimensional shape or wavefront reconstruction

DOE PAGES

Huang, Lei; Xue, Junpeng; Gao, Bo; ...

2016-12-21

In this paper, we present a novel method to handle two-dimensional shape or wavefront reconstruction from its slopes. The proposed integration method employs splines to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients. The linear least squares method is applied to estimate the height or wavefront as a final result. Numerical simulations verify that the proposed method has less algorithm errors than two other existing methods used for comparison. Especially at the boundaries, the proposed method has better performance. Themore » noise influence is studied by adding white Gaussian noise to the slope data. Finally, experimental data from phase measuring deflectometry are tested to demonstrate the feasibility of the new method in a practical measurement.« less

Spline based least squares integration for two-dimensional shape or wavefront reconstruction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Lei; Xue, Junpeng; Gao, Bo

In this paper, we present a novel method to handle two-dimensional shape or wavefront reconstruction from its slopes. The proposed integration method employs splines to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients. The linear least squares method is applied to estimate the height or wavefront as a final result. Numerical simulations verify that the proposed method has less algorithm errors than two other existing methods used for comparison. Especially at the boundaries, the proposed method has better performance. Themore » noise influence is studied by adding white Gaussian noise to the slope data. Finally, experimental data from phase measuring deflectometry are tested to demonstrate the feasibility of the new method in a practical measurement.« less

The least-squares finite element method for low-mach-number compressible viscous flows

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao

1994-01-01

The present paper reports the development of the Least-Squares Finite Element Method (LSFEM) for simulating compressible viscous flows at low Mach numbers in which the incompressible flows pose as an extreme. Conventional approach requires special treatments for low-speed flows calculations: finite difference and finite volume methods are based on the use of the staggered grid or the preconditioning technique; and, finite element methods rely on the mixed method and the operator-splitting method. In this paper, however, we show that such difficulty does not exist for the LSFEM and no special treatment is needed. The LSFEM always leads to a symmetric, positive-definite matrix through which the compressible flow equations can be effectively solved. Two numerical examples are included to demonstrate the method: first, driven cavity flows at various Reynolds numbers; and, buoyancy-driven flows with significant density variation. Both examples are calculated by using full compressible flow equations.

VizieR Online Data Catalog: Spatial deconvolution code (Quintero Noda+, 2015)

NASA Astrophysics Data System (ADS)

Quintero Noda, C.; Asensio Ramos, A.; Orozco Suarez, D.; Ruiz Cobo, B.

2015-05-01

This deconvolution method follows the scheme presented in Ruiz Cobo & Asensio Ramos (2013A&A...549L...4R) The Stokes parameters are projected onto a few spectral eigenvectors and the ensuing maps of coefficients are deconvolved using a standard Lucy-Richardson algorithm. This introduces a stabilization because the PCA filtering reduces the amount of noise. (1 data file).

3D image restoration for confocal microscopy: toward a wavelet deconvolution for the study of complex biological structures

NASA Astrophysics Data System (ADS)

Boutet de Monvel, Jacques; Le Calvez, Sophie; Ulfendahl, Mats

2000-05-01

Image restoration algorithms provide efficient tools for recovering part of the information lost in the imaging process of a microscope. We describe recent progress in the application of deconvolution to confocal microscopy. The point spread function of a Biorad-MRC1024 confocal microscope was measured under various imaging conditions, and used to process 3D-confocal images acquired in an intact preparation of the inner ear developed at Karolinska Institutet. Using these experiments we investigate the application of denoising methods based on wavelet analysis as a natural regularization of the deconvolution process. Within the Bayesian approach to image restoration, we compare wavelet denoising with the use of a maximum entropy constraint as another natural regularization method. Numerical experiments performed with test images show a clear advantage of the wavelet denoising approach, allowing to `cool down' the image with respect to the signal, while suppressing much of the fine-scale artifacts appearing during deconvolution due to the presence of noise, incomplete knowledge of the point spread function, or undersampling problems. We further describe a natural development of this approach, which consists of performing the Bayesian inference directly in the wavelet domain.

Deconvolution of interferometric data using interior point iterative algorithms

NASA Astrophysics Data System (ADS)

Theys, C.; Lantéri, H.; Aime, C.

2016-09-01

We address the problem of deconvolution of astronomical images that could be obtained with future large interferometers in space. The presentation is made in two complementary parts. The first part gives an introduction to the image deconvolution with linear and nonlinear algorithms. The emphasis is made on nonlinear iterative algorithms that verify the constraints of non-negativity and constant flux. The Richardson-Lucy algorithm appears there as a special case for photon counting conditions. More generally, the algorithm published recently by Lanteri et al. (2015) is based on scale invariant divergences without assumption on the statistic model of the data. The two proposed algorithms are interior-point algorithms, the latter being more efficient in terms of speed of calculation. These algorithms are applied to the deconvolution of simulated images corresponding to an interferometric system of 16 diluted telescopes in space. Two non-redundant configurations, one disposed around a circle and the other on an hexagonal lattice, are compared for their effectiveness on a simple astronomical object. The comparison is made in the direct and Fourier spaces. Raw "dirty" images have many artifacts due to replicas of the original object. Linear methods cannot remove these replicas while iterative methods clearly show their efficacy in these examples.

Two-way and three-way approaches to ultra high performance liquid chromatography-photodiode array dataset for the quantitative resolution of a two-component mixture containing ciprofloxacin and ornidazole.

PubMed

Dinç, Erdal; Ertekin, Zehra Ceren; Büker, Eda

2016-09-01

Two-way and three-way calibration models were applied to ultra high performance liquid chromatography with photodiode array data with coeluted peaks in the same wavelength and time regions for the simultaneous quantitation of ciprofloxacin and ornidazole in tablets. The chromatographic data cube (tensor) was obtained by recording chromatographic spectra of the standard and sample solutions containing ciprofloxacin and ornidazole with sulfadiazine as an internal standard as a function of time and wavelength. Parallel factor analysis and trilinear partial least squares were used as three-way calibrations for the decomposition of the tensor, whereas three-way unfolded partial least squares was applied as a two-way calibration to the unfolded dataset obtained from the data array of ultra high performance liquid chromatography with photodiode array detection. The validity and ability of two-way and three-way analysis methods were tested by analyzing validation samples: synthetic mixture, interday and intraday samples, and standard addition samples. Results obtained from two-way and three-way calibrations were compared to those provided by traditional ultra high performance liquid chromatography. The proposed methods, parallel factor analysis, trilinear partial least squares, unfolded partial least squares, and traditional ultra high performance liquid chromatography were successfully applied to the quantitative estimation of the solid dosage form containing ciprofloxacin and ornidazole. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Inverse models: A necessary next step in ground-water modeling

USGS Publications Warehouse

Poeter, E.P.; Hill, M.C.

1997-01-01

Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares repression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares regression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.

Fast Algorithms for Structured Least Squares and Total Least Squares Problems

PubMed Central

Kalsi, Anoop; O’Leary, Dianne P.

2006-01-01

We consider the problem of solving least squares problems involving a matrix M of small displacement rank with respect to two matrices Z1 and Z2. We develop formulas for the generators of the matrix M HM in terms of the generators of M and show that the Cholesky factorization of the matrix M HM can be computed quickly if Z1 is close to unitary and Z2 is triangular and nilpotent. These conditions are satisfied for several classes of matrices, including Toeplitz, block Toeplitz, Hankel, and block Hankel, and for matrices whose blocks have such structure. Fast Cholesky factorization enables fast solution of least squares problems, total least squares problems, and regularized total least squares problems involving these classes of matrices. PMID:27274922

Fast Algorithms for Structured Least Squares and Total Least Squares Problems.

PubMed

Kalsi, Anoop; O'Leary, Dianne P

2006-01-01

We consider the problem of solving least squares problems involving a matrix M of small displacement rank with respect to two matrices Z 1 and Z 2. We develop formulas for the generators of the matrix M (H) M in terms of the generators of M and show that the Cholesky factorization of the matrix M (H) M can be computed quickly if Z 1 is close to unitary and Z 2 is triangular and nilpotent. These conditions are satisfied for several classes of matrices, including Toeplitz, block Toeplitz, Hankel, and block Hankel, and for matrices whose blocks have such structure. Fast Cholesky factorization enables fast solution of least squares problems, total least squares problems, and regularized total least squares problems involving these classes of matrices.

A feasibility and optimization study to determine cooling time and burnup of advanced test reactor fuels using a nondestructive technique

DOE Office of Scientific and Technical Information (OSTI.GOV)

Navarro, Jorge

2013-12-01

The goal of this study presented is to determine the best available non-destructive technique necessary to collect validation data as well as to determine burn-up and cooling time of the fuel elements onsite at the Advanced Test Reactor (ATR) canal. This study makes a recommendation of the viability of implementing a permanent fuel scanning system at the ATR canal and leads3 to the full design of a permanent fuel scan system. The study consisted at first in determining if it was possible and which equipment was necessary to collect useful spectra from ATR fuel elements at the canal adjacent tomore » the reactor. Once it was establish that useful spectra can be obtained at the ATR canal the next step was to determine which detector and which configuration was better suited to predict burnup and cooling time of fuel elements non-destructively. Three different detectors of High Purity Germanium (HPGe), Lanthanum Bromide (LaBr3), and High Pressure Xenon (HPXe) in two system configurations of above and below the water pool were used during the study. The data collected and analyzed was used to create burnup and cooling time calibration prediction curves for ATR fuel. The next stage of the study was to determine which of the three detectors tested was better suited for the permanent system. From spectra taken and the calibration curves obtained, it was determined that although the HPGe detector yielded better results, a detector that could better withstand the harsh environment of the ATR canal was needed. The in-situ nature of the measurements required a rugged fuel scanning system, low in maintenance and easy to control system. Based on the ATR canal feasibility measurements and calibration results it was determined that the LaBr3 detector was the best alternative for canal in-situ measurements; however in order to enhance the quality of the spectra collected using this scintillator a deconvolution method was developed. Following the development of the deconvolution method for ATR applications the technique was tested using one-isotope, multi-isotope and fuel simulated sources. Burnup calibrations were perfomed using convoluted and deconvoluted data. The calibrations results showed burnup prediction by this method improves using deconvolution. The final stage of the deconvolution method development was to perform an irradiation experiment in order to create a surrogate fuel source to test the deconvolution method using experimental data. A conceptual design of the fuel scan system is path forward using the rugged LaBr3 detector in an above the water configuration and deconvolution algorithms.« less

Voigt deconvolution method and its applications to pure oxygen absorption spectrum at 1270 nm band.

PubMed

Al-Jalali, Muhammad A; Aljghami, Issam F; Mahzia, Yahia M

2016-03-15

Experimental spectral lines of pure oxygen at 1270 nm band were analyzed by Voigt deconvolution method. The method gave a total Voigt profile, which arises from two overlapping bands. Deconvolution of total Voigt profile leads to two Voigt profiles, the first as a result of O2 dimol at 1264 nm band envelope, and the second from O2 monomer at 1268 nm band envelope. In addition, Voigt profile itself is the convolution of Lorentzian and Gaussian distributions. Competition between thermal and collisional effects was clearly observed through competition between Gaussian and Lorentzian width for each band envelope. Voigt full width at half-maximum height (Voigt FWHM) for each line, and the width ratio between Lorentzian and Gaussian width (ΓLΓG(-1)) have been investigated. The following applied pressures were at 1, 2, 3, 4, 5, and 8 bar, while the temperatures were at 298 K, 323 K, 348 K, and 373 K range. Copyright © 2015 Elsevier B.V. All rights reserved.

Sp and Ps Receiver Function Imaging of the Cenozoic and Precambrian US

NASA Astrophysics Data System (ADS)

Keenan, James; Thurner, Sally; Levander, Alan

2013-04-01

Using teleseismic USArray data we have made Ps and Sp receiver function common conversion point stacked image volumes that extend from the Pacific coast to approximately the Mississippi River. We have used iterative time-domain deconvolution, water-level frequency-domain deconvolution, and least squares inverse filtering to form receiver functions in various frequency bands (Ps: 1.0 and, 0.5 Hz, Sp: 0.2 and 0.1 Hz). The receiver functions were stacked to give an image volume for each frequency band using a hybrid velocity model made by combining Crust2.0 (Bassin et al., 2000) and finite-frequency P and S wave tomography models (Schmandt and Humphreys, 2010; and Schmandt, unpublished). We contrast the lithospheric and asthenospheric structure of the western U.S., modified by Cenozoic tectonism, with that of the Precambrian central U.S. Here we describe 2 notable features: (1) In the Sp image volumes the upper mantle beneath the western U.S. differs dramatically from that to the east of the Rocky Mountain front. In the western U.S. the lithosphere is either thin, or highly variable in thickness (40-140 km) with neither the lithosphere nor asthenosphere having much internal structure (e.g., Levander and Miller, 2012). In contrast, east of the Rocky Mountain front the lithosphere steadily deepens to > 150 km and shows relatively strong internal layering. Individual positive and negative conversions are coherent over 100's of kilometers, suggesting the thrust stacking model of cratonic formation. (2) Beneath parts of the Archean Wyoming Province (Henstock et al, 1998; Snelson et al., 1998; Gorman et al., 2002; Mahan et al, 2012), much of the Great Plains and part of the Midwest lies a vast variable thickness (up to ~25 km) high velocity crustal layer. This layer lies roughly north of the Grenville Front, underlying much of the Yavapai-Mazatzal Province east of the Rockies, parts of the Superior Province, and possibly parts of the Trans-Hudson province.

Cost-Sharing of Ecological Construction Based on Trapezoidal Intuitionistic Fuzzy Cooperative Games.

PubMed

Liu, Jiacai; Zhao, Wenjian

2016-11-08

There exist some fuzziness and uncertainty in the process of ecological construction. The aim of this paper is to develop a direct and an effective simplified method for obtaining the cost-sharing scheme when some interested parties form a cooperative coalition to improve the ecological environment of Min River together. Firstly, we propose the solution concept of the least square prenucleolus of cooperative games with coalition values expressed by trapezoidal intuitionistic fuzzy numbers. Then, based on the square of the distance in the numerical value between two trapezoidal intuitionistic fuzzy numbers, we establish a corresponding quadratic programming model to obtain the least square prenucleolus, which can effectively avoid the information distortion and uncertainty enlargement brought about by the subtraction of trapezoidal intuitionistic fuzzy numbers. Finally, we give a numerical example about the cost-sharing of ecological construction in Fujian Province in China to show the validity, applicability, and advantages of the proposed model and method.

On estimating gravity anomalies - A comparison of least squares collocation with conventional least squares techniques

NASA Technical Reports Server (NTRS)

Argentiero, P.; Lowrey, B.

1977-01-01

The least squares collocation algorithm for estimating gravity anomalies from geodetic data is shown to be an application of the well known regression equations which provide the mean and covariance of a random vector (gravity anomalies) given a realization of a correlated random vector (geodetic data). It is also shown that the collocation solution for gravity anomalies is equivalent to the conventional least-squares-Stokes' function solution when the conventional solution utilizes properly weighted zero a priori estimates. The mathematical and physical assumptions underlying the least squares collocation estimator are described.

Methods and computer program documentation for determining anisotropic transmissivity tensor components of two-dimensional ground-water flow

USGS Publications Warehouse

Maslia, M.L.; Randolph, R.B.

1986-01-01

The theory of anisotropic aquifer hydraulic properties and a computer program, written in Fortran 77, developed to compute the components of the anisotropic transmissivity tensor of two-dimensional groundwater flow are described. To determine the tensor components using one pumping well and three observation wells, the type-curve and straight-line approximation methods are developed. These methods are based on the equation of drawdown developed for two-dimensional nonsteady flow in an infinite anisotropic aquifer. To determine tensor components using more than three observation wells, a weighted least squares optimization procedure is described for use with the type-curve and straight-line approximation methods. The computer program described in this report allows the type-curve, straight-line approximation, and weighted least squares optimization methods to be used in conjunction with data from observation and pumping wells. Three example applications using the computer program and field data gathered during geohydrologic investigations at a site near Dawsonville, Georgia , are provided to illustrate the use of the computer program. The example applications demonstrate the use of the type-curve method using three observation wells, the weighted least squares optimization method using eight observation wells and equal weighting, and the weighted least squares optimization method using eight observation wells and unequal weighting. Results obtained using the computer program indicate major transmissivity in the range of 347-296 sq ft/day, minor transmissivity in the range of 139-99 sq ft/day, aquifer anisotropy in the range of 3.54 to 2.14, principal direction of flow in the range of N. 45.9 degrees E. to N. 58.7 degrees E., and storage coefficient in the range of 0.0063 to 0.0037. The numerical results are in good agreement with field data gathered on the weathered crystalline rocks underlying the investigation site. Supplemental material provides definitions of variables, data requirements and corresponding formats, input data and output results for the example applications, and a listing of the Fortran 77 computer code. (Author 's abstract)

Robust and efficient pharmacokinetic parameter non-linear least squares estimation for dynamic contrast enhanced MRI of the prostate.

PubMed

Kargar, Soudabeh; Borisch, Eric A; Froemming, Adam T; Kawashima, Akira; Mynderse, Lance A; Stinson, Eric G; Trzasko, Joshua D; Riederer, Stephen J

2018-05-01

To describe an efficient numerical optimization technique using non-linear least squares to estimate perfusion parameters for the Tofts and extended Tofts models from dynamic contrast enhanced (DCE) MRI data and apply the technique to prostate cancer. Parameters were estimated by fitting the two Tofts-based perfusion models to the acquired data via non-linear least squares. We apply Variable Projection (VP) to convert the fitting problem from a multi-dimensional to a one-dimensional line search to improve computational efficiency and robustness. Using simulation and DCE-MRI studies in twenty patients with suspected prostate cancer, the VP-based solver was compared against the traditional Levenberg-Marquardt (LM) strategy for accuracy, noise amplification, robustness to converge, and computation time. The simulation demonstrated that VP and LM were both accurate in that the medians closely matched assumed values across typical signal to noise ratio (SNR) levels for both Tofts models. VP and LM showed similar noise sensitivity. Studies using the patient data showed that the VP method reliably converged and matched results from LM with approximate 3× and 2× reductions in computation time for the standard (two-parameter) and extended (three-parameter) Tofts models. While LM failed to converge in 14% of the patient data, VP converged in the ideal 100%. The VP-based method for non-linear least squares estimation of perfusion parameters for prostate MRI is equivalent in accuracy and robustness to noise, while being more reliably (100%) convergent and computationally about 3× (TM) and 2× (ETM) faster than the LM-based method. Copyright © 2017 Elsevier Inc. All rights reserved.

Optimal application of Morrison's iterative noise removal for deconvolution. Appendices

NASA Technical Reports Server (NTRS)

Ioup, George E.; Ioup, Juliette W.

1987-01-01

Morrison's iterative method of noise removal, or Morrison's smoothing, is applied in a simulation to noise-added data sets of various noise levels to determine its optimum use. Morrison's smoothing is applied for noise removal alone, and for noise removal prior to deconvolution. For the latter, an accurate method is analyzed to provide confidence in the optimization. The method consists of convolving the data with an inverse filter calculated by taking the inverse discrete Fourier transform of the reciprocal of the transform of the response of the system. Various length filters are calculated for the narrow and wide Gaussian response functions used. Deconvolution of non-noisy data is performed, and the error in each deconvolution calculated. Plots are produced of error versus filter length; and from these plots the most accurate length filters determined. The statistical methodologies employed in the optimizations of Morrison's method are similar. A typical peak-type input is selected and convolved with the two response functions to produce the data sets to be analyzed. Both constant and ordinate-dependent Gaussian distributed noise is added to the data, where the noise levels of the data are characterized by their signal-to-noise ratios. The error measures employed in the optimizations are the L1 and L2 norms. Results of the optimizations for both Gaussians, both noise types, and both norms include figures of optimum iteration number and error improvement versus signal-to-noise ratio, and tables of results. The statistical variation of all quantities considered is also given.

Doppler-shift estimation of flat underwater channel using data-aided least-square approach

NASA Astrophysics Data System (ADS)

Pan, Weiqiang; Liu, Ping; Chen, Fangjiong; Ji, Fei; Feng, Jing

2015-06-01

In this paper we proposed a dada-aided Doppler estimation method for underwater acoustic communication. The training sequence is non-dedicate, hence it can be designed for Doppler estimation as well as channel equalization. We assume the channel has been equalized and consider only flat-fading channel. First, based on the training symbols the theoretical received sequence is composed. Next the least square principle is applied to build the objective function, which minimizes the error between the composed and the actual received signal. Then an iterative approach is applied to solve the least square problem. The proposed approach involves an outer loop and inner loop, which resolve the channel gain and Doppler coefficient, respectively. The theoretical performance bound, i.e. the Cramer-Rao Lower Bound (CRLB) of estimation is also derived. Computer simulations results show that the proposed algorithm achieves the CRLB in medium to high SNR cases.