A new stationary gridline artifact suppression method based on the 2D discrete wavelet transform
Tang, Hui; Tong, Dan; Dong Bao, Xu; Dillenseger, Jean-Louis
2015-04-15
Purpose: In digital x-ray radiography, an antiscatter grid is inserted between the patient and the image receptor to reduce scattered radiation. If the antiscatter grid is used in a stationary way, gridline artifacts will appear in the final image. In most of the gridline removal image processing methods, the useful information with spatial frequencies close to that of the gridline is usually lost or degraded. In this study, a new stationary gridline suppression method is designed to preserve more of the useful information. Methods: The method is as follows. The input image is first recursively decomposed into several smaller subimages using a multiscale 2D discrete wavelet transform. The decomposition process stops when the gridline signal is found to be greater than a threshold in one or several of these subimages using a gridline detection module. An automatic Gaussian band-stop filter is then applied to the detected subimages to remove the gridline signal. Finally, the restored image is achieved using the corresponding 2D inverse discrete wavelet transform. Results: The processed images show that the proposed method can remove the gridline signal efficiently while maintaining the image details. The spectra of a 1D Fourier transform of the processed images demonstrate that, compared with some existing gridline removal methods, the proposed method has better information preservation after the removal of the gridline artifacts. Additionally, the performance speed is relatively high. Conclusions: The experimental results demonstrate the efficiency of the proposed method. Compared with some existing gridline removal methods, the proposed method can preserve more information within an acceptable execution time.
2-D wavelet with position controlled resolution
NASA Astrophysics Data System (ADS)
Walczak, Andrzej; Puzio, Leszek
2005-09-01
Wavelet transformation localizes all irregularities in the scene. It is most effective in the case when intensities in the scene have no sharp details. It is the case often present in a medical imaging. To identify the shape one has to extract it from the scene as typical irregularity. When the scene does not contain sharp changes then common differential filters are not efficient tool for a shape extraction. The new 2-D wavelet for such task has been proposed. Described wavelet transform is axially symmetric and has varied scale in dependence on the distance from the centre of the wavelet symmetry. The analytical form of the wavelet has been presented as well as its application for details extraction in the scene. Most important feature of the wavelet transform is that it gives a multi-scale transformation, and if zoom is on the wavelet selectivity varies proportionally to the zoom step. As a result, the extracted shape does not change during zoom operation. What is more the wavelet selectivity can be fit to the local intensity gradient properly to obtain best extraction of the irregularities.
Discrete wavelet analysis of power system transients
Wilkinson, W.A.; Cox, M.D.
1996-11-01
Wavelet analysis is a new method for studying power system transients. Through wavelet analysis, transients are decomposed into a series of wavelet components, each of which is a time-domain signal that covers a specific octave frequency band. This paper presents the basic ideas of discrete wavelet analysis. A variety of actual and simulated transient signals are then analyzed using the discrete wavelet transform that help demonstrate the power of wavelet analysis.
The 2D large deformation analysis using Daubechies wavelet
NASA Astrophysics Data System (ADS)
Liu, Yanan; Qin, Fei; Liu, Yinghua; Cen, Zhangzhi
2010-01-01
In this paper, Daubechies (DB) wavelet is used for solution of 2D large deformation problems. Because the DB wavelet scaling functions are directly used as basis function, no meshes are needed in function approximation. Using the DB wavelet, the solution formulations based on total Lagrangian approach for two-dimensional large deformation problems are established. Due to the lack of Kroneker delta properties in wavelet scaling functions, Lagrange multipliers are used for imposition of boundary condition. Numerical examples of 2D large deformation problems illustrate that this method is effective and stable.
NASA Astrophysics Data System (ADS)
Liu, Hong; Mo, Yu L.
1998-08-01
There are many textures such as woven fabrics having repeating Textron. In order to handle the textural characteristics of images with defects, this paper proposes a new method based on 2D wavelet transform. In the method, a new concept of different adaptive wavelet bases is used to match the texture pattern. The 2D wavelet transform has two different adaptive orthonormal wavelet bases for rows and columns which differ from Daubechies wavelet bases. The orthonormal wavelet bases for rows and columns are generated by genetic algorithm. The experiment result demonstrate the ability of the different adaptive wavelet bases to characterize the texture and locate the defects in the texture.
A parallel splitting wavelet method for 2D conservation laws
NASA Astrophysics Data System (ADS)
Schmidt, Alex A.; Kozakevicius, Alice J.; Jakobsson, Stefan
2016-06-01
The current work presents a parallel formulation using the MPI protocol for an adaptive high order finite difference scheme to solve 2D conservation laws. Adaptivity is achieved at each time iteration by the application of an interpolating wavelet transform in each space dimension. High order approximations for the numerical fluxes are computed by ENO and WENO schemes. Since time evolution is made by a TVD Runge-Kutta space splitting scheme, the problem is naturally suitable for parallelization. Numerical simulations and speedup results are presented for Euler equations in gas dynamics problems.
2-D Continuous Wavelet Transform for ESPI phase-maps denoising
NASA Astrophysics Data System (ADS)
Escalante, Nivia; Villa, Jesús; de la Rosa, Ismael; de la Rosa, Enrique; González-Ramírez, Efrén; Gutiérrez, Osvaldo; Olvera, Carlos; Araiza, María
2013-09-01
In this work we introduce a 2-D Continuous Wavelet Transform (2-D CWT) method for denoising ESPI phase-maps. Multiresolution analysis with 2-D wavelets can provide high directional sensitivity and high anisotropy which are proper characteristics for this task. In particular, the 2-D CWT method using Gabor atoms (Gabor mother wavelets) which can naturally model phase fringes, has a good performance against noise and can preserve phase fringes. We describe the theoretical basis of the proposed technique and show some experimental results with real and simulated ESPI phase-maps. As can be verified the proposal is robust and effective.
Multispectral image compression technology based on dual-tree discrete wavelet transform
NASA Astrophysics Data System (ADS)
Fang, Zhijun; Luo, Guihua; Liu, Zhicheng; Gan, Yun; Lu, Yu
2009-10-01
The paper proposes a combination of DCT and the Dual-Tree Discrete Wavelet Transform (DDWT) to solve the problems in multi-spectral image data storage and transmission. The proposed method not only removes spectral redundancy by1D DCT, but also removes spatial redundancy by 2D Dual-Tree Discrete Wavelet Transform. Therefore, it achieves low distortion under the conditions of high compression and high-quality reconstruction of the multi-spectral image. Tested by DCT, Haar and DDWT, the results show that the proposed method eliminates the blocking effect of wavelet and has strong visual sense and smooth image, which means the superiors with DDWT has more prominent quality of reconstruction and less noise.
A discrete simulation of 2-D fluid flow on TERASYS
Mullins, P.G.; Krolak, P.D.
1995-12-01
A discrete simulation of two-dimensional (2-D) fluid flow, on a recently designed novel architecture called TERASYS is presented. The simulation uses a cellular automaton approach, implemented in a new language called data-parallel bit C (dbC). A performance comparison between our implementation on TERASYS and an implementation on the Connection Machine is discussed. We comment briefly on the suitability of the TERASYS system for modeling fluid flow using cellular automata.
The Wavelet Element Method. Part 2; Realization and Additional Features in 2D and 3D
NASA Technical Reports Server (NTRS)
Canuto, Claudio; Tabacco, Anita; Urban, Karsten
1998-01-01
The Wavelet Element Method (WEM) provides a construction of multiresolution systems and biorthogonal wavelets on fairly general domains. These are split into subdomains that are mapped to a single reference hypercube. Tensor products of scaling functions and wavelets defined on the unit interval are used on the reference domain. By introducing appropriate matching conditions across the interelement boundaries, a globally continuous biorthogonal wavelet basis on the general domain is obtained. This construction does not uniquely define the basis functions but rather leaves some freedom for fulfilling additional features. In this paper we detail the general construction principle of the WEM to the 1D, 2D and 3D cases. We address additional features such as symmetry, vanishing moments and minimal support of the wavelet functions in each particular dimension. The construction is illustrated by using biorthogonal spline wavelets on the interval.
Image denoising with 2D scale-mixing complex wavelet transforms.
Remenyi, Norbert; Nicolis, Orietta; Nason, Guy; Vidakovic, Brani
2014-12-01
This paper introduces an image denoising procedure based on a 2D scale-mixing complex-valued wavelet transform. Both the minimal (unitary) and redundant (maximum overlap) versions of the transform are used. The covariance structure of white noise in wavelet domain is established. Estimation is performed via empirical Bayesian techniques, including versions that preserve the phase of the complex-valued wavelet coefficients and those that do not. The new procedure exhibits excellent quantitative and visual performance, which is demonstrated by simulation on standard test images. PMID:25312931
Electroencephalography data analysis by using discrete wavelet packet transform
NASA Astrophysics Data System (ADS)
Karim, Samsul Ariffin Abdul; Ismail, Mohd Tahir; Hasan, Mohammad Khatim; Sulaiman, Jumat; Muthuvalu, Mohana Sundaram; Janier Josefina, B.
2015-05-01
Electroencephalography (EEG) is the electrical activity generated by the movement of neurons in the brain. It is categorized into delta waves, theta, alpha, beta and gamma. These waves exist in a different frequency band. This paper is a continuation of our previous research. EEG data will be decomposed using Discrete Wavelet Packet Transform (DWPT). Daubechies wavelets 10 (D10) will be used as the basic functions for research purposes. From the main results, it is clear that the DWPT able to characterize the EEG signal corresponding to each wave at a specific frequency. Furthermore, the numerical results obtained better than the results using DWT. Statistical analysis support our main findings.
Long memory analysis by using maximal overlapping discrete wavelet transform
NASA Astrophysics Data System (ADS)
Shafie, Nur Amalina binti; Ismail, Mohd Tahir; Isa, Zaidi
2015-05-01
Long memory process is the asymptotic decay of the autocorrelation or spectral density around zero. The main objective of this paper is to do a long memory analysis by using the Maximal Overlapping Discrete Wavelet Transform (MODWT) based on wavelet variance. In doing so, stock market of Malaysia, China, Singapore, Japan and United States of America are used. The risk of long term and short term investment are also being looked into. MODWT can be analyzed with time domain and frequency domain simultaneously and decomposing wavelet variance to different scales without loss any information. All countries under studied show that they have long memory. Subprime mortgage crisis in 2007 is occurred in the United States of America are possible affect to the major trading countries. Short term investment is more risky than long term investment.
Contrast-based image fusion using the discrete wavelet transform
NASA Astrophysics Data System (ADS)
Pu, Tian; Ni, GuoGiang
2000-08-01
We introduce a contrast-based image fusion method using the wavelet multiresolution analysis. This method includes three steps. First, the multiresolution architectures of the two original input images are obtained using the discrete wavelet transform. A new concept called directive contrast is presented. Second, the multiresolution architecture of the fused image can be achieved by selecting the corresponding subband signals of each input image based on the directive contrast. Finally, the fused image is reconstructed using the inverse wavelet transform. This algorithm is relevant to visual sensitivity and is tested by merging visual and IR images. The result shows that the fused image can integrate the details of each original image. The visual aesthetics and the computed SNRs of the fused images show that the new approaches can provide better fusion results than some previous multiresolution fusion methods.
Wavelet regularization of the 2D incompressible Euler equations
NASA Astrophysics Data System (ADS)
Nguyen van Yen, Romain; Farge, Marie; Schneider, Kai
2009-11-01
We examine the viscosity dependence of the solutions of two-dimensional Navier-Stokes equations in periodic and wall-bounded domains, for Reynolds numbers varying from 10^3 to 10^7. We compare the Navier-Stokes solutions to those of the regularized two-dimensional Euler equations. The regularization is performed by applying at each time step the wavelet-based CVS filter (Farge et al., Phys. Fluids, 11, 1999), which splits turbulent fluctuations into coherent and incoherent contributions. We find that for Reynolds 10^5 the dissipation of coherent enstrophy tends to become independent of Reynolds, while the dissipation of total enstrophy decays to zero logarithmically with Reynolds. In the wall-bounded case, we observe an additional production of enstrophy at the wall. As a result, coherent enstrophy diverges when Reynolds tends to infinity, but its time derivative seems to remain bounded independently of Reynolds. This indicates that a balance may have been established between coherent enstrophy dissipation and coherent enstrophy production at the wall. The Reynolds number for which the dissipation of coherent enstrophy becomes independent on the Reynolds number is proposed to define the onset of the fully-turbulent regime.
Decision support system for diabetic retinopathy using discrete wavelet transform.
Noronha, K; Acharya, U R; Nayak, K P; Kamath, S; Bhandary, S V
2013-03-01
Prolonged duration of the diabetes may affect the tiny blood vessels of the retina causing diabetic retinopathy. Routine eye screening of patients with diabetes helps to detect diabetic retinopathy at the early stage. It is very laborious and time-consuming for the doctors to go through many fundus images continuously. Therefore, decision support system for diabetic retinopathy detection can reduce the burden of the ophthalmologists. In this work, we have used discrete wavelet transform and support vector machine classifier for automated detection of normal and diabetic retinopathy classes. The wavelet-based decomposition was performed up to the second level, and eight energy features were extracted. Two energy features from the approximation coefficients of two levels and six energy values from the details in three orientations (horizontal, vertical and diagonal) were evaluated. These features were fed to the support vector machine classifier with various kernel functions (linear, radial basis function, polynomial of orders 2 and 3) to evaluate the highest classification accuracy. We obtained the highest average classification accuracy, sensitivity and specificity of more than 99% with support vector machine classifier (polynomial kernel of order 3) using three discrete wavelet transform features. We have also proposed an integrated index called Diabetic Retinopathy Risk Index using clinically significant wavelet energy features to identify normal and diabetic retinopathy classes using just one number. We believe that this (Diabetic Retinopathy Risk Index) can be used as an adjunct tool by the doctors during the eye screening to cross-check their diagnosis. PMID:23662341
Interpretation of gravity data using 2-D continuous wavelet transformation and 3-D inverse modeling
NASA Astrophysics Data System (ADS)
Roshandel Kahoo, Amin; Nejati Kalateh, Ali; Salajegheh, Farshad
2015-10-01
Recently the continuous wavelet transform has been proposed for interpretation of potential field anomalies. In this paper, we introduced a 2D wavelet based method that uses a new mother wavelet for determination of the location and the depth to the top and base of gravity anomaly. The new wavelet is the first horizontal derivatives of gravity anomaly of a buried cube with unit dimensions. The effectiveness of the proposed method is compared with Li and Oldenburg inversion algorithm and is demonstrated with synthetics and real gravity data. The real gravity data is taken over the Mobrun massive sulfide ore body in Noranda, Quebec, Canada. The obtained results of the 2D wavelet based algorithm and Li and Oldenburg inversion on the Mobrun ore body had desired similarities to the drill-hole depth information. In all of the inversion algorithms the model non-uniqueness is the challenging problem. Proposed method is based on a simple theory and there is no model non-uniqueness on it.
Discrete Wavelet Transform for Fault Locations in Underground Distribution System
NASA Astrophysics Data System (ADS)
Apisit, C.; Ngaopitakkul, A.
2010-10-01
In this paper, a technique for detecting faults in underground distribution system is presented. Discrete Wavelet Transform (DWT) based on traveling wave is employed in order to detect the high frequency components and to identify fault locations in the underground distribution system. The first peak time obtained from the faulty bus is employed for calculating the distance of fault from sending end. The validity of the proposed technique is tested with various fault inception angles, fault locations and faulty phases. The result is found that the proposed technique provides satisfactory result and will be very useful in the development of power systems protection scheme.
Embolic Doppler ultrasound signal detection using discrete wavelet transform.
Aydin, Nizamettin; Marvasti, Farokh; Markus, Hugh S
2004-06-01
Asymptomatic circulating emboli can be detected by Doppler ultrasound. Embolic Doppler ultrasound signals are short duration transient like signals. The wavelet transform is an ideal method for analysis and detection of such signals by optimizing time-frequency resolution. We propose a detection system based on the discrete wavelet transform (DWT) and study some parameters, which might be useful for describing embolic signals (ES). We used a fast DWT algorithm based on the Daubechies eighth-order wavelet filters with eight scales. In order to evaluate feasibility of the DWT of ES, two independent data sets, each comprising of short segments containing an ES (N = 100), artifact (N = 100) or Doppler speckle (DS) (N = 100), were used. After applying the DWT to the data, several parameters were evaluated. The threshold values used for both data sets were optimized using the first data set. While the DWT coefficients resulting from artifacts dominantly appear at the higher scales (five, six, seven, and eight), the DWT coefficients at the lower scales (one, two, three, and four) are mainly dominated by ES and DS. The DWT is able to filter out most of the artifacts inherently during the transform process. For the first data set, 98 out of 100 ES were detected as ES. For the second data set, 95 out of 100 ES were detected as ES when the same threshold values were used. The algorithm was also tested with a third data set comprising 202 normal ES; 198 signals were detected as ES. PMID:15217263
Background Subtraction Based on Three-Dimensional Discrete Wavelet Transform
Han, Guang; Wang, Jinkuan; Cai, Xi
2016-01-01
Background subtraction without a separate training phase has become a critical task, because a sufficiently long and clean training sequence is usually unavailable, and people generally thirst for immediate detection results from the first frame of a video. Without a training phase, we propose a background subtraction method based on three-dimensional (3D) discrete wavelet transform (DWT). Static backgrounds with few variations along the time axis are characterized by intensity temporal consistency in the 3D space-time domain and, hence, correspond to low-frequency components in the 3D frequency domain. Enlightened by this, we eliminate low-frequency components that correspond to static backgrounds using the 3D DWT in order to extract moving objects. Owing to the multiscale analysis property of the 3D DWT, the elimination of low-frequency components in sub-bands of the 3D DWT is equivalent to performing a pyramidal 3D filter. This 3D filter brings advantages to our method in reserving the inner parts of detected objects and reducing the ringing around object boundaries. Moreover, we make use of wavelet shrinkage to remove disturbance of intensity temporal consistency and introduce an adaptive threshold based on the entropy of the histogram to obtain optimal detection results. Experimental results show that our method works effectively in situations lacking training opportunities and outperforms several popular techniques. PMID:27043570
Discrete wavelet transform core for image processing applications
NASA Astrophysics Data System (ADS)
Savakis, Andreas E.; Carbone, Richard
2005-02-01
This paper presents a flexible hardware architecture for performing the Discrete Wavelet Transform (DWT) on a digital image. The proposed architecture uses a variation of the lifting scheme technique and provides advantages that include small memory requirements, fixed-point arithmetic implementation, and a small number of arithmetic computations. The DWT core may be used for image processing operations, such as denoising and image compression. For example, the JPEG2000 still image compression standard uses the Cohen-Daubechies-Favreau (CDF) 5/3 and CDF 9/7 DWT for lossless and lossy image compression respectively. Simple wavelet image denoising techniques resulted in improved images up to 27 dB PSNR. The DWT core is modeled using MATLAB and VHDL. The VHDL model is synthesized to a Xilinx FPGA to demonstrate hardware functionality. The CDF 5/3 and CDF 9/7 versions of the DWT are both modeled and used as comparisons. The execution time for performing both DWTs is nearly identical at approximately 14 clock cycles per image pixel for one level of DWT decomposition. The hardware area generated for the CDF 5/3 is around 15,000 gates using only 5% of the Xilinx FPGA hardware area, at 2.185 MHz max clock speed and 24 mW power consumption.
Background Subtraction Based on Three-Dimensional Discrete Wavelet Transform.
Han, Guang; Wang, Jinkuan; Cai, Xi
2016-01-01
Background subtraction without a separate training phase has become a critical task, because a sufficiently long and clean training sequence is usually unavailable, and people generally thirst for immediate detection results from the first frame of a video. Without a training phase, we propose a background subtraction method based on three-dimensional (3D) discrete wavelet transform (DWT). Static backgrounds with few variations along the time axis are characterized by intensity temporal consistency in the 3D space-time domain and, hence, correspond to low-frequency components in the 3D frequency domain. Enlightened by this, we eliminate low-frequency components that correspond to static backgrounds using the 3D DWT in order to extract moving objects. Owing to the multiscale analysis property of the 3D DWT, the elimination of low-frequency components in sub-bands of the 3D DWT is equivalent to performing a pyramidal 3D filter. This 3D filter brings advantages to our method in reserving the inner parts of detected objects and reducing the ringing around object boundaries. Moreover, we make use of wavelet shrinkage to remove disturbance of intensity temporal consistency and introduce an adaptive threshold based on the entropy of the histogram to obtain optimal detection results. Experimental results show that our method works effectively in situations lacking training opportunities and outperforms several popular techniques. PMID:27043570
Davis, A.B.
1998-12-01
The authors compare several ways of uncovering multifractal properties of data in 1D and 2D using wavelet transforms. The WTMM or (Continuous) Wavelet Transform Maximum Modulus method has been extensively documented and widely applied by Dr. Alain Arneodo`s (Bordeaux) group, to the point where their successes have overshadowed simpler techniques that use the Discrete WT. What the latter lack in robustness is gained in efficiency, thus enabling virtually real-time multifractal analysis of data as it is collected. Another advantage of DWT-based approaches is that tensor products of dyadic and triadic branching schemes enable a straightforward attack on strong anisotropy in natural and artificial 2D random fields.
Efficient architectures for two-dimensional discrete wavelet transform using lifting scheme.
Xiong, Chengyi; Tian, Jinwen; Liu, Jian
2007-03-01
Novel architectures for 1-D and 2-D discrete wavelet transform (DWT) by using lifting schemes are presented in this paper. An embedded decimation technique is exploited to optimize the architecture for 1-D DWT, which is designed to receive an input and generate an output with the low- and high-frequency components of original data being available alternately. Based on this 1-D DWT architecture, an efficient line-based architecture for 2-D DWT is further proposed by employing parallel and pipeline techniques, which is mainly composed of two horizontal filter modules and one vertical filter module, working in parallel and pipeline fashion with 100% hardware utilization. This 2-D architecture is called fast architecture (FA) that can perform J levels of decomposition for N * N image in approximately 2N2(1 - 4(-J))/3 internal clock cycles. Moreover, another efficient generic line-based 2-D architecture is proposed by exploiting the parallelism among four subband transforms in lifting-based 2-D DWT, which can perform J levels of decomposition for N * N image in approximately N2(1 - 4(-J))/3 internal clock cycles; hence, it is called high-speed architecture. The throughput rate of the latter is increased by two times when comparing with the former 2-D architecture, but only less additional hardware cost is added. Compared with the works reported in previous literature, the proposed architectures for 2-D DWT are efficient alternatives in tradeoff among hardware cost, throughput rate, output latency and control complexity, etc. PMID:17357722
Wavelet characterization of 2D turbulence and intermittency in magnetized electron plasmas
NASA Astrophysics Data System (ADS)
Romé, M.; Chen, S.; Maero, G.
2016-06-01
A study of the free relaxation of turbulence in a two-dimensional (2D) flow is presented, with a focus on the role of the initial vorticity conditions. Exploiting a well-known analogy with 2D inviscid incompressible fluids, the system investigated here is a magnetized pure electron plasma. The dynamics of this system are simulated by means of a 2D particle-in-cell code, starting from different spiral density (vorticity) distributions. A wavelet multiresolution analysis is adopted, which allows the coherent and incoherent parts of the flow to be separated. Comparison of the turbulent evolution in the different cases is based on the investigation of the time evolution of statistical properties, including the probability distribution functions and structure functions of the vorticity increments. It is also based on an analysis of the enstrophy evolution and its spectrum for the two components. In particular, while the statistical features assess the degree of flow intermittency, spectral analysis allows us not only to estimate the time required to reach a state of fully developed turbulence, but also estimate its dependence on the thickness of the initial spiral density distribution, accurately tracking the dynamics of both the coherent structures and the turbulent background. The results are compared with those relevant to annular initial vorticity distributions (Chen et al 2015 J. Plasma Phys. 81 495810511).
An Automatic 3D Facial Landmarking Algorithm Using 2D Gabor Wavelets.
de Jong, Markus A; Wollstein, Andreas; Ruff, Clifford; Dunaway, David; Hysi, Pirro; Spector, Tim; Fan Liu; Niessen, Wiro; Koudstaal, Maarten J; Kayser, Manfred; Wolvius, Eppo B; Bohringer, Stefan
2016-02-01
In this paper, we present a novel approach to automatic 3D facial landmarking using 2D Gabor wavelets. Our algorithm considers the face to be a surface and uses map projections to derive 2D features from raw data. Extracted features include texture, relief map, and transformations thereof. We extend an established 2D landmarking method for simultaneous evaluation of these data. The method is validated by performing landmarking experiments on two data sets using 21 landmarks and compared with an active shape model implementation. On average, landmarking error for our method was 1.9 mm, whereas the active shape model resulted in an average landmarking error of 2.3 mm. A second study investigating facial shape heritability in related individuals concludes that automatic landmarking is on par with manual landmarking for some landmarks. Our algorithm can be trained in 30 min to automatically landmark 3D facial data sets of any size, and allows for fast and robust landmarking of 3D faces. PMID:26540684
Prostate segmentation algorithm using dyadic wavelet transform and discrete dynamic contour
NASA Astrophysics Data System (ADS)
Chiu, Bernard; Freeman, George H.; Salama, M. M. A.; Fenster, Aaron
2004-11-01
Knowing the location and the volume of the prostate is important for ultrasound-guided prostate brachytherapy, a commonly used prostate cancer treatment method. The prostate boundary must be segmented before a dose plan can be obtained. However, manual segmentation is arduous and time consuming. This paper introduces a semi-automatic segmentation algorithm based on the dyadic wavelet transform (DWT) and the discrete dynamic contour (DDC). A spline interpolation method is used to determine the initial contour based on four user-defined initial points. The DDC model then refines the initial contour based on the approximate coefficients and the wavelet coefficients generated using the DWT. The DDC model is executed under two settings. The coefficients used in these two settings are derived using smoothing functions with different sizes. A selection rule is used to choose the best contour based on the contours produced in these two settings. The accuracy of the final contour produced by the proposed algorithm is evaluated by comparing it with the manual contour outlined by an expert observer. A total of 114 2D TRUS images taken for six different patients scheduled for brachytherapy were segmented using the proposed algorithm. The average difference between the contour segmented using the proposed algorithm and the manually outlined contour is less than 3 pixels.
Prostate segmentation algorithm using dyadic wavelet transform and discrete dynamic contour.
Chiu, Bernard; Freeman, George H; Salama, M M A; Fenster, Aaron
2004-11-01
Knowing the location and the volume of the prostate is important for ultrasound-guided prostate brachytherapy, a commonly used prostate cancer treatment method. The prostate boundary must be segmented before a dose plan can be obtained. However, manual segmentation is arduous and time consuming. This paper introduces a semi-automatic segmentation algorithm based on the dyadic wavelet transform (DWT) and the discrete dynamic contour (DDC). A spline interpolation method is used to determine the initial contour based on four user-defined initial points. The DDC model then refines the initial contour based on the approximate coefficients and the wavelet coefficients generated using the DWT. The DDC model is executed under two settings. The coefficients used in these two settings are derived using smoothing functions with different sizes. A selection rule is used to choose the best contour based on the contours produced in these two settings. The accuracy of the final contour produced by the proposed algorithm is evaluated by comparing it with the manual contour outlined by an expert observer. A total of 114 2D TRUS images taken for six different patients scheduled for brachytherapy were segmented using the proposed algorithm. The average difference between the contour segmented using the proposed algorithm and the manually outlined contour is less than 3 pixels. PMID:15584529
NASA Astrophysics Data System (ADS)
Gareis, I.; Gentiletti, G.; Acevedo, R.; Rufiner, L.
2011-09-01
The purpose of this work is to evaluate different feature extraction alternatives to detect the event related evoked potential signal on brain computer interfaces, trying to minimize the time employed and the classification error, in terms of sensibility and specificity of the method, looking for alternatives to coherent averaging. In this context the results obtained performing the feature extraction using discrete dyadic wavelet transform using different mother wavelets are presented. For the classification a single layer perceptron was used. The results obtained with and without the wavelet decomposition were compared; showing an improvement on the classification rate, the specificity and the sensibility for the feature vectors obtained using some mother wavelets.
Wavelet diagnostics of the flow control of unsteady separation on a 2D Wind Turbine Airfoil
NASA Astrophysics Data System (ADS)
Bai, Zhe; Lewalle, Jacques; Wang, Guannan; Glauser, Mark
2013-11-01
We investigated the aerodynamic characteristics of a 2D wind turbine airfoil. Unsteadiness was associated with the wake of a cylinder upstream of the airfoil. The experiments were conducted in both the baseline case, and with active closed-loop control on the suction surface of the airfoil. The data consisted of surface pressure time series. Continuous wavelet analysis gave the phase, band-pass filtered signals and envelope of harmonics of the fundamental shedding frequency. Coherence of pairs of signals was also used to map the flow characteristics. For the baseline and controlled case, we will report on the relation between phase of the leading edge fluctuations, unsteady flow separation and lift and drag coefficients. Our goal is to develop a more effective controller. The experiment was funded by DoE through University of Minnesota Wind Energy Consortium. Thanks for the support from the MAE department of Syracuse University.
A multispeed Discrete Boltzmann Model for transcritical 2D shallow water flows
NASA Astrophysics Data System (ADS)
La Rocca, Michele; Montessori, Andrea; Prestininzi, Pietro; Succi, Sauro
2015-03-01
In this work a Discrete Boltzmann Model for the solution of transcritical 2D shallow water flows is presented and validated. In order to provide the model with transcritical capabilities, a particular multispeed velocity set has been employed for the discretization of the Boltzmann equation. It is shown that this particular set naturally yields a simple and closed procedure to determine higher order equilibrium distribution functions needed to simulate transcritical flow. The model is validated through several classical benchmarks and is proven to correctly and accurately simulate both 1D and 2D transitions between the two flow regimes.
NASA Astrophysics Data System (ADS)
Etehadtavakol, Mahnaz; Ng, E. Y. K.; Chandran, Vinod; Rabbani, Hossien
2013-11-01
Highly sensitive infrared cameras can produce high-resolution diagnostic images of the temperature and vascular changes of breasts. Wavelet transform based features are suitable in extracting the texture difference information of these images due to their scale-space decomposition. The objective of this study is to investigate the potential of extracted features in differentiating between breast lesions by comparing the two corresponding pectoral regions of two breast thermograms. The pectoral regions of breastsare important because near 50% of all breast cancer is located in this region. In this study, the pectoral region of the left breast is selected. Then the corresponding pectoral region of the right breast is identified. Texture features based on the first and the second sets of statistics are extracted from wavelet decomposed images of the pectoral regions of two breast thermograms. Principal component analysis is used to reduce dimension and an Adaboost classifier to evaluate classification performance. A number of different wavelet features are compared and it is shown that complex non-separable 2D discrete wavelet transform features perform better than their real separable counterparts.
A novel sliding window algorithm for 2D discrete Fourier transform
NASA Astrophysics Data System (ADS)
Dong, Zhifang; Wu, Jiasong; Gui, Jiyong
2015-12-01
Discrete Fourier transform (DFT) is one of the most wildly used tools for signal processing. In this paper, a novel sliding window algorithm is presented for fast computing 2D DFT when sliding window shifts more than one-point. The propose algorithm computing the DFT of the current window using that of the previous window. For fast computation, we take advantage of the recursive process of 2D SDFT and butterfly-based algorithm. So it can be directly applied to 2D signal processing. The theoretical analysis shows that the computational complexity is equal to 2D SDFT when one sample comes into current window. As well, the number of additions and multiplications of our proposed algorithm are less than those of 2D vector radix FFT when sliding window shifts mutiple-point.
A study of renal blood flow regulation using the discrete wavelet transform
NASA Astrophysics Data System (ADS)
Pavlov, Alexey N.; Pavlova, Olga N.; Mosekilde, Erik; Sosnovtseva, Olga V.
2010-02-01
In this paper we provide a way to distinguish features of renal blood flow autoregulation mechanisms in normotensive and hypertensive rats based on the discrete wavelet transform. Using the variability of the wavelet coefficients we show distinctions that occur between the normal and pathological states. A reduction of this variability in hypertension is observed on the microscopic level of the blood flow in efferent arteriole of single nephrons. This reduction is probably associated with higher flexibility of healthy cardiovascular system.
Edward Jero, S; Ramu, Palaniappan; Ramakrishnan, S
2014-10-01
ECG Steganography provides secured transmission of secret information such as patient personal information through ECG signals. This paper proposes an approach that uses discrete wavelet transform to decompose signals and singular value decomposition (SVD) to embed the secret information into the decomposed ECG signal. The novelty of the proposed method is to embed the watermark using SVD into the two dimensional (2D) ECG image. The embedding of secret information in a selected sub band of the decomposed ECG is achieved by replacing the singular values of the decomposed cover image by the singular values of the secret data. The performance assessment of the proposed approach allows understanding the suitable sub-band to hide secret data and the signal degradation that will affect diagnosability. Performance is measured using metrics like Kullback-Leibler divergence (KL), percentage residual difference (PRD), peak signal to noise ratio (PSNR) and bit error rate (BER). A dynamic location selection approach for embedding the singular values is also discussed. The proposed approach is demonstrated on a MIT-BIH database and the observations validate that HH is the ideal sub-band to hide data. It is also observed that the signal degradation (less than 0.6%) is very less in the proposed approach even with the secret data being as large as the sub band size. So, it does not affect the diagnosability and is reliable to transmit patient information. PMID:25187409
Tensor representation of color images and fast 2D quaternion discrete Fourier transform
NASA Astrophysics Data System (ADS)
Grigoryan, Artyom M.; Agaian, Sos S.
2015-03-01
In this paper, a general, efficient, split algorithm to compute the two-dimensional quaternion discrete Fourier transform (2-D QDFT), by using the special partitioning in the frequency domain, is introduced. The partition determines an effective transformation, or color image representation in the form of 1-D quaternion signals which allow for splitting the N × M-point 2-D QDFT into a set of 1-D QDFTs. Comparative estimates revealing the efficiency of the proposed algorithms with respect to the known ones are given. In particular, a proposed method of calculating the 2r × 2r -point 2-D QDFT uses 18N2 less multiplications than the well-known column-row method and method of calculation based on the symplectic decomposition. The proposed algorithm is simple to apply and design, which makes it very practical in color image processing in the frequency domain.
NASA Astrophysics Data System (ADS)
Galiana-Merino, J. J.; Rosa-Herranz, J. L.; Rosa-Cintas, S.; Martinez-Espla, J. J.
2013-01-01
A MATLAB-based computer code has been developed for the simultaneous wavelet analysis and filtering of multichannel seismic data. The considered time-frequency transforms include the continuous wavelet transform, the discrete wavelet transform and the discrete wavelet packet transform. The developed approaches provide a fast and precise time-frequency examination of the seismograms at different frequency bands. Moreover, filtering methods for noise, transients or even baseline removal, are implemented. The primary motivation is to support seismologists with a user-friendly and fast program for the wavelet analysis, providing practical and understandable results. Program summaryProgram title: SeismicWaveTool Catalogue identifier: AENG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENG_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 611072 No. of bytes in distributed program, including test data, etc.: 14688355 Distribution format: tar.gz Programming language: MATLAB (MathWorks Inc.) version 7.8.0.347 (R2009a) or higher. Wavelet Toolbox is required. Computer: Developed on a MacBook Pro. Tested on Mac and PC. No computer-specific optimization was performed. Operating system: Any supporting MATLAB (MathWorks Inc.) v7.8.0.347 (R2009a) or higher. Tested on Mac OS X 10.6.8, Windows XP and Vista. Classification: 13. Nature of problem: Numerous research works have developed a great number of free or commercial wavelet based software, which provide specific solutions for the analysis of seismic data. On the other hand, standard toolboxes, packages or libraries, such as the MathWorks' Wavelet Toolbox for MATLAB, offer command line functions and interfaces for the wavelet analysis of one-component signals. Thus, software usually is focused on very specific problems
NASA Astrophysics Data System (ADS)
Fayadh, Rashid A.; Malek, F.; Fadhil, Hilal A.; Dawood, Sameer A.; Abdullah, Farah Salwani
2015-05-01
In this paper, three levels of analysis and synthesis filter banks were used to create coefficients for a continuous wavelet transform (CWT) and discrete wavelet transform (DWT). The main property of these wavelet transform schemes is their ability to construct the transmitted signal across a log-normal fading channel over additive white Gaussian noise (AWGN). Wireless rake-receiver structure was chosen as a major application to reduce the inter-symbol interference (ISI) and to minimize the noise. In this work, a new scheme of rake receiver is proposed to receive indoor, multi-path components (MPCs) for ultra-wideband (UWB) wireless communication systems. Rake receivers consist of a continuous wavelet rake (CW-rake) and a discrete wavelet rake (DW-rake), and they use huge bandwidth (7.5 GHz), as reported by the Federal Communications Commission (FCC). The indoor channel models chose for analysis in this research were the non line-of-sight (LOS) channel model (CM4 from 4 to 10 meters) to show the behavior of bit error rate (BER) with respect to signal-to noise ratio (SNR). Two types of rake receiver were used in the simulation, i.e., partial-rake and selective-rake receivers with the maximal ratio combining (MRC) technique to capture the energy of the signal from the output of the rake's fingers.
NASA Astrophysics Data System (ADS)
Santos, C. A. G.; Freire, P. K. M. M.; Silva, G. B. L.; Silva, R. M.
2014-09-01
This paper proposes the use of discrete wavelet transform (DWT) to remove the high-frequency components (details) of an original signal, because the noises generally present in time series (e.g. streamflow records) may influence the prediction quality. Cleaner signals could then be used as inputs to an artificial neural network (ANN) in order to improve the model performance of daily discharge forecasting. Wavelet analysis provides useful decompositions of original time series in high and low frequency components. The present application uses the Coiflet wavelets to decompose hydrological data, as there have been few reports in the literature. Finally, the proposed technique is tested using the inflow records to the Três Marias reservoir in São Francisco River basin, Brazil. This transformed signal is used as input for an ANN model to forecast inflows seven days ahead, and the error RMSE decreased by more than 50% (i.e. from 454.2828 to 200.0483).
Analysis of spike-wave discharges in rats using discrete wavelet transform.
Ubeyli, Elif Derya; Ilbay, Gül; Sahin, Deniz; Ateş, Nurbay
2009-03-01
A feature is a distinctive or characteristic measurement, transform, structural component extracted from a segment of a pattern. Features are used to represent patterns with the goal of minimizing the loss of important information. The discrete wavelet transform (DWT) as a feature extraction method was used in representing the spike-wave discharges (SWDs) records of Wistar Albino Glaxo/Rijswijk (WAG/Rij) rats. The SWD records of WAG/Rij rats were decomposed into time-frequency representations using the DWT and the statistical features were calculated to depict their distribution. The obtained wavelet coefficients were used to identify characteristics of the signal that were not apparent from the original time domain signal. The present study demonstrates that the wavelet coefficients are useful in determining the dynamics in the time-frequency domain of SWD records. PMID:19230874
Modeling and 2-D discrete simulation of dislocation dynamics for plastic deformation of metal
NASA Astrophysics Data System (ADS)
Liu, Juan; Cui, Zhenshan; Ou, Hengan; Ruan, Liqun
2013-05-01
Two methods are employed in this paper to investigate the dislocation evolution during plastic deformation of metal. One method is dislocation dynamic simulation of two-dimensional discrete dislocation dynamics (2D-DDD), and the other is dislocation dynamics modeling by means of nonlinear analysis. As screw dislocation is prone to disappear by cross-slip, only edge dislocation is taken into account in simulation. First, an approach of 2D-DDD is used to graphically simulate and exhibit the collective motion of a large number of discrete dislocations. In the beginning, initial grains are generated in the simulation cells according to the mechanism of grain growth and the initial dislocation is randomly distributed in grains and relaxed under the internal stress. During the simulation process, the externally imposed stress, the long range stress contribution of all dislocations and the short range stress caused by the grain boundaries are calculated. Under the action of these forces, dislocations begin to glide, climb, multiply, annihilate and react with each other. Besides, thermal activation process is included. Through the simulation, the distribution of dislocation and the stress-strain curves can be obtained. On the other hand, based on the classic dislocation theory, the variation of the dislocation density with time is described by nonlinear differential equations. Finite difference method (FDM) is used to solve the built differential equations. The dislocation evolution at a constant strain rate is taken as an example to verify the rationality of the model.
HPLC analysis of discrete haptoglobin isoform N-linked oligosaccharides following 2D-PAGE isolation.
He, Zhicong; Aristoteli, Lina P; Kritharides, Leonard; Garner, Brett
2006-05-01
Glycosylation is a common but variable modification that regulates glycoprotein structure and function. We combined small format 2D-PAGE with HPLC to analyse discrete human haptoglobin isoform N-glycans. Seven major and several minor haptoglobin isoforms were detected by 2D-PAGE. N-Glycans released from Coomassie-stained gel spots using PNGase were labeled at their reducing termini with 2-aminobenzamide. HPLC analysis of selected major isoform N-glycans indicated that sialic acid composition determined their separation by isoelectric focussing. N-Glycans from two doublets of quantitatively minor isoforms were also analysed. Although separation of each pair of doublets was influenced by sialylation, individual spots within each doublet contained identical N-glycans. Thus, heterogeneity in minor haptoglobin isoforms was due to modifications distinct from N-glycan structure. These studies describe a simple method for analysing low abundance protein N-glycans and provide details of discrete haptoglobin isoform N-glycan structures which will be useful in proteomic analysis of human plasma samples. PMID:16546121
A 2D Electromechanical Model of Human Atrial Tissue Using the Discrete Element Method
Brocklehurst, Paul; Adeniran, Ismail; Yang, Dongmin; Sheng, Yong; Zhang, Henggui; Ye, Jianqiao
2015-01-01
Cardiac tissue is a syncytium of coupled cells with pronounced intrinsic discrete nature. Previous models of cardiac electromechanics often ignore such discrete properties and treat cardiac tissue as a continuous medium, which has fundamental limitations. In the present study, we introduce a 2D electromechanical model for human atrial tissue based on the discrete element method (DEM). In the model, single-cell dynamics are governed by strongly coupling the electrophysiological model of Courtemanche et al. to the myofilament model of Rice et al. with two-way feedbacks. Each cell is treated as a viscoelastic body, which is physically represented by a clump of nine particles. Cell aggregations are arranged so that the anisotropic nature of cardiac tissue due to fibre orientations can be modelled. Each cell is electrically coupled to neighbouring cells, allowing excitation waves to propagate through the tissue. Cell-to-cell mechanical interactions are modelled using a linear contact bond model in DEM. By coupling cardiac electrophysiology with mechanics via the intracellular Ca2+ concentration, the DEM model successfully simulates the conduction of cardiac electrical waves and the tissue's corresponding mechanical contractions. The developed DEM model is numerically stable and provides a powerful method for studying the electromechanical coupling problem in the heart. PMID:26583141
Use of switched capacitor filters to implement the discrete wavelet transform
NASA Technical Reports Server (NTRS)
Kaiser, Kraig E.; Peterson, James N.
1993-01-01
This paper analyzes the use of IIR switched capacitor filters to implement the discrete wavelet transform and the inverse transform, using quadrature mirror filters (QMF) which have the necessary symmetry for reconstruction of the data. This is done by examining the sensitivity of the QMF transforms to the manufacturing variance in the desired capacitances. The performance is evaluated at the outputs of the separate filter stages and the error in the reconstruction of the inverse transform is compared with the desired results.
Sibillano, Teresa; Ancona, Antonio; Rizzi, Domenico; Lupo, Valentina; Tricarico, Luigi; Lugarà, Pietro Mario
2010-01-01
The plasma optical radiation emitted during CO2 laser welding of stainless steel samples has been detected with a Si-PIN photodiode and analyzed under different process conditions. The discrete wavelet transform (DWT) has been used to decompose the optical signal into various discrete series of sequences over different frequency bands. The results show that changes of the process settings may yield different signal features in the range of frequencies between 200 Hz and 30 kHz. Potential applications of this method to monitor in real time the laser welding processes are also discussed. PMID:22319311
2D resistivity inversion using conjugate gradients for a finite element discretization
NASA Astrophysics Data System (ADS)
Bortolozo, C. A.; Santos, F. M.; Porsani, J. L.
2014-12-01
In this work we present a DC 2D inversion algorithm using conjugate gradients relaxation to solve the maximum likelihood inverse equations. We apply, according to Zhang (1995), the maximum likelihood inverse theory developed by Tarantola and Valette (1982) to our 2D resistivity inversion. This algorithm was chosen to this research because it doesn't need to calculate the field's derivatives. Since conjugate gradient techniques only need the results of the sensitivity matrix Ã or its transpose ÃT multiplying a vector, the actual computation of the sensitivity matrix are not performed, according to the methodology described in Zhang (1995). In Zhang (1995), the terms Ãx and ÃTy, are dependent of the stiffness matrix K and its partial derivative ∂K⁄∂ρ. The inversion methodology described in Zhang (1995) is for the case of 3D electrical resistivity by finite differences discretization. So it was necessary to make a series of adjustments to obtain a satisfactory result for 2D electrical inversion using finite element method. The difference between the modeling of 3D resistivity with finite difference and the 2D finite element method are in the integration variable, used in the 2D case. In the 2D case the electrical potential are initially calculated in the transformed domain, including the stiffness matrix, and only in the end is transformed in Cartesian domain. In the case of 3D, described by Zhang (1995) this is done differently, the calculation is done directly in the Cartesian domain. In the literature was not found any work describing how to deal with this problem. Because the calculations of Ãx and ÃTy must be done without having the real stiffness matrix, the adaptation consist in calculate the stiffness matrix and its partial derivative using a set of integration variables. We transform those matrix in the same form has in the potential case, but with different sets of variables. The results will be presented and are very promising.
Cojocaru, E
2004-02-20
Thin-film wavelets are further analyzed for the design of dichroic mirrors for ultrafast solid-state lasers that provide both high reflectance on the lasing wavelength range and high transmittance of the pump light. Discrete quarter-wave-thick dielectric thin-film structures of homogeneous refractive indices following a quintic-wavelet envelope are considered. Relations for the reflectance on the lasing wavelength range are given. Adding several index-matching quarter-wave layers to both sides of the discrete wavelet optimizes the transmittance of the pump light. The design is further optimized to get minimum phase distortion on the lasing wavelength range. PMID:15008528
Davis, A. B.; Petrov, N. P.; Clothiaux, E. E.; Marshak, A.
2002-01-01
Spatial and/or temporal variabilities of clouds is of paramount importance for at least two in tensely researched sub-problems in global and regional climate modeling: (1) cloud-radiation interaction where correlations can trigger 3D radiative transfer effects; and (2) dynamical cloud modeling where the goal is to realistically reproduce the said correlations. We propose wavelets as a simple yet powerful way of quantifying cloud variability. More precisely, we use 'semi-discrete' wavelet transforms which, at least in the present statistical applications, have advantages over both its continuous and discrete counterparts found in the bulk of the wavelet literature. With the particular choice of normalization we adopt, the scale-dependence of the variance of the wavelet coefficients (i.e,, the wavelet energy spectrum) is always a better discriminator of transition from 'stationary' to 'nonstationary' behavior than conventional methods based on auto-correlation analysis, second-order structure function (a.k.a. the semi-variogram), or Fourier analysis. Indeed, the classic statistics go at best from monotonically scale- or wavenumber-dependent to flat at such a transition; by contrast, the wavelet spectrum changes the sign of its derivative with respect to scale. We apply 1D and 2D semi-discrete wavelet transforms to remote sensing data on cloud structure from two sources: (1) an upward-looking milli-meter cloud radar (MMCR) at DOE's climate observation site in Oklahoma deployed as part of the Atmospheric Radiation Measurement (ARM) Progrm; and (2) DOE's Multispectral Thermal Imager (MTI), a high-resolution space-borne instrument in sunsynchronous orbit that is described in sufficient detail for our present purposes by Weber et al. (1999). For each type of data, we have at least one theoretical prediction - with empirical validation already in existence - for a power-law relation for wavelet statistics with respect to scale. This is what is expected in physical (i
Application of the 2-D discrete-ordinates method to multiple scattering of laser radiation
Zardecki, A.; Gerstl, S.A.W.; Embury, J.F.
1983-05-01
The discrete-ordinates finite-element radiation transport code twotran is applied to describe the multiple scattering of a laser beam from a reflecting target. For a model scenario involving a 99% relative humidity rural aerosol we compute the average intensity of the scattered radiation and correction factors to the Beer-Lambert law arising from multiple scattering. As our results indicate, 2-D x-y and r-z geometry modeling can reliably describe a realistic 3-D scenario. Specific results are presented for the two visual ranges of 1.52 and 0.76 km which show that, for sufficiently high aerosol concentrations (e.g., equivalent to V = 0.76 km), the target signature in a distant detector becomes dominated by multiply scattered radiation from interactions of the laser light with the aerosol environment. The merits of the scaling group and the delta-M approximation for the transfer equation are also explored.
A framework for grand scale parallelization of the combined finite discrete element method in 2d
NASA Astrophysics Data System (ADS)
Lei, Z.; Rougier, E.; Knight, E. E.; Munjiza, A.
2014-09-01
Within the context of rock mechanics, the Combined Finite-Discrete Element Method (FDEM) has been applied to many complex industrial problems such as block caving, deep mining techniques (tunneling, pillar strength, etc.), rock blasting, seismic wave propagation, packing problems, dam stability, rock slope stability, rock mass strength characterization problems, etc. The reality is that most of these were accomplished in a 2D and/or single processor realm. In this work a hardware independent FDEM parallelization framework has been developed using the Virtual Parallel Machine for FDEM, (V-FDEM). With V-FDEM, a parallel FDEM software can be adapted to different parallel architecture systems ranging from just a few to thousands of cores.
FPGA implementation of 2-D discrete cosine transforms algorithm using systemC
NASA Astrophysics Data System (ADS)
Liu, Yifei; Ding, Mingyue
2007-12-01
Discrete Cosine Transform (DCT) is widely applied in image and video compression. This paper presented the software and hardware co-design method based on SystemC. As a case of study, a two dimension (2D) DCT Algorithm was implemented on Programmable Gate Arrays (FPGAs) chip. The short simulation time and verification process greatly increases the design efficiency of SystemC, making the product designed by SystemC more quickly into the market. The design effect using SystemC is compared between the expertise hardware designer and the software designer with little hardware knowledge. The result shows SystemC is an excellent and high efficiency hardware design method for an expertise hardware designer.
Robust H(∞) control for a class of 2-D discrete delayed systems.
Ye, Shuxia; Li, Jianzhen; Yao, Juan
2014-09-01
In this paper, we deal with the problem of robust H∞ control for a class of 2-D discrete uncertain systems with delayed perturbations described by the Roesser state-space model (RM). The problem to be addressed is the design of robust controllers via state feedback such that the stability of the resulting closed-loop system is guaranteed and a prescribed H∞ performance level is ensured for all delayed perturbations. By utilizing the Lyapunov method and some results, H∞ controllers are given. The results are delay-dependent and can be expressed in terms of linear matrix inequalities (LMIs). Finally, some numerical examples are given to illustrate the effectiveness of the proposed results. PMID:24411024
NASA Astrophysics Data System (ADS)
Liu, Zhiyong; Zhou, Ping; Chen, Gang; Guo, Ledong
2014-11-01
This study investigated the performance and potential of a hybrid model that combined the discrete wavelet transform and support vector regression (the DWT-SVR model) for daily and monthly streamflow forecasting. Three key factors of the wavelet decomposition phase (mother wavelet, decomposition level, and edge effect) were proposed to consider for improving the accuracy of the DWT-SVR model. The performance of DWT-SVR models with different combinations of these three factors was compared with the regular SVR model. The effectiveness of these models was evaluated using the root-mean-squared error (RMSE) and Nash-Sutcliffe model efficiency coefficient (NSE). Daily and monthly streamflow data observed at two stations in Indiana, United States, were used to test the forecasting skill of these models. The results demonstrated that the different hybrid models did not always outperform the SVR model for 1-day and 1-month lead time streamflow forecasting. This suggests that it is crucial to consider and compare the three key factors when using the DWT-SVR model (or other machine learning methods coupled with the wavelet transform), rather than choosing them based on personal preferences. We then combined forecasts from multiple candidate DWT-SVR models using a model averaging technique based upon Akaike's information criterion (AIC). This ensemble prediction was superior to the single best DWT-SVR model and regular SVR model for both 1-day and 1-month ahead predictions. With respect to longer lead times (i.e., 2- and 3-day and 2-month), the ensemble predictions using the AIC averaging technique were consistently better than the best DWT-SVR model and SVR model. Therefore, integrating model averaging techniques with the hybrid DWT-SVR model would be a promising approach for daily and monthly streamflow forecasting. Additionally, we strongly recommend considering these three key factors when using wavelet-based SVR models (or other wavelet-based forecasting models).
A hybrid group method of data handling with discrete wavelet transform for GDP forecasting
NASA Astrophysics Data System (ADS)
Isa, Nadira Mohamed; Shabri, Ani
2013-09-01
This study is proposed the application of hybridization model using Group Method of Data Handling (GMDH) and Discrete Wavelet Transform (DWT) in time series forecasting. The objective of this paper is to examine the flexibility of the hybridization GMDH in time series forecasting by using Gross Domestic Product (GDP). A time series data set is used in this study to demonstrate the effectiveness of the forecasting model. This data are utilized to forecast through an application aimed to handle real life time series. This experiment compares the performances of a hybrid model and a single model of Wavelet-Linear Regression (WR), Artificial Neural Network (ANN), and conventional GMDH. It is shown that the proposed model can provide a promising alternative technique in GDP forecasting.
NASA Astrophysics Data System (ADS)
Palaniswamy, Sumithra; Duraisamy, Prakash; Alam, Mohammad Showkat; Yuan, Xiaohui
2012-04-01
Automatic speech processing systems are widely used in everyday life such as mobile communication, speech and speaker recognition, and for assisting the hearing impaired. In speech communication systems, the quality and intelligibility of speech is of utmost importance for ease and accuracy of information exchange. To obtain an intelligible speech signal and one that is more pleasant to listen, noise reduction is essential. In this paper a new Time Adaptive Discrete Bionic Wavelet Thresholding (TADBWT) scheme is proposed. The proposed technique uses Daubechies mother wavelet to achieve better enhancement of speech from additive non- stationary noises which occur in real life such as street noise and factory noise. Due to the integration of human auditory system model into the wavelet transform, bionic wavelet transform (BWT) has great potential for speech enhancement which may lead to a new path in speech processing. In the proposed technique, at first, discrete BWT is applied to noisy speech to derive TADBWT coefficients. Then the adaptive nature of the BWT is captured by introducing a time varying linear factor which updates the coefficients at each scale over time. This approach has shown better performance than the existing algorithms at lower input SNR due to modified soft level dependent thresholding on time adaptive coefficients. The objective and subjective test results confirmed the competency of the TADBWT technique. The effectiveness of the proposed technique is also evaluated for speaker recognition task under noisy environment. The recognition results show that the TADWT technique yields better performance when compared to alternate methods specifically at lower input SNR.
NASA Astrophysics Data System (ADS)
Jones, J. P.; Carniel, R.; Malone, S.
2005-12-01
The time-varying properties of volcanic tremor demand advanced techniques capable of analyzing changes in both time and frequency domains. Specifically, rapid data preprocessing techniques with the ability to distinguish signal from noise are especially valuable in analyzing the temporal, spatial, and spectral properties of these signals. To this end, we use the Discrete Wavelet Packet Transform and the Best Shift Basis algorithm to select an orthonormal basis for continuous volcanic tremor data, then apply a simple statistical test to eliminate frequency bands that primarily consist of Gaussian white noise. We then use the Maximal Overlap Discrete Wavelet Packet Transform to compute and analyze features in the detail coefficients of each "signal" band. Because MODWPT detail coefficients are equivalent to a time series convolved with a zero phase filter, we apply standard polarization and amplitude-based location techniques to each frequency band's detail coefficients to analyze possible source locations and mechanisms. To demonstrate the usefulness of these techniques, we present a sample analysis of data from Erta 'Ale volcano, Ethiopia, recorded on a temporary network in November 2003. Data were sampled at 100 Hz and the DWPT was computed with the LA(16) wavelet to a maximum level of j = 7. The optimal basis for this data set consists of 54 frequency bands, but only 9 contain meaningful "signal" energy. We identify two frequency bands whose locations suggest a distributed source; three frequency bands whose signals may come from the lava lake itself; three high-frequency bands of scattered energy; and one very high frequency band of non-Gaussian instrument noise. Finally, we discuss optimization efforts, computational efficiency, and the feasibility of using similar wavelet methods to preprocess data in real time or near real time.
The shift-invariant discrete wavelet transform and application to speech waveform analysis
NASA Astrophysics Data System (ADS)
Enders, Jörg; Geng, Weihua; Li, Peijun; Frazier, Michael W.; Scholl, David J.
2005-04-01
The discrete wavelet transform may be used as a signal-processing tool for visualization and analysis of nonstationary, time-sampled waveforms. The highly desirable property of shift invariance can be obtained at the cost of a moderate increase in computational complexity, and accepting a least-squares inverse (pseudoinverse) in place of a true inverse. A new algorithm for the pseudoinverse of the shift-invariant transform that is easier to implement in array-oriented scripting languages than existing algorithms is presented together with self-contained proofs. Representing only one of the many and varied potential applications, a recorded speech waveform illustrates the benefits of shift invariance with pseudoinvertibility. Visualization shows the glottal modulation of vowel formants and frication noise, revealing secondary glottal pulses and other waveform irregularities. Additionally, performing sound waveform editing operations (i.e., cutting and pasting sections) on the shift-invariant wavelet representation automatically produces quiet, click-free section boundaries in the resulting sound. The capabilities of this wavelet-domain editing technique are demonstrated by changing the rate of a recorded spoken word. Individual pitch periods are repeated to obtain a half-speed result, and alternate individual pitch periods are removed to obtain a double-speed result. The original pitch and formant frequencies are preserved. In informal listening tests, the results are clear and understandable. .
Saini, Shiwani; Dewan, Lillie
2016-01-01
This paper highlights the potential of discrete wavelet transforms in the analysis and comparison of genomic sequences of Mycobacterium tuberculosis (MTB) with different resistance characteristics. Graphical representations of wavelet coefficients and statistical estimates of their parameters have been used to determine the extent of similarity between different sequences of MTB without the use of conventional methods such as Basic Local Alignment Search Tool. Based on the calculation of the energy of wavelet decomposition coefficients of complete genomic sequences, their broad classification of the type of resistance can be done. All the given genomic sequences can be grouped into two broad categories wherein the drug resistant and drug susceptible sequences form one group while the multidrug resistant and extensive drug resistant sequences form the other group. This method of segregation of the sequences is faster than conventional laboratory methods which require 3-4 weeks of culture of sputum samples. Thus the proposed method can be used as a tool to enhance clinical diagnostic investigations in near real-time. PMID:26839757
NASA Astrophysics Data System (ADS)
Campo, D.; Quintero, O. L.; Bastidas, M.
2016-04-01
We propose a study of the mathematical properties of voice as an audio signal. This work includes signals in which the channel conditions are not ideal for emotion recognition. Multiresolution analysis- discrete wavelet transform – was performed through the use of Daubechies Wavelet Family (Db1-Haar, Db6, Db8, Db10) allowing the decomposition of the initial audio signal into sets of coefficients on which a set of features was extracted and analyzed statistically in order to differentiate emotional states. ANNs proved to be a system that allows an appropriate classification of such states. This study shows that the extracted features using wavelet decomposition are enough to analyze and extract emotional content in audio signals presenting a high accuracy rate in classification of emotional states without the need to use other kinds of classical frequency-time features. Accordingly, this paper seeks to characterize mathematically the six basic emotions in humans: boredom, disgust, happiness, anxiety, anger and sadness, also included the neutrality, for a total of seven states to identify.
Ho, B.K.T.; Tsai, M.J.; Wei, J.; Ma, M.; Saipetch, P.
1996-12-01
A new method of video compression for angiographic images has been developed to achieve high compression ratio ({approximately}20:1) while eliminating block artifacts which leads to loss of diagnostic accuracy. This method adopts motion picture experts group`s (MPEG`s) motion compensated prediction to take advantage of frame to frame correlation. However, in contrast to MPEG, the error images arising from mismatches in the motion estimation are encoded by discrete wavelet transform (DWT) rather than block discrete cosine transform (DCT). Furthermore, the authors developed a classification scheme which label each block in an image as intra, error, or background type and encode it accordingly. This hybrid coding can significantly improve the compression efficiency in certain cases. This method can be generalized for any dynamic image sequences applications sensitive to block artifacts.
NASA Astrophysics Data System (ADS)
Chevrot, Sébastien; Martin, Roland; Komatitsch, Dimitri
2012-12-01
Wavelets are extremely powerful to compress the information contained in finite-frequency sensitivity kernels and tomographic models. This interesting property opens the perspective of reducing the size of global tomographic inverse problems by one to two orders of magnitude. However, introducing wavelets into global tomographic problems raises the problem of computing fast wavelet transforms in spherical geometry. Using a Cartesian cubed sphere mapping, which grids the surface of the sphere with six blocks or 'chunks', we define a new algorithm to implement fast wavelet transforms with the lifting scheme. This algorithm is simple and flexible, and can handle any family of discrete orthogonal or bi-orthogonal wavelets. Since wavelet coefficients are local in space and scale, aliasing effects resulting from a parametrization with global functions such as spherical harmonics are avoided. The sparsity of tomographic models expanded in wavelet bases implies that it is possible to exploit the power of compressed sensing to retrieve Earth's internal structures optimally. This approach involves minimizing a combination of a ℓ2 norm for data residuals and a ℓ1 norm for model wavelet coefficients, which can be achieved through relatively minor modifications of the algorithms that are currently used to solve the tomographic inverse problem.
Nie, Xinhua; Pan, Zhongming; Zhang, Dasha; Zhou, Han; Chen, Min; Zhang, Wenna
2014-01-01
Magnetic anomaly detection (MAD) is a passive approach for detection of a ferromagnetic target, and its performance is often limited by external noises. In consideration of one major noise source is the fractal noise (or called 1/f noise) with a power spectral density of 1/fa (0wavelet decomposition can play the role of a Karhunen-Loève-type expansion to the 1/f-type signal by its decorrelation abilities, an effective energy detection method based on undecimated discrete wavelet transform (UDWT) is proposed in this paper. Firstly, the foundations of magnetic anomaly detection and UDWT are introduced in brief, while a possible detection system based on giant magneto-impedance (GMI) magnetic sensor is also given out. Then our proposed energy detection based on UDWT is described in detail, and the probabilities of false alarm and detection for given the detection threshold in theory are presented. It is noticeable that no a priori assumptions regarding the ferromagnetic target or the magnetic noise probability are necessary for our method, and different from the discrete wavelet transform (DWT), the UDWT is shift invariant. Finally, some simulations are performed and the results show that the detection performance of our proposed detector is better than that of the conventional energy detector even utilized in the Gaussian white noise, especially when the spectral parameter α is less than 1.0. In addition, a real-world experiment was done to demonstrate the advantages of the proposed method. PMID:25343484
NASA Astrophysics Data System (ADS)
Tang, Xiangyang; Ning, Ruola; Yu, Rongfeng; Conover, David L.
1999-05-01
The application of the newly developed flat panel x-ray imaging detector in cone beam volume CT has attracted increasing interest recently. Due to an imperfect solid state array manufacturing process, however, defective elements, gain non-uniformity and offset image unavoidably exist in all kinds of flat panel x-ray imaging detectors, which will cause severe streak and ring artifacts in a cone beam reconstruction image and severely degrade image quality. A calibration technique, in which the artifacts resulting from the defective elements, gain non-uniformity and offset image can be reduced significantly, is presented in this paper. The detection of defective elements is distinctively based upon two-dimensional (2D) wavelet analysis. Because of its inherent localizability in recognizing singularities or discontinuities, wavelet analysis possesses the capability of detecting defective elements over a rather large x-ray exposure range, e.g., 20% to approximately 60% of the dynamic range of the detector used. Three-dimensional (3D) images of a low-contrast CT phantom have been reconstructed from projection images acquired by a flat panel x-ray imaging detector with and without calibration process applied. The artifacts caused individually by defective elements, gain non-uniformity and offset image have been separated and investigated in detail, and the correlation with each other have also been exposed explicitly. The investigation is enforced by quantitative analysis of the signal to noise ratio (SNR) and the image uniformity of the cone beam reconstruction image. It has been demonstrated that the ring and streak artifacts resulting from the imperfect performance of a flat panel x-ray imaging detector can be reduced dramatically, and then the image qualities of a cone beam reconstruction image, such as contrast resolution and image uniformity are improved significantly. Furthermore, with little modification, the calibration technique presented here is also applicable
Jemcov, A.; Matovic, M.D.
1996-12-31
This paper examines the sparse representation and preconditioning of a discrete Steklov-Poincare operator which arises in domain decomposition methods. A non-overlapping domain decomposition method is applied to a second order self-adjoint elliptic operator (Poisson equation), with homogeneous boundary conditions, as a model problem. It is shown that the discrete Steklov-Poincare operator allows sparse representation with a bounded condition number in wavelet basis if the transformation is followed by thresholding and resealing. These two steps combined enable the effective use of Krylov subspace methods as an iterative solution procedure for the system of linear equations. Finding the solution of an interface problem in domain decomposition methods, known as a Schur complement problem, has been shown to be equivalent to the discrete form of Steklov-Poincare operator. A common way to obtain Schur complement matrix is by ordering the matrix of discrete differential operator in subdomain node groups then block eliminating interface nodes. The result is a dense matrix which corresponds to the interface problem. This is equivalent to reducing the original problem to several smaller differential problems and one boundary integral equation problem for the subdomain interface.
NASA Astrophysics Data System (ADS)
Mishra, D. C.; Sharma, R. K.; Dawar, Mayank; Hanmandlu, M.
2015-09-01
In this cryptosystem, we have presented a novel technique for security of video data by using matrix affine cipher (MAC) combined with two-dimensional discrete wavelet transform (2D-DWT). Existing schemes for security of video data provides only one layer of security, but the presented technique provides two layers of security for video data. In this cryptosystem, keys and arrangement of MAC parameters are imperative for decryption process. In this cryptosystem, if the attacker knows about all the exact keys, but has no information about the specific arrangement of MAC parameters, then the information of original video cannot be recovered from the encrypted video. Experimental results on standard examples support to the robustness and appropriateness of the presented cryptosystem of video encryption and decryption. The statistical analysis of the experimental results based on standard examples critically examine the behavior of the proposed technique. Comparison between existing schemes for security of video with the presented cryptosystem is also provided for the robustness of the proposed cryptosystem.
Sebastian Schunert; Yousry Y. Azmy; Damien Fournier
2011-05-01
We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen’s benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the discontinuous Galerkin Finite Element method (DGFEM) and the recently proposed higher order diamond difference method (HODD) of spatial expansion orders 0 through 3. While AHOTN and AHOTC rely on approximate analytical solutions of the transport equation within a mesh cell, DGFEM and HODD utilize a polynomial expansion to mimick the angular flux profile across each mesh cell. Intuitively, due to the higher degree of analyticity, we expect AHOTN and AHOTC to feature superior accuracy compared with DGFEM and HODD, but at the price of potentially longer grind times and numerical instabilities. The latter disadvantages can result from the presence of exponential terms evaluated at the cell optical thickness that arise from the semianalytical solution process. This work quantifies the order of accuracy and the magnitude of the error of all four discretization methods for different optical thicknesses, scattering ratios and degrees of smoothness of the underlying exact solutions in order to verify or contradict the aforementioned intuitive expectation.
Damage Detection on Sudden Stiffness Reduction Based on Discrete Wavelet Transform
Chen, Bo; Chen, Zhi-wei; Wang, Gan-jun; Xie, Wei-ping
2014-01-01
The sudden stiffness reduction in a structure may cause the signal discontinuity in the acceleration responses close to the damage location at the damage time instant. To this end, the damage detection on sudden stiffness reduction of building structures has been actively investigated in this study. The signal discontinuity of the structural acceleration responses of an example building is extracted based on the discrete wavelet transform. It is proved that the variation of the first level detail coefficients of the wavelet transform at damage instant is linearly proportional to the magnitude of the stiffness reduction. A new damage index is proposed and implemented to detect the damage time instant, location, and severity of a structure due to a sudden change of structural stiffness. Numerical simulation using a five-story shear building under different types of excitation is carried out to assess the effectiveness and reliability of the proposed damage index for the building at different damage levels. The sensitivity of the damage index to the intensity and frequency range of measurement noise is also investigated. The made observations demonstrate that the proposed damage index can accurately identify the sudden damage events if the noise intensity is limited. PMID:24991647
Medical image interpolation method based on similarity analysis of discrete wavelet transforms
NASA Astrophysics Data System (ADS)
Peng, Shichun; Liu, Jian
2007-12-01
A new interpolation method based on multi-resolution technique is presented and used for medical image zooming. The aim of this work is to focus on similarity analysis of adjacent sub-bands provided by Discrete Wavelet Transform (DWT) to enhance the accuracy of the interpolation. First, decompose the original image into sub-bands by the DWT; second, consider the similarity between adjacent sub-bands to calculate the high frequency components; third, use the original image as the low frequency component and apply the inverse DWT to obtain the final interpolation result. Experimental results on magnetic resonance (MR) images and positron emission tomography (PET) images illustrate the effectiveness of the proposed method.
Lamb wave feature extraction using discrete wavelet transformation and Principal Component Analysis
NASA Astrophysics Data System (ADS)
Ghodsi, Mojtaba; Ziaiefar, Hamidreza; Amiryan, Milad; Honarvar, Farhang; Hojjat, Yousef; Mahmoudi, Mehdi; Al-Yahmadi, Amur; Bahadur, Issam
2016-04-01
In this research, a new method is presented for eliciting the proper features for recognizing and classifying the kinds of the defects by guided ultrasonic waves. After applying suitable preprocessing, the suggested method extracts the base frequency band from the received signals by discrete wavelet transform and discrete Fourier transform. This frequency band can be used as a distinctive feature of ultrasonic signals in different defects. Principal Component Analysis with improving this feature and decreasing extra data managed to improve classification. In this study, ultrasonic test with A0 mode lamb wave is used and is appropriated to reduce the difficulties around the problem. The defects under analysis included corrosion, crack and local thickness reduction. The last defect is caused by electro discharge machining (EDM). The results of the classification by optimized Neural Network depicts that the presented method can differentiate different defects with 95% precision and thus, it is a strong and efficient method. Moreover, comparing the elicited features for corrosion and local thickness reduction and also the results of the two's classification clarifies that modeling the corrosion procedure by local thickness reduction which was previously common, is not an appropriate method and the signals received from the two defects are different from each other.
NASA Astrophysics Data System (ADS)
Xuan, Songbai; Shen, Chongyang; Li, Hui; Tan, Hongbo
2016-07-01
The Chuan-Dian tectonic block is a transitional zone between the Tibetan Plateau and the South China block. The crustal structure in this region has been studied in several ways, and in this work we present Bouguer gravity anomaly data with which to investigate the Chuan-Dian block and surrounding regions. Regional and local anomalies are decomposed using a method of discrete wavelet transform (DWT), and furthermore, the relief of the Moho is inverted based on the regional anomalies. Results of the transform show that there is a distinct belt of regional anomalies on the east and southeast margins of the Tibetan Plateau. In addition, there are two distinct gradient belts evident in the maps of the local gravity anomalies. The first of these, in the western Indo-China block, has a north-south strike with high anomalies around this belt, and the second is along the Longmenshan fault zone in the eastern margin of the Tibetan Plateau. The Chuan-Dian block can be divided into two discrete parts, separated by a broad and indistinct boundary observed from the fifth-order DWT detail and Moho relief. The DWT details reveal that parallel anomalies existing in the Indo-China block region were induced by subduction of the Burmese block. We conclude that the clockwise rotation of the Chuan-Dian block was synthetically affected by the extrusion of the Tibetan lithosphere and subduction of the Burmese block.
Discrete wavelet transform-based spatial-temporal approach for quantized video watermarking
NASA Astrophysics Data System (ADS)
Faragallah, Osama S.
2011-07-01
We propose a new public digital watermarking technique for video copyright protection working in the discrete wavelet transform (DWT) domain. The proposed scheme is a combination of spread-spectrum and quantization-based watermarking. The proposed scheme is characterized by two achievements: (i) a spread-spectrum technique is used to spread the power spectrum of the watermark data and (ii) an error correction code is applied and embeds the watermark with spatial and temporal redundancy. The goal of these two achievements is to increase robustness against attacks, protect the watermark against bit errors, and achieve a very good perceptual quality. The effectiveness of the proposed scheme is verified through a series of experiments in which a number of video and standard image-processing attacks are conducted. The proposed scheme achieves a very good perceptual quality with mean peak signal-to-noise-ratio values of the watermarked videos of >40 dB and high resistance to a large spectrum of attacks.
Discrete wavelet transform to improve guided-wave-based health monitoring of tendons and cables
NASA Astrophysics Data System (ADS)
Rizzo, Piervincenzo; Lanza di Scalea, Francesco
2004-07-01
Multi-wire steel strands are used in civil structures as pre-stressing tendons in prestressed concrete and as stay-cables in cable-stayed and suspension bridges. Monitoring the structural performance of these components is important to ensure the proper functioning and safety of the entire structure. Among the various NDE techniques that are under investigation for monitoring tendons and cables, the use of ultrasonic guided waves shows good promises. The main advantage of this approach is the possibility for the simultaneous monitoring of loads and detection of defects, such as corrosion and broken wires, by using the same ultrasonic setup. Load monitoring is achieved by measuring the travel time of the wave across a given length of the cable. Defect detection is achieved by measuring the reflections of the wave from the geometrical discontinuities. The new contributions of the current paper are two-fold. First, the study identifies those ultrasonic frequencies propagating with low attenuation for long-range defect detection. Second, the technique is substantially improved by implementing the Discrete Wavelet Transform (DWT) as a data post-processing tool. The data de-noising and data compression abilities of the DWT allow for greater sensitivity, larger ranges and higher monitoring speed. It is shown that the implementation of the DWT in the ultrasonic guided-wave technique becomes necessary for monitoring tendons and cables in the field.
Choi, Hyun Ho; Lee, Ju Hwan; Kim, Sung Min; Park, Sung Yun
2015-01-01
Here, the speckle noise in ultrasonic images is removed using an image fusion-based denoising method. To optimize the denoising performance, each discrete wavelet transform (DWT) and filtering technique was analyzed and compared. In addition, the performances were compared in order to derive the optimal input conditions. To evaluate the speckle noise removal performance, an image fusion algorithm was applied to the ultrasound images, and comparatively analyzed with the original image without the algorithm. As a result, applying DWT and filtering techniques caused information loss and noise characteristics, and did not represent the most significant noise reduction performance. Conversely, an image fusion method applying SRAD-original conditions preserved the key information in the original image, and the speckle noise was removed. Based on such characteristics, the input conditions of SRAD-original had the best denoising performance with the ultrasound images. From this study, the best denoising technique proposed based on the results was confirmed to have a high potential for clinical application. PMID:26405924
Image denoising with the dual-tree complex wavelet transform
NASA Astrophysics Data System (ADS)
Yaseen, Alauldeen S.; Pavlova, Olga N.; Pavlov, Alexey N.; Hramov, Alexander E.
2016-04-01
The purpose of this study is to compare image denoising techniques based on real and complex wavelet-transforms. Possibilities provided by the classical discrete wavelet transform (DWT) with hard and soft thresholding are considered, and influences of the wavelet basis and image resizing are discussed. The quality of image denoising for the standard 2-D DWT and the dual-tree complex wavelet transform (DT-CWT) is studied. It is shown that DT-CWT outperforms 2-D DWT at the appropriate selection of the threshold level.
Effective Temperature of 2D Dusty Plasma Liquids at the Discrete Level
Io, C.-W.; Chan, C.-L.; I Lin
2007-07-13
Fluctuation-dissipation theory has been used to measure the effective temperature of non-equilibrium system. In this work, using a 2D dusty plasma liquid formed by the negatively charged fine particles suspending in weakly ionized discharges and sheared by two CW counter parallel laser beams, we measure the micro-transport at the kinetic level. The effective temperatures Teff at different time scales are obtained through the Stokes-Einstein relation which relates the diffusion coefficient (D) and the viscosity ({eta}). The external energy is cascaded from the slow hopping modes to the fast caging modes through mutual coupling, which leads to the higher effective temperature of the slow hopping modes.
Al-Ajlouni, A F; Abo-Zahhad, M; Ahmed, S M; Schilling, R J
2008-01-01
Compression of electrocardiography (ECG) is necessary for efficient storage and transmission of the digitized ECG signals. Discrete wavelet transform (DWT) has recently emerged as a powerful technique for ECG signal compression due to its multi-resolution signal decomposition and locality properties. This paper presents an ECG compressor based on the selection of optimum threshold levels of DWT coefficients in different subbands that achieve maximum data volume reduction while preserving the significant signal morphology features upon reconstruction. First, the ECG is wavelet transformed into m subbands and the wavelet coefficients of each subband are thresholded using an optimal threshold level. Thresholding removes excessively small features and replaces them with zeroes. The threshold levels are defined for each signal so that the bit rate is minimized for a target distortion or, alternatively, the distortion is minimized for a target compression ratio. After thresholding, the resulting significant wavelet coefficients are coded using multi embedded zero tree (MEZW) coding technique. In order to assess the performance of the proposed compressor, records from the MIT-BIH Arrhythmia Database were compressed at different distortion levels, measured by the percentage rms difference (PRD), and compression ratios (CR). The method achieves good CR values with excellent reconstruction quality that compares favourably with various classical and state-of-the-art ECG compressors. Finally, it should be noted that the proposed method is flexible in controlling the quality of the reconstructed signals and the volume of the compressed signals by establishing a target PRD and a target CR a priori, respectively. PMID:19005960
Statistical Analysis of Large Scale Structure by the Discrete Wavelet Transform
NASA Astrophysics Data System (ADS)
Pando, Jesus
1997-10-01
The discrete wavelet transform (DWT) is developed as a general statistical tool for the study of large scale structures (LSS) in astrophysics. The DWT is used in all aspects of structure identification including cluster analysis, spectrum and two-point correlation studies, scale-scale correlation analysis and to measure deviations from Gaussian behavior. The techniques developed are demonstrated on 'academic' signals, on simulated models of the Lymanα (Lyα) forests, and on observational data of the Lyα forests. This technique can detect clustering in the Ly-α clouds where traditional techniques such as the two-point correlation function have failed. The position and strength of these clusters in both real and simulated data is determined and it is shown that clusters exist on scales as large as at least 20 h-1 Mpc at significance levels of 2-4 σ. Furthermore, it is found that the strength distribution of the clusters can be used to distinguish between real data and simulated samples even where other traditional methods have failed to detect differences. Second, a method for measuring the power spectrum of a density field using the DWT is developed. All common features determined by the usual Fourier power spectrum can be calculated by the DWT. These features, such as the index of a power law or typical scales, can be detected even when the samples are geometrically complex, the samples are incomplete, or the mean density on larger scales is not known (the infrared uncertainty). Using this method the spectra of Ly-α forests in both simulated and real samples is calculated. Third, a method for measuring hierarchical clustering is introduced. Because hierarchical evolution is characterized by a set of rules of how larger dark matter halos are formed by the merging of smaller halos, scale-scale correlations of the density field should be one of the most sensitive quantities in determining the merging history. We show that these correlations can be completely
Decision support system for age-related macular degeneration using discrete wavelet transform.
Mookiah, Muthu Rama Krishnan; Acharya, U Rajendra; Koh, Joel E W; Chua, Chua Kuang; Tan, Jen Hong; Chandran, Vinod; Lim, Choo Min; Noronha, Kevin; Laude, Augustinus; Tong, Louis
2014-09-01
Age-related macular degeneration (AMD) affects the central vision and subsequently may lead to visual loss in people over 60 years of age. There is no permanent cure for AMD, but early detection and successive treatment may improve the visual acuity. AMD is mainly classified into dry and wet type; however, dry AMD is more common in aging population. AMD is characterized by drusen, yellow pigmentation, and neovascularization. These lesions are examined through visual inspection of retinal fundus images by ophthalmologists. It is laborious, time-consuming, and resource-intensive. Hence, in this study, we have proposed an automated AMD detection system using discrete wavelet transform (DWT) and feature ranking strategies. The first four-order statistical moments (mean, variance, skewness, and kurtosis), energy, entropy, and Gini index-based features are extracted from DWT coefficients. We have used five (t test, Kullback-Lieber Divergence (KLD), Chernoff Bound and Bhattacharyya Distance, receiver operating characteristics curve-based, and Wilcoxon) feature ranking strategies to identify optimal feature set. A set of supervised classifiers namely support vector machine (SVM), decision tree, [Formula: see text]-nearest neighbor ([Formula: see text]-NN), Naive Bayes, and probabilistic neural network were used to evaluate the highest performance measure using minimum number of features in classifying normal and dry AMD classes. The proposed framework obtained an average accuracy of 93.70%, sensitivity of 91.11%, and specificity of 96.30% using KLD ranking and SVM classifier. We have also formulated an AMD Risk Index using selected features to classify the normal and dry AMD classes using one number. The proposed system can be used to assist the clinicians and also for mass AMD screening programs. PMID:25112273
Functional decomposition of the human ERG based on the discrete wavelet transform.
Gauvin, Mathieu; Little, John M; Lina, Jean-Marc; Lachapelle, Pierre
2015-01-01
The morphology of the electroretinogram (ERG) can be altered as a result of normal and pathological processes of the retina. However, given that the ERG is almost solely assessed in terms of its amplitude and timing, defining the shape of the ERG waveform so that subtle, physiologically driven, morphological changes can be systematically and reproducibly detected remains a challenging problem. We examined if the discrete wavelet transform (DWT) could meet this challenge. Normal human photopic ERGs evoked to a broad range of luminance intensities (to yield waveforms of various shapes, amplitudes, and timings) were analyzed using DWT descriptors of the ERG. Luminance-response curves that were generated using the various DWT descriptors revealed distinct (p < 0.05) luminance-dependence patterns, indicating that the stimulus luminance differently modulates the various time-frequency components of the ERG and thus its morphology. The latter represents the first attempt to study the luminance-dependence of ERG descriptors obtained with the DWT. Analyses of ERGs obtained from patients affected with ON or OFF retinal pathway anomalies were also presented. We show here for the first time that distinct time-frequency descriptors can be specifically associated to the function of the ON and OFF cone pathway. Therefore, in this study, the DWT revealed reproducible, physiologically meaningful and diagnostically relevant descriptors of the ERG over a wide range of signal amplitudes and morphologies. The DWT analysis thus represents a valuable addition to the electrophysiologist's armamentarium that will improve the quantification and interpretation of normal and pathological ERG responses. PMID:26746684
Some notes on the application of discrete wavelet transform in image processing
Caria, Egydio C. S.; Costa A, Trajano A. de; Rebello, Joao Marcos A.
2011-06-23
Mathematical transforms are used in signal processing in order to extract what is known as 'hidden' information. One of these mathematical tools is the Discrete Wavelet Transform (DWT), which has been increasingly employed in non-destructive testing and, more specifically, in image processing. The main concern in the present work is to employ DWT to suppress noise without losing relevant image features. However, some aspects must be taken into consideration when applying DWT in image processing, mainly in the case of weld radiographs, in order to achieve consistent results. Three topics were selected as representative of these difficulties, as follows: 1) How can image matrix be filled to fit the 2{sup n} lines and 2{sup n} rows requirement? 2) How can the most suitable decomposition level of the DWT function and the correct choice of their coefficient suppression be selected? 3) Is there any influence of the scanning direction and the weld radiograph image, e.g., longitudinal or transversal, on the final processing image? It is known that some artifacts may be present in weld radiograph images. Indeed, the weld surface is frequently rough and rippled, what can be seen as gray level variation on the radiograph, being sometimes mistaken as defective areas. Depending on the position of these artifacts, longitudinal or transversal to the weld bead, they may have different influences on the image processing procedure. This influence is clearly seen in the distribution of the DWT Function coefficients. In the present work, examples of two weld radiographs of quite different image quality were given in order to exemplify it.
Some Notes on the Application of Discrete Wavelet Transform in Image Processing
NASA Astrophysics Data System (ADS)
Caria, Egydio C. S.; de A. Costa, Trajano A.; Rebello, João Marcos A.
2011-06-01
Mathematical transforms are used in signal processing in order to extract what is known as "hidden" information. One of these mathematical tools is the Discrete Wavelet Transform (DWT), which has been increasingly employed in non-destructive testing and, more specifically, in image processing. The main concern in the present work is to employ DWT to suppress noise without losing relevant image features. However, some aspects must be taken into consideration when applying DWT in image processing, mainly in the case of weld radiographs, in order to achieve consistent results. Three topics were selected as representative of these difficulties, as follows: 1) How can image matrix be filled to fit the 2n lines and 2n rows requirement? 2) How can the most suitable decomposition level of the DWT function and the correct choice of their coefficient suppression be selected? 3) Is there any influence of the scanning direction and the weld radiograph image, e.g., longitudinal or transversal, on the final processing image? It is known that some artifacts may be present in weld radiograph images. Indeed, the weld surface is frequently rough and rippled, what can be seen as gray level variation on the radiograph, being sometimes mistaken as defective areas. Depending on the position of these artifacts, longitudinal or transversal to the weld bead, they may have different influences on the image processing procedure. This influence is clearly seen in the distribution of the DWT Function coefficients. In the present work, examples of two weld radiographs of quite different image quality were given in order to exemplify it.
NASA Astrophysics Data System (ADS)
Bakhouche, A.; Doghmane, N.
2008-06-01
In this paper, a new adaptive watermarking algorithm is proposed for still image based on the wavelet transform. The two major applications for watermarking are protecting copyrights and authenticating photographs. Our robust watermarking [3] [22] is used for copyright protection owners. The main reason for protecting copyrights is to prevent image piracy when the provider distributes the image on the Internet. Embed watermark in low frequency band is most resistant to JPEG compression, blurring, adding Gaussian noise, rescaling, rotation, cropping and sharpening but embedding in high frequency is most resistant to histogram equalization, intensity adjustment and gamma correction. In this paper, we extend the idea to embed the same watermark in two bands (LL and HH bands or LH and HL bands) at the second level of Discrete Wavelet Transform (DWT) decomposition. Our generalization includes all the four bands (LL, HL, LH, and HH) by modifying coefficients of the all four bands in order to compromise between acceptable imperceptibility level and attacks' resistance.
Talhaoui, Hicham; Menacer, Arezki; Kessal, Abdelhalim; Kechida, Ridha
2014-09-01
This paper presents new techniques to evaluate faults in case of broken rotor bars of induction motors. Procedures are applied with closed-loop control. Electrical and mechanical variables are treated using fast Fourier transform (FFT), and discrete wavelet transform (DWT) at start-up and steady state. The wavelet transform has proven to be an excellent mathematical tool for the detection of the faults particularly broken rotor bars type. As a performance, DWT can provide a local representation of the non-stationary current signals for the healthy machine and with fault. For sensorless control, a Luenberger observer is applied; the estimation rotor speed is analyzed; the effect of the faults in the speed pulsation is compensated; a quadratic current appears and used for fault detection. PMID:25004798
NASA Astrophysics Data System (ADS)
Sandirasegaram, Nicholas; English, Ryan
2005-05-01
The performance of several combinations of feature extraction and target classification algorithms is analyzed for Synthetic Aperture Radar (SAR) imagery using the standard Moving and Stationary Target Acquisition and Recognition (MSTAR) evaluation method. For feature extraction, 2D Fast Fourier Transform (FFT) is used to extract Fourier coefficients (frequency information) while 2D wavelet decomposition is used to extract wavelet coefficients (time-frequency information), from which subsets of characteristic in-class "invariant" coefficients are developed. Confusion matrices and Receiver Operating Characteristic (ROC) curves are used to evaluate and compare combinations of these characteristic coefficients with several classification methods, including Lp metric distances, a Multi Layer Perceptron (MLP) Neural Network (NN) and AND Corporation's Holographic Neural Technology (HNeT) classifier. The evaluation method examines the trade-off between correct detection rate and false alarm rate for each combination of feature-classifier systems. It also measures correct classification, misclassification and rejection rates for a 90% detection rate. Our analysis demonstrates the importance of feature and classifier selection in accurately classifying new target images.
NASA Astrophysics Data System (ADS)
Kandala, Chari V.; Sundaram, Jaya; Govindarajan, K. N.; Butts, Chris L.; Subbiah, Jeyam
2009-03-01
Moisture and oil contents are important quality factors often measured and monitored in the processing and storage of food products such as corn and peanuts. For estimating these parameters for peanuts nondestructively a parallel-plate capacitance sensor was used in conjunction with an impedance analyzer. Impedance, phase angle and dissipation factor were measured for the parallel-plate system, holding the in-shell peanut samples between its plates, at frequencies ranging between 1MHz and 30 MHz in intervals of 0.5 MHz. The acquired signals were analyzed with discrete wavelet analysis. The signals were decomposed to 6 levels using Daubechies mother wavelet. The decomposition coefficients of the sixth level were passed onto a stepwise variable selection routine to select significant variables. A linear regression was developed using only the significant variables to predict the moisture and oil content of peanut pods (inshell peanuts) from the impedance measurements. The wavelet analysis yielded similar R2 values with fewer variables as compared to multiple linear and partial least squares regressions. The estimated values were found to be in good agreement with the standard values for the samples tested. Ability to estimate the moisture and oil contents in peanuts without shelling them will be of considerable help to the peanut industry.
NASA Astrophysics Data System (ADS)
Qiu, Z.; Lee, C.-M.; Xu, Z. H.; Sui, L. N.
2016-01-01
We have developed a new active control algorithm based on discrete wavelet transform (DWT) for both stationary and non-stationary noise control. First, the Mallat pyramidal algorithm is introduced to implement the DWT, which can decompose the reference signal into several sub-bands with multi-resolution and provides a perfect reconstruction (PR) procedure. To reduce the extra computational complexity introduced by DWT, an efficient strategy is proposed that updates the adaptive filter coefficients in the frequency domainDeepthi B.B using a fast Fourier transform (FFT). Based on the reference noise source, a 'Haar' wavelet is employed and by decomposing the noise signal into two sub-band (3-band), the proposed DWT-FFT-based FXLMS (DWT-FFT-FXLMS) algorithm has greatly reduced complexity and a better convergence performance compared to a time domain filtered-x least mean square (TD-FXLMS) algorithm. As a result of the outstanding time-frequency characteristics of wavelet analysis, the proposed DWT-FFT-FXLMS algorithm can effectively cancel both stationary and non-stationary noise, whereas the frequency domain FXLMS (FD-FXLMS) algorithm cannot approach this point.
NASA Astrophysics Data System (ADS)
Gallego, A.; Moreno-García, P.; Casanova, Cesar F.
2013-06-01
Structural studies to find defects (in particular delaminations) in composite plates have been very prevalent in the Structural Health Monitoring field. The present work develops a new method to detect delaminations in CFRP (Carbon Fiber Reinforced Polymer) plates. In this paper the method is validated with numerical simulations, which come to support its adequacy for use with real acquisition data. This is done firstly through the implementation of a delaminated plate finite element. Using the classical lamination plate theory, delamination is considered in the kinematic equations through jump functions and additional degrees of freedom. The element allows the introduction of nd delaminations through its thickness. Classical QMITC (Quadrilateral Mixed Interpolation Tensorial Components) and DKQ (Discrete Kirchhoff Quadrilateral) elements are used for the membrane and bending FEM (Finite Element Method) formulation. Second, using the vibration modes obtained with the FEM, a damage location technique based on the variational Ritz method and Wavelet Analysis is proposed. The approach has the advantage of requiring only damaged modes and not the healthy ones. Both FEM simulations and Ritz/Wavelet damage detection schemes are applied in an orthotropic CFRP plate with the stacking sequence [0/90]3S. In addition, the influence of delamination thickness position, boundary conditions and added noise (in order to simulate experimental measures) was studied.
Acharya, U R; Yanti, R; Swapna, G; Sree, V S; Martis, R J; Suri, J S
2013-03-01
Epilepsy is a disorder of the brain depicted by recurrent seizures. Electroencephalogram signals can be used to study the characteristics of epileptic seizures. In this study, we propose a method for the automated classification of electroencephalogram into normal, interictal and ictal classes using 6, 12, 18 and 23.6 s of data. We employed discrete wavelet transform to decompose electroencephalogram signals into frequency sub-bands. These discrete wavelet transform coefficients were then subjected to independent component analysis for reducing the data dimension. The independent component analysis features were then fed to six classifiers, namely, decision tree, K-nearest neighbor, probabilistic neural network, fuzzy, Gaussian mixture model and support vector machine to select the best classifier. We observed that the support vector machine classifier with radial basis function kernel function gave the best results with an average accuracy of 96%, sensitivity of 96% and specificity of 97% for 23.6 s of electroencephalogram data. Our results show that as the duration of the data increases, the classification accuracy increases. This proposed technique can be used as an automatic seizure monitoring software to aid the doctors in providing timely quality care for the patients suffering from epilepsy. PMID:23662339
NASA Astrophysics Data System (ADS)
Steinke, R. C.
2015-12-01
Discretizing 1-D vadose zone simulations in the moisture content domain, such as is done in the Talbot-Ogden method, provides some advantages over discretizing in depth, such as is done in Richards' Equation. These advantages include inherent mass conservation and lower computational cost. However, doing so presents a difficulty for integration with 2-D groundwater interflow simulations. The equations of motion of the bins of discrete moisture content take the depth of the water table as an input. They do not produce it as an output. Finding the correct water table depth so that the groundwater recharge from the 1-D vadose zone simulation mass balances with the lateral flows from the 2-D groundwater interflow simulation was a previously unsolved problem. In this paper we present a net-groundwater-recharge method to solve to this problem and compare it with the source-term method used with Richards' Equation.
The Discrete Wavelet Transform with Lifting : A Step by Step Introduction
Elofson, C
2004-08-26
There is a great deal of information pertaining to wavelets readily available from various sources; several of the more recent sources describe the lifting technique for constructing wavelets. The tutorial paper by Sweldens and Schr{umlt o}der [1] gives a thorough explanation of the lifting approach for Haar bases. While it provides an excellent introduction to the topic, it is not immediately obvious how this approach is extended to nonuniformly spaced data on finite intervals. The present paper provides intermediate steps that supplement the material in [1]. After working through the following discussion, the reader should have no problem deriving the relevant equations presented in Sweldens and Schr{umlt o}der's article. Because of the abundance of information on the Haar basis, this discussion will instead work through the steps using a linear basis set.
Workman, Michael J; Serov, Alexey; Halevi, Barr; Atanassov, Plamen; Artyushkova, Kateryna
2015-05-01
The discrete wavelet transform (DWT) has found significant utility in process monitoring, filtering, and feature isolation of SEM, AFM, and optical images. Current use of the DWT for surface analysis assumes initial knowledge of the sizes of the features of interest in order to effectively isolate and analyze surface components. Current methods do not adequately address complex, heterogeneous surfaces in which features across multiple size ranges are of interest. Further, in situations where structure-to-property relationships are desired, the identification of features relevant for the function of the material is necessary. In this work, the DWT is examined as a tool for quantitative, length-scale specific surface metrology without prior knowledge of relevant features or length-scales. A new method is explored for determination of the best wavelet basis to minimize variation in roughness and skewness measurements with respect to change in position and orientation of surface features. It is observed that the size of the wavelet does not directly correlate with the size of features on the surface, and a method to measure the true length-scale specific roughness of the surface is presented. This method is applied to SEM and AFM images of non-precious metal catalysts, yielding new length-scale specific structure-to-property relationships for chemical speciation and fuel cell performance. The relationship between SEM and AFM length-scale specific roughness is also explored. Evidence is presented that roughness distributions of SEM images, as measured by the DWT, is representative of the true surface roughness distribution obtained from AFM. PMID:25879382
Gur, Berke M; Niezrecki, Christopher
2007-07-01
Recent interest in the West Indian manatee (Trichechus manatus latirostris) vocalizations has been primarily induced by an effort to reduce manatee mortality rates due to watercraft collisions. A warning system based on passive acoustic detection of manatee vocalizations is desired. The success and feasibility of such a system depends on effective denoising of the vocalizations in the presence of high levels of background noise. In the last decade, simple and effective wavelet domain nonlinear denoising methods have emerged as an alternative to linear estimation methods. However, the denoising performances of these methods degrades considerably with decreasing signal-to-noise ratio (SNR) and therefore are not suited for denoising manatee vocalizations in which the typical SNR is below 0 dB. Manatee vocalizations possess a strong harmonic content and a slow decaying autocorrelation function. In this paper, an efficient denoising scheme that exploits both the autocorrelation function of manatee vocalizations and effectiveness of the nonlinear wavelet transform based denoising algorithms is introduced. The suggested wavelet-based denoising algorithm is shown to outperform linear filtering methods, extending the detection range of vocalizations. PMID:17614478
Casson, Alexander J
2015-01-01
Ultra low power signal processing is an essential part of all sensor nodes, and particularly so in emerging wearable sensors for biomedical applications. Analog signal processing has an important role in these low power, low voltage, low frequency applications, and there is a key drive to decrease the power consumption of existing analog domain signal processing and to map more signal processing approaches into the analog domain. This paper presents an analog domain signal processing circuit which approximates the output of the Discrete Wavelet Transform (DWT) for use in ultra low power wearable sensors. Analog filters are used for the DWT filters and it is demonstrated how these generate analog domain DWT-like information that embeds information from Butterworth and Daubechies maximally flat mother wavelet responses. The Analog DWT is realised in hardware via g(m)C circuits, designed to operate from a 1.3 V coin cell battery, and provide DWT-like signal processing using under 115 nW of power when implemented in a 0.18 μm CMOS process. Practical examples demonstrate the effective use of the new Analog DWT on ECG (electrocardiogram) and EEG (electroencephalogram) signals recorded from humans. PMID:26694414
Casson, Alexander J.
2015-01-01
Ultra low power signal processing is an essential part of all sensor nodes, and particularly so in emerging wearable sensors for biomedical applications. Analog signal processing has an important role in these low power, low voltage, low frequency applications, and there is a key drive to decrease the power consumption of existing analog domain signal processing and to map more signal processing approaches into the analog domain. This paper presents an analog domain signal processing circuit which approximates the output of the Discrete Wavelet Transform (DWT) for use in ultra low power wearable sensors. Analog filters are used for the DWT filters and it is demonstrated how these generate analog domain DWT-like information that embeds information from Butterworth and Daubechies maximally flat mother wavelet responses. The Analog DWT is realised in hardware via gmC circuits, designed to operate from a 1.3 V coin cell battery, and provide DWT-like signal processing using under 115 nW of power when implemented in a 0.18 μm CMOS process. Practical examples demonstrate the effective use of the new Analog DWT on ECG (electrocardiogram) and EEG (electroencephalogram) signals recorded from humans. PMID:26694414
Avci, Derya; Leblebicioglu, Mehmet Kemal; Poyraz, Mustafa; Dogantekin, Esin
2014-02-01
So far, analysis and classification of urine cells number has become an important topic for medical diagnosis of some diseases. Therefore, in this study, we suggest a new technique based on Adaptive Discrete Wavelet Entropy Energy and Neural Network Classifier (ADWEENN) for Recognition of Urine Cells from Microscopic Images Independent of Rotation and Scaling. Some digital image processing methods such as noise reduction, contrast enhancement, segmentation, and morphological process are used for feature extraction stage of this ADWEENN in this study. Nowadays, the image processing and pattern recognition topics have come into prominence. The image processing concludes operation and design of systems that recognize patterns in data sets. In the past years, very difficulty in classification of microscopic images was the deficiency of enough methods to characterize. Lately, it is seen that, multi-resolution image analysis methods such as Gabor filters, discrete wavelet decompositions are superior to other classic methods for analysis of these microscopic images. In this study, the structure of the ADWEENN method composes of four stages. These are preprocessing stage, feature extraction stage, classification stage and testing stage. The Discrete Wavelet Transform (DWT) and adaptive wavelet entropy and energy is used for adaptive feature extraction in feature extraction stage to strengthen the premium features of the Artificial Neural Network (ANN) classifier in this study. Efficiency of the developed ADWEENN method was tested showing that an avarage of 97.58% recognition succes was obtained. PMID:24493072
Bailey, T S; Adams, M L; Chang, J H
2008-10-01
We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional cylindrical (RZ) geometry for arbitrary polygonal meshes. This discretization is a discontinuous finite element method that utilizes the piecewise linear basis functions developed by Stone and Adams. We describe an asymptotic analysis that shows this method to be accurate for many problems in the thick diffusion limit on arbitrary polygons, allowing this method to be applied to radiative transfer problems with these types of meshes. We also present numerical results for multiple problems on quadrilateral grids and compare these results to the well-known bi-linear discontinuous finite element method.
Homogeneous hierarchies: A discrete analogue to the wavelet-based multiresolution approximation
Mirkin, B.
1996-12-31
A correspondence between discrete binary hierarchies and some orthonormal bases of the n-dimensional Euclidean space can be applied to such problems as clustering, ordering, identifying/testing in very large data bases, or multiresolution image/signal processing. The latter issue is considered in the paper. The binary hierarchy based multiresolution theory is expected to lead to effective methods for data processing because of relaxing the regularity restrictions of the classical theory.
NASA Astrophysics Data System (ADS)
G, A., Major; Fretwell, H. M.; Dugdale, S. B.; Alam, M. A.
1998-11-01
A novel method for reconstructing the Fermi surface from experimental two-dimensional angular correlation of positron annihilation radiation (2D-ACAR) projections is proposed. In this algorithm, the 3D electron momentum-density distribution is expanded in terms of a basis of wavelet-like functions. The parameters of the model, the wavelet coefficients, are determined by maximizing the likelihood function corresponding to the experimental data and the projections calculated from the model. In contrast to other expansions, in the case of that in terms of wavelets a relatively small number of model parameters are sufficient for representing the relevant parts of the 3D distribution, thus keeping computation times reasonably short. Unlike other reconstruction methods, this algorithm takes full account of the statistical information content of the data and therefore may help to reduce the amount of time needed for data acquisition. An additional advantage of wavelet expansion may be the possibility of retrieving the Fermi surface directly from the wavelet coefficients rather than indirectly using the reconstructed 3D distribution.
Chen, Hong-Yan; Zhao, Geng-Xing; Li, Xi-Can; Wang, Xiang-Feng; Li, Yu-Ling
2013-11-01
Taking the Qihe County in Shandong Province of East China as the study area, soil samples were collected from the field, and based on the hyperspectral reflectance measurement of the soil samples and the transformation with the first deviation, the spectra were denoised and compressed by discrete wavelet transform (DWT), the variables for the soil alkali hydrolysable nitrogen quantitative estimation models were selected by genetic algorithms (GA), and the estimation models for the soil alkali hydrolysable nitrogen content were built by using partial least squares (PLS) regression. The discrete wavelet transform and genetic algorithm in combining with partial least squares (DWT-GA-PLS) could not only compress the spectrum variables and reduce the model variables, but also improve the quantitative estimation accuracy of soil alkali hydrolysable nitrogen content. Based on the 1-2 levels low frequency coefficients of discrete wavelet transform, and under the condition of large scale decrement of spectrum variables, the calibration models could achieve the higher or the same prediction accuracy as the soil full spectra. The model based on the second level low frequency coefficients had the highest precision, with the model predicting R2 being 0.85, the RMSE being 8.11 mg x kg(-1), and RPD being 2.53, indicating the effectiveness of DWT-GA-PLS method in estimating soil alkali hydrolysable nitrogen content. PMID:24564148
Duarte-Galvan, Carlos; Romero-Troncoso, Rene de J; Torres-Pacheco, Irineo; Guevara-Gonzalez, Ramon G; Fernandez-Jaramillo, Arturo A; Contreras-Medina, Luis M; Carrillo-Serrano, Roberto V; Millan-Almaraz, Jesus R
2014-01-01
Soil drought represents one of the most dangerous stresses for plants. It impacts the yield and quality of crops, and if it remains undetected for a long time, the entire crop could be lost. However, for some plants a certain amount of drought stress improves specific characteristics. In such cases, a device capable of detecting and quantifying the impact of drought stress in plants is desirable. This article focuses on testing if the monitoring of physiological process through a gas exchange methodology provides enough information to detect drought stress conditions in plants. The experiment consists of using a set of smart sensors based on Field Programmable Gate Arrays (FPGAs) to monitor a group of plants under controlled drought conditions. The main objective was to use different digital signal processing techniques such as the Discrete Wavelet Transform (DWT) to explore the response of plant physiological processes to drought. Also, an index-based methodology was utilized to compensate the spatial variation inside the greenhouse. As a result, differences between treatments were determined to be independent of climate variations inside the greenhouse. Finally, after using the DWT as digital filter, results demonstrated that the proposed system is capable to reject high frequency noise and to detect drought conditions. PMID:25302811
NASA Astrophysics Data System (ADS)
Kenna, A.; Basu, B.
2015-07-01
Wind turbine support towers at heights in excess of 90m are nowadays being formed in steel, concrete and hybrid concrete and steel structures. As is the case for all towers of this height, the towers will be assembled using a number of segments, which will be connected in some way. These local connections are to be viewed as areas of potential local weakness in the overall tower assembly and require care in terms of design and construction. This work concentrates on identifying local damage which can occur at an interface connection by either material or bolt/tendon failure. Spatial strain patterns will be used to try to identify local damage areas around a 3 dimensional tower shell. A Finite Element (FE) model will be assembled which will describe a hybrid tower as a continuum of four-noded, two-dimensional Reisser- Mindlin shell elements. In order to simulate local damage, an element around the circumference of the tower interface will be subjected to a reduced stiffness. Strain patterns will be observed both in the undamaged and damaged states and these signals will be processed using a Discrete Wavelet Transform (DWT) algorithm to investigate if the damaged element can be identified.
Yassin, Ali A.
2014-01-01
Now, the security of digital images is considered more and more essential and fingerprint plays the main role in the world of image. Furthermore, fingerprint recognition is a scheme of biometric verification that applies pattern recognition techniques depending on image of fingerprint individually. In the cloud environment, an adversary has the ability to intercept information and must be secured from eavesdroppers. Unluckily, encryption and decryption functions are slow and they are often hard. Fingerprint techniques required extra hardware and software; it is masqueraded by artificial gummy fingers (spoof attacks). Additionally, when a large number of users are being verified at the same time, the mechanism will become slow. In this paper, we employed each of the partial encryptions of user's fingerprint and discrete wavelet transform to obtain a new scheme of fingerprint verification. Moreover, our proposed scheme can overcome those problems; it does not require cost, reduces the computational supplies for huge volumes of fingerprint images, and resists well-known attacks. In addition, experimental results illustrate that our proposed scheme has a good performance of user's fingerprint verification. PMID:27355051
Duarte-Galvan, Carlos; de J. Romero-Troncoso, Rene; Torres-Pacheco, Irineo; Guevara-Gonzalez, Ramon G.; Fernandez-Jaramillo, Arturo A.; Contreras-Medina, Luis M.; Carrillo-Serrano, Roberto V.; Millan-Almaraz, Jesus R.
2014-01-01
Soil drought represents one of the most dangerous stresses for plants. It impacts the yield and quality of crops, and if it remains undetected for a long time, the entire crop could be lost. However, for some plants a certain amount of drought stress improves specific characteristics. In such cases, a device capable of detecting and quantifying the impact of drought stress in plants is desirable. This article focuses on testing if the monitoring of physiological process through a gas exchange methodology provides enough information to detect drought stress conditions in plants. The experiment consists of using a set of smart sensors based on Field Programmable Gate Arrays (FPGAs) to monitor a group of plants under controlled drought conditions. The main objective was to use different digital signal processing techniques such as the Discrete Wavelet Transform (DWT) to explore the response of plant physiological processes to drought. Also, an index-based methodology was utilized to compensate the spatial variation inside the greenhouse. As a result, differences between treatments were determined to be independent of climate variations inside the greenhouse. Finally, after using the DWT as digital filter, results demonstrated that the proposed system is capable to reject high frequency noise and to detect drought conditions. PMID:25302811
Wavelet analysis and scaling properties of time series
NASA Astrophysics Data System (ADS)
Manimaran, P.; Panigrahi, Prasanta K.; Parikh, Jitendra C.
2005-10-01
We propose a wavelet based method for the characterization of the scaling behavior of nonstationary time series. It makes use of the built-in ability of the wavelets for capturing the trends in a data set, in variable window sizes. Discrete wavelets from the Daubechies family are used to illustrate the efficacy of this procedure. After studying binomial multifractal time series with the present and earlier approaches of detrending for comparison, we analyze the time series of averaged spin density in the 2D Ising model at the critical temperature, along with several experimental data sets possessing multifractal behavior.
Wavelet analysis and scaling properties of time series.
Manimaran, P; Panigrahi, Prasanta K; Parikh, Jitendra C
2005-10-01
We propose a wavelet based method for the characterization of the scaling behavior of nonstationary time series. It makes use of the built-in ability of the wavelets for capturing the trends in a data set, in variable window sizes. Discrete wavelets from the Daubechies family are used to illustrate the efficacy of this procedure. After studying binomial multifractal time series with the present and earlier approaches of detrending for comparison, we analyze the time series of averaged spin density in the 2D Ising model at the critical temperature, along with several experimental data sets possessing multifractal behavior. PMID:16383481
NASA Astrophysics Data System (ADS)
Mei, Hong-Xin; Zhang, Ting; Huang, Hua-Qi; Huang, Rong-Bin; Zheng, Lan-Sun
2016-03-01
Three mix-ligand Ag(I) coordination compounds, namely, {[Ag10(tpyz) 5(L1) 5(H2 O)2].(H2 O)4}n (1, tpyz = 2,3,4,5-tetramethylpyrazine, H2 L1 = phthalic acid), [Ag4(tpyz) 2(L2) 2(H2 O)].(H2 O)5}n (2, H2 L2 = isophthalic acid) {[Ag2(tpyz) 2(L3) (H2 O)4].(H2 O)8}n (3, H2 L3 = terephthalic acid), have been synthesized and characterized by elemental analysis, IR, PXRD and X-ray single-crystal diffraction. 1 exhibits a 2D layer which can be simplified as a (4,4) net. 2 is a 3D network which can be simplified as a (3,3)-connected 2-nodal net with a point symbol of {102.12}{102}. 3 consists of linear [Ag(tpyz) (H2 O)2]n chain. Of particular interest, discrete hexamer water clusters were observed in 1 and 2, while a 2D L10(6) water layer exists in 3. The results suggest that the benzene dicarboxylates play pivotal roles in the formation of the different host architectures as well as different water aggregations. Moreover, thermogravimetric analysis (TGA) and emissive behaviors of these compounds were investigated.
NASA Astrophysics Data System (ADS)
Igami, M.; Shibazaki, B.; Nakama, Y.
2002-12-01
Particle based simulations such as the lattice solid modeling (Mora and Place, 1994; Abe et al., 2002) and the modeling using the discrete element method (Morgan and Boettcher, 1999) are very useful for investigating frictional behavior of the fault zone. We investigate the fault behavior using the discrete element method considering the effect of the time-dependent increase of contact area between particles. In our model the tangential force due to the frictional contact is assumed to be SA, where S is the shear stress within microcontacts and A is the contact area. For stationary contact, the contact area is assumed to increase with time following the equation A(t)=A0}(1+k{BT/E ln (1+t/t0)) (Brechet and Estrin, 1994), where t0 is an increasing function of temperature T. On the other hand, when sliding velocity V is not equal to 0, t is replaced with D c/V. Based on the elastic contact theory, A0 is assumed to be in proportion to Fn3/2, where Fn is the normal force that acts on each grain. As a test, we perform velocity step experiments. We consider the particle size distribution of r max/r min=2, where r max and r min represent maximum and minimum particle size, respectively. We found that stability of the fault zone is controlled by T. For small T or t0, velocity weakening behavior was observed. When T or t0 is large, however, no velocity weakening was observed. Our model is able to include the increase of contact area due to solution-transfer proposed by Hickman and Evans (1992). We also report the results of numerical simulation using the functional form of contact area when the solution-transfer is at work within microcontacts.
Latifoğlu, Fatma; Kara, Sadik; Imal, Erkan
2009-06-01
In this paper, a more effective use of Doppler techniques is presented for the purpose of diagnosing atherosclerosis in its early stages using the carotid artery Doppler signals. The power spectral density (PSD) graphics are obtained by applying the short-time Fourier transform (STFT)-Welch and the Eigenvector MUSIC methods to the discrete wavelet transform (DWT) of Doppler signals. The PSDs for the fourth approximation component (A4) of both methods estimated that the patients with atherosclerosis in its early phase had lower maximum frequency components. On the other hand, the healthy subjects had higher maximum frequency components. The area under the curve (AUC), which belongs to the receiver operating characteristic (ROC) curve for the frequency level of the maximum PSDs of the A4 approximation obtained from the STFT modeling, is computed as 0.97. The AUC for the MUSIC modeling is computed as 0.996. The AUC belonging to the ROC curve for the higher maximum frequency component is computed as 0.87. The AUC belonging to the ROC curve for the test parameter of the frequency level of the maximum PSDs derived from the MUSIC modeling is determined to be 0.882. The results of this study clearly demonstrate that it is possible to distinguish between the healthy people and the patients with atherosclerosis by using the frequency level of the maximum PSDs for the A4 approximation. Furthermore, it is concluded that the power of Eigenvector-MUSIC method in terms of the resolution of the high frequencies is better than that of the STFT methods. PMID:19408452
Energy Science and Technology Software Center (ESTSC)
2005-07-01
Aniso2d is a two-dimensional seismic forward modeling code. The earth is parameterized by an X-Z plane in which the seismic properties Can have monoclinic with x-z plane symmetry. The program uses a user define time-domain wavelet to produce synthetic seismograms anrwhere within the two-dimensional media.
Nosich, Andrey A; Gandel, Yuriy V; Magath, Thore; Altintas, Ayhan
2007-09-01
Considered is the beam wave guidance and scattering by 2D quasi-optical reflectors modeling the components of beam waveguides. The incident field is taken as the complex-source-point field to simulate a finite-width beam generated by a small-aperture source. A numerical solution is obtained from the coupled singular integral equations (SIEs) for the surface currents on reflectors, discretized by using the recently introduced Nystrom-type quadrature formulas. This analysis is applied to study what effect the edge illumination has on the performance of a chain of confocal elliptic reflectors. We also develop a semianalytical approach for shaped reflector synthesis after a prescribed near-field pattern. Here a new point is the use of auxiliary SIEs of the same type as in the scattering analysis problem, however, for the gradient of the objective function. Sample results are presented for the synthesis of a reflector-type beam splitter. PMID:17767252
NASA Astrophysics Data System (ADS)
Maginot, Peter G.; Morel, Jim E.; Ragusa, Jean C.
2012-08-01
We present a new nonlinear spatial finite-element method for the linearized Boltzmann transport equation with Sn angular discretization in 1-D and 2-D Cartesian geometries. This method has two central characteristics. First, it is equivalent to the linear-discontinuous (LD) Galerkin method whenever that method yields a strictly non-negative solution. Second, it always satisfies both the zeroth and first spatial moment equations. Because it yields the LD solution when that solution is non-negative, one might interpret our method as a classical fix-up to the LD scheme. However, fix-up schemes for the LD equations derived in the past have given up solution of the first moment equations when the LD solution is negative in order to satisfy positivity in a simple manner. We present computational results comparing our method in 1-D to the strictly non-negative linear exponential-discontinuous method and to the LD method. We present computational results in 2-D comparing our method to a recently developed LD fix-up scheme and to the LD scheme. It is demonstrated that our method is a valuable alternative to existing methods.
Two-dimensional quantum propagation using wavelets in space and time
Sparks, Douglas K.; Johnson, Bruce R.
2006-09-21
A recent method for solving the time-dependent Schroedinger equation has been developed using expansions in compact-support wavelet bases in both space and time [H. Wang et al., J. Chem. Phys. 121, 7647 (2004)]. This method represents an exact quantum mixed time-frequency approach, with special initial temporal wavelets used to solve the initial value problem. The present work is a first extension of the method to multiple spatial dimensions applied to a simple two-dimensional (2D) coupled anharmonic oscillator problem. A wavelet-discretized version of norm preservation for time-independent Hamiltonians discovered in the earlier one-dimensional investigation is verified to hold as well in 2D and, by implication, in higher numbers of spatial dimensions. The wavelet bases are not restricted to rectangular domains, a fact which is exploited here in a 2D adaptive version of the algorithm.
Applications of a fast, continuous wavelet transform
Dress, W.B.
1997-02-01
A fast, continuous, wavelet transform, based on Shannon`s sampling theorem in frequency space, has been developed for use with continuous mother wavelets and sampled data sets. The method differs from the usual discrete-wavelet approach and the continuous-wavelet transform in that, here, the wavelet is sampled in the frequency domain. Since Shannon`s sampling theorem lets us view the Fourier transform of the data set as a continuous function in frequency space, the continuous nature of the functions is kept up to the point of sampling the scale-translation lattice, so the scale-translation grid used to represent the wavelet transform is independent of the time- domain sampling of the signal under analysis. Computational cost and nonorthogonality aside, the inherent flexibility and shift invariance of the frequency-space wavelets has advantages. The method has been applied to forensic audio reconstruction speaker recognition/identification, and the detection of micromotions of heavy vehicles associated with ballistocardiac impulses originating from occupants` heart beats. Audio reconstruction is aided by selection of desired regions in the 2-D representation of the magnitude of the transformed signal. The inverse transform is applied to ridges and selected regions to reconstruct areas of interest, unencumbered by noise interference lying outside these regions. To separate micromotions imparted to a mass-spring system (e.g., a vehicle) by an occupants beating heart from gross mechanical motions due to wind and traffic vibrations, a continuous frequency-space wavelet, modeled on the frequency content of a canonical ballistocardiogram, was used to analyze time series taken from geophone measurements of vehicle micromotions. By using a family of mother wavelets, such as a set of Gaussian derivatives of various orders, features such as the glottal closing rate and word and phrase segmentation may be extracted from voice data.
An Introduction to Wavelet Theory and Analysis
Miner, N.E.
1998-10-01
This report reviews the history, theory and mathematics of wavelet analysis. Examination of the Fourier Transform and Short-time Fourier Transform methods provides tiormation about the evolution of the wavelet analysis technique. This overview is intended to provide readers with a basic understanding of wavelet analysis, define common wavelet terminology and describe wavelet amdysis algorithms. The most common algorithms for performing efficient, discrete wavelet transforms for signal analysis and inverse discrete wavelet transforms for signal reconstruction are presented. This report is intended to be approachable by non- mathematicians, although a basic understanding of engineering mathematics is necessary.
Yahia, K; Cardoso, A J M; Ghoggal, A; Zouzou, S E
2014-03-01
Fast Fourier transform (FFT) analysis has been successfully used for fault diagnosis in induction machines. However, this method does not always provide good results for the cases of load torque, speed and voltages variation, leading to a variation of the motor-slip and the consequent FFT problems that appear due to the non-stationary nature of the involved signals. In this paper, the discrete wavelet transform (DWT) of the apparent-power signal for the airgap-eccentricity fault detection in three-phase induction motors is presented in order to overcome the above FFT problems. The proposed method is based on the decomposition of the apparent-power signal from which wavelet approximation and detail coefficients are extracted. The energy evaluation of a known bandwidth permits to define a fault severity factor (FSF). Simulation as well as experimental results are provided to illustrate the effectiveness and accuracy of the proposed method presented even for the case of load torque variations. PMID:24461376
Li, Chuan; Peng, Juan; Liang, Ming
2014-01-01
Oil debris sensors are effective tools to monitor wear particles in lubricants. For in situ applications, surrounding noise and vibration interferences often distort the oil debris signature of the sensor. Hence extracting oil debris signatures from sensor signals is a challenging task for wear particle monitoring. In this paper we employ the maximal overlap discrete wavelet transform (MODWT) with optimal decomposition depth to enhance the wear particle monitoring capability. The sensor signal is decomposed by the MODWT into different depths for detecting the wear particle existence. To extract the authentic particle signature with minimal distortion, the root mean square deviation of kurtosis value of the segmented signal residue is adopted as a criterion to obtain the optimal decomposition depth for the MODWT. The proposed approach is evaluated using both simulated and experimental wear particles. The results show that the present method can improve the oil debris monitoring capability without structural upgrade requirements. PMID:24686730
Texture image retrieval using new rotated complex wavelet filters.
Kokare, Manesh; Biswas, P K; Chatterji, B N
2005-12-01
A new set of two-dimensional (2-D) rotated complex wavelet filters (RCWFs) are designed with complex wavelet filter coefficients, which gives texture information strongly oriented in six different directions (45 degrees apart from complex wavelet transform). The 2-D RCWFs are nonseparable and oriented, which improves characterization of oriented textures. Most texture image retrieval systems are still incapable of providing retrieval result with high retrieval accuracy and less computational complexity. To address this problem, we propose a novel approach for texture image retrieval by using a set of dual-tree rotated complex wavelet filter (DT-RCWF) and dual-tree-complex wavelet transform (DT-CWT) jointly, which obtains texture features in 12 different directions. The information provided by DT-RCWF complements the information generated by DT-CWT. Features are obtained by computing the energy and standard deviation on each subband of the decomposed image. To check the retrieval performance, texture database D1 of 1856 textures from Brodatz album and database D2 of 640 texture images from VisTex image database is created. Experimental results indicates that the proposed method improves retrieval rate from 69.61% to 77.75% on database D1, and from 64.83% to 82.81% on database D2, in comparing with traditional discrete wavelet transform based approach. The proposed method also retains comparable levels of computational complexity. PMID:16366243
Applications of a fast continuous wavelet transform
NASA Astrophysics Data System (ADS)
Dress, William B.
1997-04-01
A fast, continuous, wavelet transform, justified by appealing to Shannon's sampling theorem in frequency space, has been developed for use with continuous mother wavelets and sampled data sets. The method differs from the usual discrete-wavelet approach and from the standard treatment of the continuous-wavelet transform in that, here, the wavelet is sampled in the frequency domain. Since Shannon's sampling theorem lets us view the Fourier transform of the data set as representing the continuous function in frequency space, the continuous nature of the functions is kept up to the point of sampling the scale-translation lattice, so the scale-translation grid used to represent the wavelet transform is independent of the time-domain sampling of the signal under analysis. Although more computationally costly and not represented by an orthogonal basis, the inherent flexibility and shift invariance of the frequency-space wavelets are advantageous for certain applications. The method has been applied to forensic audio reconstruction, speaker recognition/identification, and the detection of micromotions of heavy vehicles associated with ballistocardiac impulses originating from occupants' heart beats. Audio reconstruction is aided by selection of desired regions in the 2D representation of the magnitude of the transformed signals. The inverse transform is applied to ridges and selected regions to reconstruct areas of interest, unencumbered by noise interference lying outside these regions. To separate micromotions imparted to a mass- spring system by an occupant's beating heart from gross mechanical motions due to wind and traffic vibrations, a continuous frequency-space wavelet, modeled on the frequency content of a canonical ballistocardiogram, was used to analyze time series taken from geophone measurements of vehicle micromotions. By using a family of mother wavelets, such as a set of Gaussian derivatives of various orders, different features may be extracted from voice
NASA Astrophysics Data System (ADS)
Ma, Long; Li, Changjun; Song, Shuni; Zhao, Deping
2011-11-01
Kaarna et al. [pro. Scand. Cof. Image Analysis, SCIA 2003, pages 320-327] proposed a watermarking method based on the three dimensional wavelet transform for spectral images. kaarna et al [J. Imaging SCI. Technol. 52, pages 30502-1 - 30502-18, 2008] reported that the robustness of the watermarking method to different illumination conditions. The spectral image database provider stores the reflectance or radiance spectra of the images. Depending on the client's requirements, the effects from illumination can be added to the spectra, i.e., the viewing conditions change the perceived color of the spectrum. External illumination can be compensated through convoluting the spectra of the image with the spectrum of the illuminant. In this paper, a hybrid watermarking method based on the three-dimensional wavelet transform and singular value decomposition is proposed. The proposed method is compared with the 3D-DWT method of kaarna et al in the cases both with and without effect of different illumination conditions. Experiments were performed on a spectral image of natural scenes. Inlab2 was selected. The color reproduction is done using CIE XYZ basis function with D65 light model. Inlab2 image have the following dimensions: 256x256 pixels, and 31 spectral components per each pixel. Images were captured by a CCD (charge coupled device) camera in a 400-700 nm wavelength range at 10 nm intervals. The image selected was taken indoor (in a controlled environment, i.e. dark-lab or glass-house). The performance of the proposed technique is compared with the work of kaarna et al against different illumination conditions and attacks including median and mean filtering, lossy compression. The experiments indicate, the proposed method outperforms the work of kaarna et al.
Salas-Boni, Rebeca; Bai, Yong; Harris, Patricia Rae Eileen; Drew, Barbara J; Hu, Xiao
2014-01-01
Over the past few years, reducing the number of false positive cardiac monitor alarms (FA) in the intensive care unit (ICU) has become an issue of the utmost importance. In our work, we developed a robust methodology that, without the need for additional non-ECG waveforms, suppresses false positive ventricular tachycardia (VT) alarms without resulting in false negative alarms. Our approach is based on features extracted from the ECG signal 20 seconds prior to a triggered alarm. We applied a multi resolution wavelet transform to the ECG data 20seconds prior to the alarm trigger, extracted features from appropriately chosen scales and combined them across all available leads. These representations are presented to a L1-regularized logistic regression classifier. Results are shown in two datasets of physiological waveforms with manually assessed cardiac monitor alarms: the MIMIC II dataset, where we achieved a false alarm (FA) suppression of 21% with zero true alarm (TA) suppression; and a dataset compiled by UCSF and General Electric, where a 36% FA suppression was achieved with a zero TA suppression. The methodology described in this work could be implemented to reduce the number of false monitor alarms in other arrhythmias. PMID:25172188
NASA Technical Reports Server (NTRS)
Barrie, Alexander C.; Yeh, Penshu; Dorelli, John C.; Clark, George B.; Paterson, William R.; Adrian, Mark L.; Holland, Matthew P.; Lobell, James V.; Simpson, David G.; Pollock, Craig J.; Moore, Thomas E.
2015-01-01
Plasma measurements in space are becoming increasingly faster, higher resolution, and distributed over multiple instruments. As raw data generation rates can exceed available data transfer bandwidth, data compression is becoming a critical design component. Data compression has been a staple of imaging instruments for years, but only recently have plasma measurement designers become interested in high performance data compression. Missions will often use a simple lossless compression technique yielding compression ratios of approximately 2:1, however future missions may require compression ratios upwards of 10:1. This study aims to explore how a Discrete Wavelet Transform combined with a Bit Plane Encoder (DWT/BPE), implemented via a CCSDS standard, can be used effectively to compress count information common to plasma measurements to high compression ratios while maintaining little or no compression error. The compression ASIC used for the Fast Plasma Investigation (FPI) on board the Magnetospheric Multiscale mission (MMS) is used for this study. Plasma count data from multiple sources is examined: resampled data from previous missions, randomly generated data from distribution functions, and simulations of expected regimes. These are run through the compression routines with various parameters to yield the greatest possible compression ratio while maintaining little or no error, the latter indicates that fully lossless compression is obtained. Finally, recommendations are made for future missions as to what can be achieved when compressing plasma count data and how best to do so.
Agnew, Christina Elizabeth; McCann, A J; Lockhart, C J; Hamilton, P K; McVeigh, G E; McGivern, R C
2011-04-01
The earliest signs of cardiovascular disease occur in microcirculations. Changes to mechanical and structural properties of these small resistive vessels alter the impedance to flow, subsequent reflected waves, and consequently, flow waveform morphology. In this paper, we compare two frequency analysis techniques: 1) rootMUSIC and 2) the discrete wavelet transform (DWT) to extract features of flow velocity waveform morphology captured using Doppler ultrasound from the ophthalmic artery (OA) in 30 controls and 38 age and sex matched Type I diabetics. Conventional techniques for characterizing Doppler velocity waveforms, such as mean velocity, resistive index, and pulsatility index, revealed no significant differences between the groups. However, rootMUSIC and the DWT provided highly correlated results with the spectral content in bands 2-7 (30-0.8 Hz) significantly elevated in the diabetic group (p < 0.05). The spectral distinction between the groups may be attributable to manifestations of underlying pathophysiological processes in vascular impedance and consequent wave reflections, with bands 5 and 7 related to age. Spectral descriptors of OA blood velocity waveforms are better indicators of preclinical microvascular abnormalities in Type I diabetes than conventional measures. Although highly correlated DWT proved slightly more discriminatory than rootMUSIC and has the advantage of extending to subheart rate frequencies, which may be of interest. PMID:21138796
Acharya, U Rajendra; Faust, Oliver; Sree, S Vinitha; Molinari, Filippo; Suri, Jasjit S
2012-08-01
Using right equipment and well trained personnel, ultrasound of the neck can detect a large number of non-palpable thyroid nodules. However, this technique often suffers from subjective interpretations and poor accuracy in the differential diagnosis of malignant and benign thyroid lesions. Therefore, we developed an automated identification system based on knowledge representation techniques for characterizing the intra-nodular vascularization of thyroid lesions. Twenty nodules (10 benign and 10 malignant), taken from 3-D high resolution ultrasound (HRUS) images were used for this work. Malignancy was confirmed using fine needle aspiration biopsy and subsequent histological studies. A combination of discrete wavelet transformation (DWT) and texture algorithms were used to extract relevant features from the thyroid images. These features were fed to different configurations of AdaBoost classifier. The performance of these configurations was compared using receiver operating characteristic (ROC) curves. Our results show that the combination of texture features and DWT features presented an accuracy value higher than that reported in the literature. Among the different classifier setups, the perceptron based AdaBoost yielded very good result and the area under the ROC curve was 1 and classification accuracy, sensitivity and specificity were 100%. Finally, we have composed an Integrated Index called thyroid malignancy index (TMI) made up of these DWT and texture features, to facilitate distinguishing and diagnosing benign or malignant nodules using just one index or number. This index would help the clinicians in more quantitative assessment of the thyroid nodules. PMID:22054816
Entanglement Renormalization and Wavelets.
Evenbly, Glen; White, Steven R
2016-04-01
We establish a precise connection between discrete wavelet transforms and entanglement renormalization, a real-space renormalization group transformation for quantum systems on the lattice, in the context of free particle systems. Specifically, we employ Daubechies wavelets to build approximations to the ground state of the critical Ising model, then demonstrate that these states correspond to instances of the multiscale entanglement renormalization ansatz (MERA), producing the first known analytic MERA for critical systems. PMID:27104687
Entanglement Renormalization and Wavelets
NASA Astrophysics Data System (ADS)
Evenbly, Glen; White, Steven R.
2016-04-01
We establish a precise connection between discrete wavelet transforms and entanglement renormalization, a real-space renormalization group transformation for quantum systems on the lattice, in the context of free particle systems. Specifically, we employ Daubechies wavelets to build approximations to the ground state of the critical Ising model, then demonstrate that these states correspond to instances of the multiscale entanglement renormalization ansatz (MERA), producing the first known analytic MERA for critical systems.
Wavelet analysis of atmospheric turbulence
Hudgins, L.H.
1992-12-31
After a brief review of the elementary properties of Fourier Transforms, the Wavelet Transform is defined in Part I. Basic results are given for admissable wavelets. The Multiresolution Analysis, or MRA (a mathematical structure which unifies a large class of wavelets with Quadrature Mirror Filters) is then introduced. Some fundamental aspects of wavelet design are then explored. The Discrete Wavelet Transform is discussed and, in the context of an MRA, is seen to supply a Fast Wavelet Transform which competes with the Fast Fourier Transform for efficiency. In Part II, the Wavelet Transform is developed in terms of the scale number variable s instead of the scale length variable a where a = 1/s. Basic results such as the admissibility condition, conservation of energy, and the reconstruction theorem are proven in this context. After reviewing some motivation for the usual Fourier power spectrum, a definition is given for the wavelet power spectrum. This `spectral density` is then intepreted in the context of spectral estimation theory. Parseval`s theorem for Wavelets then leads naturally to the Wavelet Cross Spectrum, Wavelet Cospectrum, and Wavelet Quadrature Spectrum. Wavelet Transforms are then applied in Part III to the analysis of atmospheric turbulence. Data collected over the ocean is examined in the wavelet transform domain for underlying structure. A brief overview of atmospheric turbulence is provided. Then the overall method of applying Wavelet Transform techniques to time series data is described. A trace study is included, showing some of the aspects of choosing the computational algorithm, and selection of a specific analyzing wavelet. A model for generating synthetic turbulence data is developed, and seen to yield useful results in comparing with real data for structural transitions. Results from the theory of Wavelet Spectral Estimation and Wavelength Cross-Transforms are applied to studying the momentum transport and the heat flux.
Spectral Laplace-Beltrami wavelets with applications in medical images.
Tan, Mingzhen; Qiu, Anqi
2015-05-01
The spectral graph wavelet transform (SGWT) has recently been developed to compute wavelet transforms of functions defined on non-Euclidean spaces such as graphs. By capitalizing on the established framework of the SGWT, we adopt a fast and efficient computation of a discretized Laplace-Beltrami (LB) operator that allows its extension from arbitrary graphs to differentiable and closed 2-D manifolds (smooth surfaces embedded in the 3-D Euclidean space). This particular class of manifolds are widely used in bioimaging to characterize the morphology of cells, tissues, and organs. They are often discretized into triangular meshes, providing additional geometric information apart from simple nodes and weighted connections in graphs. In comparison with the SGWT, the wavelet bases constructed with the LB operator are spatially localized with a more uniform "spread" with respect to underlying curvature of the surface. In our experiments, we first use synthetic data to show that traditional applications of wavelets in smoothing and edge detectio can be done using the wavelet bases constructed with the LB operator. Second, we show that multi-resolutional capabilities of the proposed framework are applicable in the classification of Alzheimer's patients with normal subjects using hippocampal shapes. Wavelet transforms of the hippocampal shape deformations at finer resolutions registered higher sensitivity (96%) and specificity (90%) than the classification results obtained from the direct usage of hippocampal shape deformations. In addition, the Laplace-Beltrami method requires consistently a smaller number of principal components (to retain a fixed variance) at higher resolution as compared to the binary and weighted graph Laplacians, demonstrating the potential of the wavelet bases in adapting to the geometry of the underlying manifold. PMID:25343758
Wavelet for Ultrasonic Flaw Enhancement and Image Compression
NASA Astrophysics Data System (ADS)
Cheng, W.; Tsukada, K.; Li, L. Q.; Hanasaki, K.
2003-03-01
Ultrasonic imaging has been widely used in Non-destructive Testing (NDT) and medical application. However, the image is always degraded by blur and noise. Besides, the pressure on both storage and transmission gives rise to the need of image compression. We apply 2-D Discrete Wavelet Transform (DWT) to C-scan 2-D images to realize flaw enhancement and image compression, taking advantage of DWT scale and orientation selectivity. The Wavelet coefficient thresholding and scalar quantization are employed respectively. Furthermore, we realize the unification of flaw enhancement and image compression in one process. The reconstructed image from the compressed data gives a clearer interpretation of the flaws at a much smaller bit rate.
NASA Astrophysics Data System (ADS)
Song, Hengxu; Papanikolaou, Stefanos; van der Giessen, Erik
2015-03-01
It is well known for almost three decades that crystal plasticity in metals, such as Cu, is strongly rate dependent at strain rates higher than 10⌃3/s. This rate sensitivity is typically attributed to dislocation drag effects, but there appears to be a large range of possible high-rate-sensitivity exponents, depending on the sample and the experimental group. Thus, one may hypothesize that the dislocation structure has a strong influence on these effects. We elucidate the origins of rate effects in crystal plasticity and their connection with relaxed, before applying stress, dislocation structures by investigating simple bending in a model of discrete dislocation plasticity in two dimensions. We find that the high-strain-rate sensitivity changes significantly as a function of strain, different material treatment (annealed or not) and properties of dislocation sources (surface vs. bulk nucleation). We characterize in detail the emerging patterning in the dislocation structure and we provide predictions for future experiments on the dependence of the rate sensitivity on dislocation-related characteristics.
Compression of 3D integral images using wavelet decomposition
NASA Astrophysics Data System (ADS)
Mazri, Meriem; Aggoun, Amar
2003-06-01
This paper presents a wavelet-based lossy compression technique for unidirectional 3D integral images (UII). The method requires the extraction of different viewpoint images from the integral image. A single viewpoint image is constructed by extracting one pixel from each microlens, then each viewpoint image is decomposed using a Two Dimensional Discrete Wavelet Transform (2D-DWT). The resulting array of coefficients contains several frequency bands. The lower frequency bands of the viewpoint images are assembled and compressed using a 3 Dimensional Discrete Cosine Transform (3D-DCT) followed by Huffman coding. This will achieve decorrelation within and between 2D low frequency bands from the different viewpoint images. The remaining higher frequency bands are Arithmetic coded. After decoding and decompression of the viewpoint images using an inverse 3D-DCT and an inverse 2D-DWT, each pixel from every reconstructed viewpoint image is put back into its original position within the microlens to reconstruct the whole 3D integral image. Simulations were performed on a set of four different grey level 3D UII using a uniform scalar quantizer with deadzone. The results for the average of the four UII intensity distributions are presented and compared with previous use of 3D-DCT scheme. It was found that the algorithm achieves better rate-distortion performance, with respect to compression ratio and image quality at very low bit rates.
Integrated wavelets for medical image analysis
NASA Astrophysics Data System (ADS)
Heinlein, Peter; Schneider, Wilfried
2003-11-01
Integrated wavelets are a new method for discretizing the continuous wavelet transform (CWT). Independent of the choice of discrete scale and orientation parameters they yield tight families of convolution operators. Thus these families can easily be adapted to specific problems. After presenting the fundamental ideas, we focus primarily on the construction of directional integrated wavelets and their application to medical images. We state an exact algorithm for implementing this transform and present applications from the field of digital mammography. The first application covers the enhancement of microcalcifications in digital mammograms. Further, we exploit the directional information provided by integrated wavelets for better separation of microcalcifications from similar structures.
NASA Astrophysics Data System (ADS)
Fadili, Jalal M.; Bullmore, Edward T.
2003-11-01
Wavelet-based methods for multiple hypothesis testing are described and their potential for activation mapping of human functional magnetic resonance imaging (fMRI) data is investigated. In this approach, we emphasize convergence between methods of wavelet thresholding or shrinkage and the problem of multiple hypothesis testing in both classical and Bayesian contexts. Specifically, our interest will be focused on ensuring a trade off between type I probability error control and power dissipation. We describe a technique for controlling the false discovery rate at an arbitrary level of type 1 error in testing multiple wavelet coefficients generated by a 2D discrete wavelet transform (DWT) of spatial maps of {fMRI} time series statistics. We also describe and apply recursive testing methods that can be used to define a threshold unique to each level and orientation of the 2D-DWT. Bayesian methods, incorporating a formal model for the anticipated sparseness of wavelet coefficients representing the signal or true image, are also tractable. These methods are comparatively evaluated by analysis of "null" images (acquired with the subject at rest), in which case the number of positive tests should be exactly as predicted under the hull hypothesis, and an experimental dataset acquired from 5 normal volunteers during an event-related finger movement task. We show that all three wavelet-based methods of multiple hypothesis testing have good type 1 error control (the FDR method being most conservative) and generate plausible brain activation maps.
Schlossnagle, G.; Restrepo, J.M.; Leaf, G.K.
1993-12-01
The properties of periodized Daubechies wavelets on [0,1] are detailed and contrasted against their counterparts which form a basis for L{sup 2}(R). Numerical examples illustrate the analytical estimates for convergence and demonstrate by comparison with Fourier spectral methods the superiority of wavelet projection methods for approximations. The analytical solution to inner products of periodized wavelets and their derivatives, which are known as connection coefficients, is presented, and several tabulated values are included.
NASA Astrophysics Data System (ADS)
Oruç, B.
2014-04-01
In this work, gravity anomalies have been analyzed using gradient analytic signal (GAS) obtained from the square root of the sum of the squares of the second complex and vertical gradients. The gravity anomalies have been decomposed at 1, 2 and 3 levels with Haar mother wavelet. The DWT leads to a decomposition of the approximation coefficients in four distinct components: the approximation, horizontal, vertical and diagonal. I have tested the maxima of the magnitude computed from the square root of the sum of the squares of the horizontal, vertical and diagonal components (HVDM), and maxima of GAS in imaging the source edges in theoretical examples, with and without random Gaussian noise.
Wavelet transforms as solutions of partial differential equations
Zweig, G.
1997-10-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). Wavelet transforms are useful in representing transients whose time and frequency structure reflect the dynamics of an underlying physical system. Speech sound, pressure in turbulent fluid flow, or engine sound in automobiles are excellent candidates for wavelet analysis. This project focused on (1) methods for choosing the parent wavelet for a continuous wavelet transform in pattern recognition applications and (2) the more efficient computation of continuous wavelet transforms by understanding the relationship between discrete wavelet transforms and discretized continuous wavelet transforms. The most interesting result of this research is the finding that the generalized wave equation, on which the continuous wavelet transform is based, can be used to understand phenomena that relate to the process of hearing.
Saadi, Slami; Touiza, Maamar; Kharfi, Fayçal; Guessoum, Abderrezak
2013-12-01
In this work, we present a mixed software/hardware implementation of 2-D signals encoder/decoder using dyadic discrete wavelet transform (DWT) based on quadrature mirror filters (QMF); using fast wavelet Mallat's algorithm. This work is designed and compiled on the embedded development kit EDK6.3i, and the synthesis software, ISE6.3i, which is available with Xilinx Virtex-IIV2MB1000 FPGA. Huffman coding scheme is used to encode the wavelet coefficients so that they can be transmitted progressively through an Ethernet TCP/IP based connection. The possible reconfiguration can be exploited to attain higher performance. The design will be integrated with the neutron radiography system that is used with the Es-Salem research reactor. PMID:24041807
Image-based scene representation using wavelet-based interval morphing
NASA Astrophysics Data System (ADS)
Bao, Paul; Xu, Dan
1999-07-01
Scene appearance for a continuous range of viewpoint can be represented by a discrete set of images via image morphing. In this paper, we present a new robust image morphing scheme based on 2D wavelet transform and interval field interpolation. Traditional mesh-base and field-based morphing algorithms, usually designed in the spatial image space, suffer from very high time complexity and therefore make themselves impractical in real-time virtual environment applications. Compared with traditional morphing methods, the proposed wavelet-based interval morphing scheme performs interval interpolation in both the frequency and spatial spaces. First, the images of the scene can be significantly compressed in the frequency domain with little degradation in visual quality and therefore the complexity of the scene can be significantly reduced. Second, since a feature point in the image may correspond to a neighborhood in a subband image in the wavelet domain, we define feature interval for the wavelet-transformed images for an accurate feature matching between the morphing images. Based on the feature intervals, we employ the interval field interpolation to morph the images progressively in a coarse-to-fine process. Finally, we use a post-warping procedure to transform the interpolated views to its desired position. A nice future of using wavelet transformation is its multiresolution representation mode, which enables the progressive morphing of scene.
Critically sampled wavelets with composite dilations.
Easley, Glenn R; Labate, Demetrio
2012-02-01
Wavelets with composite dilations provide a general framework for the construction of waveforms defined not only at various scales and locations, as traditional wavelets, but also at various orientations and with different scaling factors in each coordinate. As a result, they are useful to analyze the geometric information that often dominate multidimensional data much more efficiently than traditional wavelets. The shearlet system, for example, is a particular well-known realization of this framework, which provides optimally sparse representations of images with edges. In this paper, we further investigate the constructions derived from this approach to develop critically sampled wavelets with composite dilations for the purpose of image coding. Not only do we show that many nonredundant directional constructions recently introduced in the literature can be derived within this setting, but we also introduce new critically sampled discrete transforms that achieve much better nonlinear approximation rates than traditional discrete wavelet transforms and outperform the other critically sampled multiscale transforms recently proposed. PMID:21843993
NASA Astrophysics Data System (ADS)
Aytac Korkmaz, Sevcan
2016-05-01
The aim of this article is to provide early detection of cervical cancer by using both Atomic Force Microscope (AFM) and Scanning Electron Microscope (SEM) images of same patient. When the studies in the literature are examined, it is seen that the AFM and SEM images of the same patient are not used together for early diagnosis of cervical cancer. AFM and SEM images can be limited when using only one of them for the early detection of cervical cancer. Therefore, multi-modality solutions which give more accuracy results than single solutions have been realized in this paper. Optimum feature space has been obtained by Discrete Wavelet Entropy Energy (DWEE) applying to the 3 × 180 AFM and SEM images. Then, optimum features of these images are classified with Jensen Shannon, Hellinger, and Triangle Measure (JHT) Classifier for early diagnosis of cervical cancer. However, between classifiers which are Jensen Shannon, Hellinger, and triangle distance have been validated the measures via relationships. Afterwards, accuracy diagnosis of normal, benign, and malign cervical cancer cell was found by combining mean success rates of Jensen Shannon, Hellinger, and Triangle Measure which are connected with each other. Averages of accuracy diagnosis for AFM and SEM images by averaging the results obtained from these 3 classifiers are found as 98.29% and 97.10%, respectively. It has been observed that AFM images for early diagnosis of cervical cancer have higher performance than SEM images. Also in this article, surface roughness of malign AFM images in the result of the analysis made for the AFM images, according to the normal and benign AFM images is observed as larger, If the volume of particles has found as smaller. She has been a Faculty Member at Fırat University in the Electrical- Electronic Engineering Department since 2007. Her research interests include image processing, computer vision systems, pattern recognition, data fusion, wavelet theory, artificial neural
A Wavelet Perspective on the Allan Variance.
Percival, Donald B
2016-04-01
The origins of the Allan variance trace back 50 years ago to two seminal papers, one by Allan (1966) and the other by Barnes (1966). Since then, the Allan variance has played a leading role in the characterization of high-performance time and frequency standards. Wavelets first arose in the early 1980s in the geophysical literature, and the discrete wavelet transform (DWT) became prominent in the late 1980s in the signal processing literature. Flandrin (1992) briefly documented a connection between the Allan variance and a wavelet transform based upon the Haar wavelet. Percival and Guttorp (1994) noted that one popular estimator of the Allan variance-the maximal overlap estimator-can be interpreted in terms of a version of the DWT now widely referred to as the maximal overlap DWT (MODWT). In particular, when the MODWT is based on the Haar wavelet, the variance of the resulting wavelet coefficients-the wavelet variance-is identical to the Allan variance when the latter is multiplied by one-half. The theory behind the wavelet variance can thus deepen our understanding of the Allan variance. In this paper, we review basic wavelet variance theory with an emphasis on the Haar-based wavelet variance and its connection to the Allan variance. We then note that estimation theory for the wavelet variance offers a means of constructing asymptotically correct confidence intervals (CIs) for the Allan variance without reverting to the common practice of specifying a power-law noise type a priori. We also review recent work on specialized estimators of the wavelet variance that are of interest when some observations are missing (gappy data) or in the presence of contamination (rogue observations or outliers). It is a simple matter to adapt these estimators to become estimators of the Allan variance. Finally we note that wavelet variances based upon wavelets other than the Haar offer interesting generalizations of the Allan variance. PMID:26529757
VHDL implementation of wavelet packet transforms using SIMULINK tools
NASA Astrophysics Data System (ADS)
Shirvaikar, Mukul; Bushnaq, Tariq
2008-02-01
The wavelet transform is currently being used in many engineering fields. The real-time implementation of the Discrete Wavelet Transform (DWT) is a current area of research as it is one of the most time consuming steps in the JPEG2000 standard. The standard implements two different wavelet transforms: irreversible and reversible Daubechies. The former is a lossy transform, whereas the latter is a lossless transform. Many current JPEG2000 implementations are software-based and not efficient enough to meet real-time deadlines. Field Programmable Gate Arrays (FPGAs) are revolutionizing image and signal processing. Many major FPGA vendors like Altera and Xilinx have recently developed SIMULINK tools to support their FPGAs. These tools are intended to provide a seamless path from system-level algorithm design to FPGA implementation. In this paper, we investigate FPGA implementation of 2-D lifting-based Daubechies 9/7 and Daubechies 5/3 transforms using a Matlab/Simulink tool that generates synthesizable VHSIC Hardware Description Language (VHDL) code. The goal is to study the feasibility of this approach for real time image processing by comparing the performance of the high-level toolbox with a handwritten VHDL implementation. The hardware platform used is an Altera DE2 board with a 50MHz Cyclone II FPGA chip and the Simulink tool chosen is DSPBuilder by Altera.
Spherical wavelet transform: linking global seismic tomography and imaging
NASA Astrophysics Data System (ADS)
Pan, J.
2001-12-01
Each year, numerous seismic tomographic images are published based on either new parameterization, damping schemes or datasets. Though people agree generally on the longer- wavelength seismic structures, large discrepencies still exist among various models. Normally the data is noisy, thus the inverse problem is often ill-conditioned. Sampling rate may be enough to resolve for long-wavelength structures when we parameterize the earth to a low harmonic order. However, higher order signals (slabs, plume-like structures, and local seismic velocity anomalies (SVA)) on a global scale remain under-sampled. Finer discretization of the model space increases the problem size dramatically but does not alleviate the nature of the problem. The main challenge thus is to find an efficient representation of the model space to solve for the lower- and higher- degree SVAs simultaneously. Spherical wavelets are a good choice because of their compact support (locaized) in both spatial and frequency domains. If SVAs can be viewed as an image, they consist of smooth-varying signals superpositioned by small-scale local changes and can be compressed greatly and represented better using spherical wavelets. By mapping the model parameters into a nested multi-resolution analysis (MRA) space, the signals become comparable in size therefore stable solutions can be achieved at every level of the resolution without introducing subjective damping. The efficiency of using wavelets and MRA to denoise and compress signals can be used to reduce the problem size and eliminate effects of noisy data. This new algorithm can achieve better resolving power for 2D and 3D seismic tomography, by linking image processing with inverse theory. Advances in spherical wavelets enable the introduction of wavelet analysis and a new parameterization of MRA into global tomography studies. In this paper, we present the new inversion method based on spherical wavelet transform. An application to 2D surface wave
Wavelet analysis in virtual colonoscopy
NASA Astrophysics Data System (ADS)
Greenblum, Sharon; Li, Jiang; Huang, Adam; Summers, Ronald M.
2006-03-01
The computed tomographic colonography (CTC) computer aided detection (CAD) program is a new method in development to detect colon polyps in virtual colonoscopy. While high sensitivity is consistently achieved, additional features are desired to increase specificity. In this paper, a wavelet analysis was applied to CTCCAD outputs in an attempt to filter out false positive detections. 52 CTCCAD detection images were obtained using a screen capture application. 26 of these images were real polyps, confirmed by optical colonoscopy and 26 were false positive detections. A discrete wavelet transform of each image was computed with the MATLAB wavelet toolbox using the Haar wavelet at levels 1-5 in the horizontal, vertical and diagonal directions. From the resulting wavelet coefficients at levels 1-3 for all directions, a 72 feature vector was obtained for each image, consisting of descriptive statistics such as mean, variance, skew, and kurtosis at each level and orientation, as well as error statistics based on a linear predictor of neighboring wavelet coefficients. The vectors for each of the 52 images were then run through a support vector machine (SVM) classifier using ten-fold cross-validation training to determine its efficiency in distinguishing polyps from false positives. The SVM results showed 100% sensitivity and 51% specificity in correctly identifying the status of detections. If this technique were added to the filtering process of the CTCCAD polyp detection scheme, the number of false positive results could be reduced significantly.
Doppler ultrasound signal denoising based on wavelet frames.
Zhang, Y; Wang, Y; Wang, W; Liu, B
2001-05-01
A novel approach was proposed to denoise the Doppler ultrasound signal. Using this method, wavelet coefficients of the Doppler signal at multiple scales were first obtained using the discrete wavelet frame analysis. Then, a soft thresholding-based denoising algorithm was employed to deal with these coefficients to get the denoised signal. In the simulation experiments, the SNR improvements and the maximum frequency estimation precision were studied for the denoised signal. From the simulation and clinical studies, it was concluded that the performance of this discrete wavelet frame (DWF) approach is higher than that of the standard (critically sampled) wavelet transform (DWT) for the Doppler ultrasound signal denoising. PMID:11381694
Adaptive wavelets and relativistic magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Hirschmann, Eric; Neilsen, David; Anderson, Matthe; Debuhr, Jackson; Zhang, Bo
2016-03-01
We present a method for integrating the relativistic magnetohydrodynamics equations using iterated interpolating wavelets. Such provide an adaptive implementation for simulations in multidimensions. A measure of the local approximation error for the solution is provided by the wavelet coefficients. They place collocation points in locations naturally adapted to the flow while providing expected conservation. We present demanding 1D and 2D tests includingthe Kelvin-Helmholtz instability and the Rayleigh-Taylor instability. Finally, we consider an outgoing blast wave that models a GRB outflow.
Perceptually Lossless Wavelet Compression
NASA Technical Reports Server (NTRS)
Watson, Andrew B.; Yang, Gloria Y.; Solomon, Joshua A.; Villasenor, John
1996-01-01
The Discrete Wavelet Transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter, which we call DWT uniform quantization noise. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2(exp -1), where r is display visual resolution in pixels/degree, and L is the wavelet level. Amplitude thresholds increase rapidly with spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from low-pass to horizontal/vertical to diagonal. We propose a mathematical model for DWT noise detection thresholds that is a function of level, orientation, and display visual resolution. This allows calculation of a 'perceptually lossless' quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.
Adapting overcomplete wavelet models to natural images
NASA Astrophysics Data System (ADS)
Sallee, Phil; Olshausen, Bruno A.
2003-11-01
Overcomplete wavelet representations have become increasingly popular for their ability to provide highly sparse and robust descriptions of natural signals. We describe a method for incorporating an overcomplete wavelet representation as part of a statistical model of images which includes a sparse prior distribution over the wavelet coefficients. The wavelet basis functions are parameterized by a small set of 2-D functions. These functions are adapted to maximize the average log-likelihood of the model for a large database of natural images. When adapted to natural images, these functions become selective to different spatial orientations, and they achieve a superior degree of sparsity on natural images as compared with traditional wavelet bases. The learned basis is similar to the Steerable Pyramid basis, and yields slightly higher SNR for the same number of active coefficients. Inference with the learned model is demonstrated for applications such as denoising, with results that compare favorably with other methods.
Comparative study of different wavelet based neural network models for rainfall-runoff modeling
NASA Astrophysics Data System (ADS)
Shoaib, Muhammad; Shamseldin, Asaad Y.; Melville, Bruce W.
2014-07-01
The use of wavelet transformation in rainfall-runoff modeling has become popular because of its ability to simultaneously deal with both the spectral and the temporal information contained within time series data. The selection of an appropriate wavelet function plays a crucial role for successful implementation of the wavelet based rainfall-runoff artificial neural network models as it can lead to further enhancement in the model performance. The present study is therefore conducted to evaluate the effects of 23 mother wavelet functions on the performance of the hybrid wavelet based artificial neural network rainfall-runoff models. The hybrid Multilayer Perceptron Neural Network (MLPNN) and the Radial Basis Function Neural Network (RBFNN) models are developed in this study using both the continuous wavelet and the discrete wavelet transformation types. The performances of the 92 developed wavelet based neural network models with all the 23 mother wavelet functions are compared with the neural network models developed without wavelet transformations. It is found that among all the models tested, the discrete wavelet transform multilayer perceptron neural network (DWTMLPNN) and the discrete wavelet transform radial basis function (DWTRBFNN) models at decomposition level nine with the db8 wavelet function has the best performance. The result also shows that the pre-processing of input rainfall data by the wavelet transformation can significantly increases performance of the MLPNN and the RBFNN rainfall-runoff models.
Wavelet frames and admissibility in higher dimensions
Fuehr, H.
1996-12-01
This paper is concerned with the relations between discrete and continuous wavelet transforms on {ital k}-dimensional Euclidean space. We start with the construction of continuous wavelet transforms with the help of square-integrable representations of certain semidirect products, thereby generalizing results of Bernier and Taylor. We then turn to frames of L{sup 2}({bold R}{sup {ital k}}) and to the question, when the functions occurring in a given frame are admissible for a given continuous wavelet transform. For certain frames we give a characterization which generalizes a result of Daubechies to higher dimensions. {copyright} {ital 1996 American Institute of Physics.}
Transionospheric signal detection with chirped wavelets
Doser, A.B.; Dunham, M.E.
1997-11-01
Chirped wavelets are utilized to detect dispersed signals in the joint time scale domain. Specifically, pulses that become dispersed by transmission through the ionosphere and are received by satellites as nonlinear chirps are investigated. Since the dispersion greatly lowers the signal to noise ratios, it is difficult to isolate the signals in the time domain. Satellite data are examined with discrete wavelet expansions. Detection is accomplished via a template matching threshold scheme. Quantitative experimental results demonstrate that the chirped wavelet detection scheme is successful in detecting the transionospheric pulses at very low signal to noise ratios.
Aytac Korkmaz, Sevcan
2016-05-01
The aim of this article is to provide early detection of cervical cancer by using both Atomic Force Microscope (AFM) and Scanning Electron Microscope (SEM) images of same patient. When the studies in the literature are examined, it is seen that the AFM and SEM images of the same patient are not used together for early diagnosis of cervical cancer. AFM and SEM images can be limited when using only one of them for the early detection of cervical cancer. Therefore, multi-modality solutions which give more accuracy results than single solutions have been realized in this paper. Optimum feature space has been obtained by Discrete Wavelet Entropy Energy (DWEE) applying to the 3×180 AFM and SEM images. Then, optimum features of these images are classified with Jensen Shannon, Hellinger, and Triangle Measure (JHT) Classifier for early diagnosis of cervical cancer. However, between classifiers which are Jensen Shannon, Hellinger, and triangle distance have been validated the measures via relationships. Afterwards, accuracy diagnosis of normal, benign, and malign cervical cancer cell was found by combining mean success rates of Jensen Shannon, Hellinger, and Triangle Measure which are connected with each other. Averages of accuracy diagnosis for AFM and SEM images by averaging the results obtained from these 3 classifiers are found as 98.29% and 97.10%, respectively. It has been observed that AFM images for early diagnosis of cervical cancer have higher performance than SEM images. Also in this article, surface roughness of malign AFM images in the result of the analysis made for the AFM images, according to the normal and benign AFM images is observed as larger, If the volume of particles has found as smaller. PMID:26921605
Adaptive Multilinear Tensor Product Wavelets.
Weiss, Kenneth; Lindstrom, Peter
2016-01-01
Many foundational visualization techniques including isosurfacing, direct volume rendering and texture mapping rely on piecewise multilinear interpolation over the cells of a mesh. However, there has not been much focus within the visualization community on techniques that efficiently generate and encode globally continuous functions defined by the union of multilinear cells. Wavelets provide a rich context for analyzing and processing complicated datasets. In this paper, we exploit adaptive regular refinement as a means of representing and evaluating functions described by a subset of their nonzero wavelet coefficients. We analyze the dependencies involved in the wavelet transform and describe how to generate and represent the coarsest adaptive mesh with nodal function values such that the inverse wavelet transform is exactly reproduced via simple interpolation (subdivision) over the mesh elements. This allows for an adaptive, sparse representation of the function with on-demand evaluation at any point in the domain. We focus on the popular wavelets formed by tensor products of linear B-splines, resulting in an adaptive, nonconforming but crack-free quadtree (2D) or octree (3D) mesh that allows reproducing globally continuous functions via multilinear interpolation over its cells. PMID:26529742
Image registration using redundant wavelet transforms
NASA Astrophysics Data System (ADS)
Brown, Richard K.; Claypoole, Roger L., Jr.
2001-12-01
Imagery is collected much faster and in significantly greater quantities today compared to a few years ago. Accurate registration of this imagery is vital for comparing the similarities and differences between multiple images. Image registration is a significant component in computer vision and other pattern recognition problems, medical applications such as Medical Resonance Images (MRI) and Positron Emission Tomography (PET), remotely sensed data for target location and identification, and super-resolution algorithms. Since human analysis is tedious and error prone for large data sets, we require an automatic, efficient, robust, and accurate method to register images. Wavelet transforms have proven useful for a variety of signal and image processing tasks. In our research, we present a fundamentally new wavelet-based registration algorithm utilizing redundant transforms and a masking process to suppress the adverse effects of noise and improve processing efficiency. The shift-invariant wavelet transform is applied in translation estimation and a new rotation-invariant polar wavelet transform is effectively utilized in rotation estimation. We demonstrate the robustness of these redundant wavelet transforms for the registration of two images (i.e., translating or rotating an input image to a reference image), but extensions to larger data sets are feasible. We compare the registration accuracy of our redundant wavelet transforms to the critically sampled discrete wavelet transform using the Daubechies wavelet to illustrate the power of our algorithm in the presence of significant additive white Gaussian noise and strongly translated or rotated images.
Theory and application of frequency-selective wavelets
Tomas, B.
1992-01-01
Orthonormal compactly supported wavelets have been successfully applied to generate sparse representations of piecewise-smooth functions, yielding fast numerical algorithms. The authors consider the case of case of piecewise oscillatory functions, and construct a variation of the original Daubechies family of wavelets which efficiently represents the oscillations. This new family is constructed by moving some of the zeros of the underlying symbol away from [pi], shifting the approximation properties of the wavelets. The zeros may be chosen to give a sparse representation of an oscillatory function whose spectrum is known. In this sense, these wavelets are frequency-selective. Existence, uniqueness, and regularity results are proved for this family of wavelets. A natural application is the numerical solution of the electric field integral equation in two spatial dimensions: The kernel is singular on the diagonal, and oscillatory within a narrow frequency spectrum away from the diagonal. Applying frequency selective wavelets with the discrete wavelet transform, the discrete equations are transformed into a sparse linear system which is economically solved by a multi-grid scheme based upon the discrete wavelet transform. Substantial computational savings are obtained over the same method using the original Daubechies family of wavelets, and a factor of 10 savings is obtained over standard LU-factorization.
Digital audio signal filtration based on the dual-tree wavelet transform
NASA Astrophysics Data System (ADS)
Yaseen, A. S.; Pavlov, A. N.
2015-07-01
A new method of digital audio signal filtration based on the dual-tree wavelet transform is described. An adaptive approach is proposed that allows the automatic adjustment of parameters of the wavelet filter to be optimized. A significant improvement of the quality of signal filtration is demonstrated in comparison to the traditionally used filters based on the discrete wavelet transform.
Compression of echocardiographic scan line data using wavelet packet transform
NASA Technical Reports Server (NTRS)
Hang, X.; Greenberg, N. L.; Qin, J.; Thomas, J. D.
2001-01-01
An efficient compression strategy is indispensable for digital echocardiography. Previous work has suggested improved results utilizing wavelet transforms in the compression of 2D echocardiographic images. Set partitioning in hierarchical trees (SPIHT) was modified to compress echocardiographic scanline data based on the wavelet packet transform. A compression ratio of at least 94:1 resulted in preserved image quality.
NASA Astrophysics Data System (ADS)
Saadi, S.; Touiza, M.; Guessoum, A.
In this study, we present an implementation on FPGA of 2D signals Encoder/Decoder using dyadic Discrete Wavelet Transform based on quadrature mirror filters, by applying fast wavelet Mallat`s algorithm. The wavelet coefficients will be encoded by Huffman code in order to be transmitted progressively through an Ethernet TCP/IP based connection. The proposed study is implemented and synthesized in VHDL for Xilinx Virtex-IIV2MB1000 FPGA device using ISE 8.1 and simulated on Modelsim PE 6.0d. The synthesis results are presented in detail. The proposed design can substantially accelerate the DWT and the possible reconfiguration can be exploited to reach a higher performance in the future. The system is designed to be integrated as an extension to the nuclear imaging system implemented around our nuclear research reactor. Assuming a Pentium4 processor with clock frequency of 3.3 GHz for the Matlab software implementation, a speed up of over 5 times for a picture size of 256 x 256 was achieved.
Modelling Elastic Media With Arbitrary Shapes Using the Wavelet Transform
NASA Astrophysics Data System (ADS)
Rosa, J. W.; Cardoso, F. A.; Rosa, J. W.; Aki, K.
2004-12-01
We extend the new method proposed by Rosa et al. (2001) for the study of elastic bodies with complete arbitrary shapes. The method was originally developed for modelling 2-D elastic media with the application of the wavelet transform, and was extended to cases where discontinuities simulated geologic faults between two different elastic media. In addition to extending the method for the study of bodies with complete arbitrary shapes, we also test new transforms with the objective of making the related matrices more compact, which are also applied to the most general case of the method. The basic method consists of the discretization of the polynomial expansion for the boundary conditions of the 2-D problem involving the stress and strain relations for the media. This parameterization leads to a system of linear equations that should be solved for the determination of the expansion coefficients, which are the model parameters, and their determination leads to the solution of the problem. Despite the fact that the media we studied originally were 2-D bodies, the result of the application of this new method can be viewed as an approximate solution to some specific 3-D problems. Among the motivations for developing this method are possible geological applications (that is, the study of tectonic plates and geologic faults) and simulations of the elastic behaviour of materials in several other fields of science. The wavelet transform is applied with two main objectives, namely to decrease the error related to the truncation of the polynomial expansion and to make the system of linear equations more compact for computation. Having validated this method for the original 2-D elastic media, we plan that this extension to elastic bodies with complete arbitrary shapes will enable it to be even more attractive for modelling real media. Reference Rosa, J. W. C., F. A. C. M. Cardoso, K. Aki, H. S. Malvar, F. A. V. Artola, and J. W. C. Rosa, Modelling elastic media with the
NASA Astrophysics Data System (ADS)
Sui, Liansheng; Duan, Kuaikuai; Liang, Junli
2016-05-01
A secure double-image sharing scheme is proposed by using the Shamir's three-pass protocol in the discrete multiple-parameter fractional angular transform domain. First, an enlarged image is formed by assembling two plain images successively in the horizontal direction and scrambled in the chaotic permutation process, in which the sequences of chaotic pairs are generated by the two-dimensional Sine Logistic modulation map. Second, the scrambled image is divided into two components which are used to constitute a complex image. One component is normalized and regarded as the phase part of the complex image as well as other is considered as the amplitude part. Finally, the complex image is shared between the sender and the receiver by using the Shamir's three-pass protocol, in which the discrete multiple-parameter fractional angular transform is used as the encryption function due to its commutative property. The proposed double-image sharing scheme has an obvious advantage that the key management is convenient without distributing the random phase mask keys in advance. Moreover, the security of the image sharing scheme is enhanced with the help of extra parameters of the discrete multiple-parameter fractional angular transform. To the best of our knowledge, this is the first report on integrating the Shamir's three-pass protocol with double-image sharing scheme in the information security field. Simulation results and security analysis verify the feasibility and effectiveness of the proposed scheme.
Wavelet periodicity detection algorithms
NASA Astrophysics Data System (ADS)
Benedetto, John J.; Pfander, Goetz E.
1998-10-01
This paper deals with the analysis of time series with respect to certain known periodicities. In particular, we shall present a fast method aimed at detecting periodic behavior inherent in noise data. The method is composed of three steps: (1) Non-noisy data are analyzed through spectral and wavelet methods to extract specific periodic patterns of interest. (2) Using these patterns, we construct an optimal piecewise constant wavelet designed to detect the underlying periodicities. (3) We introduce a fast discretized version of the continuous wavelet transform, as well as waveletgram averaging techniques, to detect occurrence and period of these periodicities. The algorithm is formulated to provide real time implementation. Our procedure is generally applicable to detect locally periodic components in signals s which can be modeled as s(t) equals A(t)F(h(t)) + N(t) for t in I, where F is a periodic signal, A is a non-negative slowly varying function, and h is strictly increasing with h' slowly varying, N denotes background activity. For example, the method can be applied in the context of epileptic seizure detection. In this case, we try to detect seizure periodics in EEG and ECoG data. In the case of ECoG data, N is essentially 1/f noise. In the case of EEG data and for t in I,N includes noise due to cranial geometry and densities. In both cases N also includes standard low frequency rhythms. Periodicity detection has other applications including ocean wave prediction, cockpit motion sickness prediction, and minefield detection.
NASA Astrophysics Data System (ADS)
Abuturab, Muhammad Rafiq
2015-11-01
A novel gyrator wavelet transform based non-linear multiple single channel information fusion and authentication is introduced. In this technique, each user channel is normalized, phase encoded, and modulated by random phase function, and then multiplexed into a single channel user ciphertext. Now, the secret channel of corresponding user is phase encoded, modulated by random phase function, and gyrator transformed, and then multiplexed into a single channel secret ciphertext. The user ciphertext and secret ciphertext are multiplied to get a single channel multiplex image and then inverse gyrator transformed. The resultant spectrum is phase- and amplitude-truncated to obtain the encrypted image and the asymmetric key, respectively. The encrypted image is a single-level 2-D discrete wavelet transformed. The information is decomposed into LL, HL, LH, and HH sub-bands. This process is repeated to obtain three sets of four sub-bands of three different images. Next, the individual sub-band of each encrypted image is fused to get four fused sub-bands. Finally, the four fused sub-bands are inverse single-level 2-D discrete wavelet transformed to obtain final encrypted image. This is the main advantage for the proposed system: using multiple individual decryption keys (authentication key, asymmetric key, secret keys, and sub-band keys) for each user not only expands the key spaces but also supplies non-linear keys to control the system security. Moreover, the orders of gyrator transform provide extra degrees of freedom. The theoretical analysis and numerical simulation results support the proposed method.
Abuturab, Muhammad Rafiq
2015-10-01
A novel method of group multiple-image encoding and watermarking using coupled logistic maps and gyrator wavelet transform is presented. The proposed method employs three different groups of multiple images. The color images of each group are individually segregated into R, G, and B channels. Each channel is first permutated by using a sequence of chaotic pairs generated with a system of two symmetrically coupled identical logistic maps and then gyrator transformed. The gyrator spectrum of each channel is multiplied together and then modulated by a random phase function to obtain a corresponding multiplex channel. The encoded multiplex image is restituted through a concatenation of R, G, and B multiplex channels. The phase and amplitude functions of the first, second, and third groups of encoded multiplex images are generated. The host image is a single-level 2D discrete wavelet transformed to decompose into LL, HL, LH, and HH subbands. HL, LH, and HH subbands are then replaced with phase functions of the first, second, and third groups, respectively. Finally, the resultant image is an inverse single-level 2D discrete wavelet transformed to construct a watermarked image. The three groups of multiple images are protected not only by the encryption algorithm but also visually by the host image. Thus, a high level of security can be achieved. Each group includes group decryption keys, and each image of the group comprises individual decryption keys beside parameters of coupled logistic maps and gyrator transform. As a result, the key space is very large. The decryption system can be realized by using an optoelectronic device. The numerical simulation results confirm the validity and security of the proposed scheme. PMID:26479935
Visibility of wavelet quantization noise
NASA Technical Reports Server (NTRS)
Watson, A. B.; Yang, G. Y.; Solomon, J. A.; Villasenor, J.
1997-01-01
The discrete wavelet transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that we call DWT uniform quantization noise; it is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2-lambda, where r is display visual resolution in pixels/degree, and lambda is the wavelet level. Thresholds increase rapidly with wavelet spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from lowpass to horizontal/vertical to diagonal. We construct a mathematical model for DWT noise detection thresholds that is a function of level, orientation, and display visual resolution. This allows calculation of a "perceptually lossless" quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.
Wavelet Approximation in Data Assimilation
NASA Technical Reports Server (NTRS)
Tangborn, Andrew; Atlas, Robert (Technical Monitor)
2002-01-01
Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation.
Perception-based reversible watermarking for 2D vector maps
NASA Astrophysics Data System (ADS)
Men, Chaoguang; Cao, Liujuan; Li, Xiang
2010-07-01
This paper presents an effective and reversible watermarking approach for digital copyright protection of 2D-vector maps. To ensure that the embedded watermark is insensitive for human perception, we only select the noise non-sensitive regions for watermark embedding by estimating vertex density within each polyline. To ensure the exact recovery of original 2D-vector map after watermark extraction, we introduce a new reversible watermarking scheme based on reversible high-frequency wavelet coefficients modification. Within the former-selected non-sensitive regions, our watermarking operates on the lower-order vertex coordinate decimals with integer wavelet transform. Such operation further reduces the visual distortion caused by watermark embedding. We have validated the effectiveness of our scheme on our real-world city river/building 2D-vector maps. We give extensive experimental comparisons with state-of-the-art methods, including embedding capability, invisibility, and robustness over watermark attacking.
Directional spherical multipole wavelets
Hayn, Michael; Holschneider, Matthias
2009-07-15
We construct a family of admissible analysis reconstruction pairs of wavelet families on the sphere. The construction is an extension of the isotropic Poisson wavelets. Similar to those, the directional wavelets allow a finite expansion in terms of off-center multipoles. Unlike the isotropic case, the directional wavelets are not a tight frame. However, at small scales, they almost behave like a tight frame. We give an explicit formula for the pseudodifferential operator given by the combination analysis-synthesis with respect to these wavelets. The Euclidean limit is shown to exist and an explicit formula is given. This allows us to quantify the asymptotic angular resolution of the wavelets.
Optimal wavelet denoising for smart biomonitor systems
NASA Astrophysics Data System (ADS)
Messer, Sheila R.; Agzarian, John; Abbott, Derek
2001-03-01
Future smart-systems promise many benefits for biomedical diagnostics. The ideal is for simple portable systems that display and interpret information from smart integrated probes or MEMS-based devices. In this paper, we will discuss a step towards this vision with a heart bio-monitor case study. An electronic stethoscope is used to record heart sounds and the problem of extracting noise from the signal is addressed via the use of wavelets and averaging. In our example of heartbeat analysis, phonocardiograms (PCGs) have many advantages in that they may be replayed and analysed for spectral and frequency information. Many sources of noise may pollute a PCG including foetal breath sounds if the subject is pregnant, lung and breath sounds, environmental noise and noise from contact between the recording device and the skin. Wavelets can be employed to denoise the PCG. The signal is decomposed by a discrete wavelet transform. Due to the efficient decomposition of heart signals, their wavelet coefficients tend to be much larger than those due to noise. Thus, coefficients below a certain level are regarded as noise and are thresholded out. The signal can then be reconstructed without significant loss of information in the signal. The questions that this study attempts to answer are which wavelet families, levels of decomposition, and thresholding techniques best remove the noise in a PCG. The use of averaging in combination with wavelet denoising is also addressed. Possible applications of the Hilbert Transform to heart sound analysis are discussed.
Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's
NASA Technical Reports Server (NTRS)
Cai, Wei; Wang, Jian-Zhong
1993-01-01
We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.
NASA Astrophysics Data System (ADS)
Jones, B. J. T.
Wavelet analysis has become a major tool in many aspects of data handling, whether it be statistical analysis, noise removal or image reconstruction. Wavelet analysis has worked its way into fields as diverse as economics, medicine, geophysics, music and cosmology.
Fryer, M.O.
1997-05-01
This paper describes the use of wavelet transform techniques to analyze typical data found in industrial applications. A way of detecting system changes using wavelet transforms is described. The results of applying this method are described for several typical applications. The wavelet technique is compared with the use of Fourier transform methods.
Szu, H.; Hsu, C.
1996-12-31
Human sensors systems (HSS) may be approximately described as an adaptive or self-learning version of the Wavelet Transforms (WT) that are capable to learn from several input-output associative pairs of suitable transform mother wavelets. Such an Adaptive WT (AWT) is a redundant combination of mother wavelets to either represent or classify inputs.
Frequency Domain Modelling by a Direct-Iterative Solver: A Space and Wavelet Approach
NASA Astrophysics Data System (ADS)
Hustedt, B.; Operto, S.; Virieux, J.
2002-12-01
Seismic forward modelling of wave propagation phenomena in complex rheologic media using a frequency domain finite-difference (FDFD) technique is of special interest for multisource experiments and waveform inversion schemes, because the complete wavefield solution can be computed in a fast and efficient way. FDFD modelling requires the inversion of an extremely large matrix-equation A x x = b, by either a direct or an iterative solver. The direct solver computes an effective inverse of A, called LU factorization. The main handicap is additional computer memory required for storing matrix fill-in coefficients, that are created during the factorization process. Iterative solvers are not limited by memory constraints (additional coefficients), but the convergence depends on a good initial solution difficult to guess before hand. For both solvers, available computer resources has limited wide-spread FDFD modelling applications to mainly two-dimensional (2D) and rarely three-dimensional (3D) problems. In order to overcome these limits, we propose the combination of a direct solver and an iterative solver, called Direct-Iterative Solver (DIS). The direct solver is used to compute an exact wavefield solution on a coarse discretized grid. We use a multifrontal decomposition technique. The coarse-grid size is determined preliminary by limits of the available computer resources, rather than by the wave simulation problem. We project the exact coarse-grid solution on a fine-grid, and use it as an initial solution for an iterative solver, which convergences to an acceptable approximation of the desired fine-grid solution. Two different DIS schemes have been implemented and tested for numerical accuracy and computational performance. The first approach, called the Direct-Iterative-Space Solver (DISS), projects the coarse-grid solution on the fine-grid by a bilinear interpolation. Though the interpolated solution nicely approximates the desired fine-grid solution, still for
Greg Flach, Frank Smith
2011-12-31
Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j0) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assigns an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations.
Energy Science and Technology Software Center (ESTSC)
2011-12-31
Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j0) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assignsmore » an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations.« less
Visibility of Wavelet Quantization Noise
NASA Technical Reports Server (NTRS)
Watson, Andrew B.; Yang, Gloria Y.; Solomon, Joshua A.; Villasenor, John; Null, Cynthia H. (Technical Monitor)
1995-01-01
The Discrete Wavelet Transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter, which we call DWT uniform quantization noise. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2(exp)-L , where r is display visual resolution in pixels/degree, and L is the wavelet level. Amplitude thresholds increase rapidly with spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from low-pass to horizontal/vertical to diagonal. We describe a mathematical model to predict DWT noise detection thresholds as a function of level, orientation, and display visual resolution. This allows calculation of a "perceptually lossless" quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.
NASA Astrophysics Data System (ADS)
Lotsch, Bettina V.
2015-07-01
Graphene's legacy has become an integral part of today's condensed matter science and has equipped a whole generation of scientists with an armory of concepts and techniques that open up new perspectives for the postgraphene area. In particular, the judicious combination of 2D building blocks into vertical heterostructures has recently been identified as a promising route to rationally engineer complex multilayer systems and artificial solids with intriguing properties. The present review highlights recent developments in the rapidly emerging field of 2D nanoarchitectonics from a materials chemistry perspective, with a focus on the types of heterostructures available, their assembly strategies, and their emerging properties. This overview is intended to bridge the gap between two major—yet largely disjunct—developments in 2D heterostructures, which are firmly rooted in solid-state chemistry or physics. Although the underlying types of heterostructures differ with respect to their dimensions, layer alignment, and interfacial quality, there is common ground, and future synergies between the various assembly strategies are to be expected.
[An improved wavelet threshold algorithm for ECG denoising].
Liu, Xiuling; Qiao, Lei; Yang, Jianli; Dong, Bin; Wang, Hongrui
2014-06-01
Due to the characteristics and environmental factors, electrocardiogram (ECG) signals are usually interfered by noises in the course of signal acquisition, so it is crucial for ECG intelligent analysis to eliminate noises in ECG signals. On the basis of wavelet transform, threshold parameters were improved and a more appropriate threshold expression was proposed. The discrete wavelet coefficients were processed using the improved threshold parameters, the accurate wavelet coefficients without noises were gained through inverse discrete wavelet transform, and then more original signal coefficients could be preserved. MIT-BIH arrythmia database was used to validate the method. Simulation results showed that the improved method could achieve better denoising effect than the traditional ones. PMID:25219225
Symplectic wavelet transformation.
Fan, Hong-Yi; Lu, Hai-Liang
2006-12-01
Usually a wavelet transform is based on dilated-translated wavelets. We propose a symplectic-transformed-translated wavelet family psi(*)(r,s)(z-kappa) (r,s are the symplectic transform parameters, |s|(2)-|r|(2)=1, kappa is a translation parameter) generated from the mother wavelet psi and the corresponding wavelet transformation W(psi)f(r,s;kappa)=integral(infinity)(-infinity)(d(2)z/pi)f(z)psi(*)(r,s)(z-kappa). This new transform possesses well-behaved properties and is related to the optical Fresnel transform in quantum mechanical version. PMID:17099740
Wavelet-assisted volume ray casting.
He, T
1998-01-01
Volume rendering is an important technique for computational biology. In this paper we propose a new wavelet-assisted volume ray casting algorithm. The main idea is to use the wavelet coefficients for detecting the local frequency, and decide the appropriate sampling rate along the ray according to the maximum frequency. Our algorithm is to first apply the 3D discrete wavelet transform on the volume, then create an index volume to indicate the necessary sampling distance at each voxel. During ray casting, the original volume is traversed in the spatial domain, while the index volume is used to decide the appropriate sampling distance. We demonstrate that our algorithm provides a framework for approximating the volume rendering at different levels of quality in a rapid and controlled way. PMID:9697179
NASA Technical Reports Server (NTRS)
Baxes, Gregory A. (Inventor); Linger, Timothy C. (Inventor)
2011-01-01
Systems and methods are provided for progressive mesh storage and reconstruction using wavelet-encoded height fields. A method for progressive mesh storage includes reading raster height field data, and processing the raster height field data with a discrete wavelet transform to generate wavelet-encoded height fields. In another embodiment, a method for progressive mesh storage includes reading texture map data, and processing the texture map data with a discrete wavelet transform to generate wavelet-encoded texture map fields. A method for reconstructing a progressive mesh from wavelet-encoded height field data includes determining terrain blocks, and a level of detail required for each terrain block, based upon a viewpoint. Triangle strip constructs are generated from vertices of the terrain blocks, and an image is rendered utilizing the triangle strip constructs. Software products that implement these methods are provided.
NASA Technical Reports Server (NTRS)
Baxes, Gregory A. (Inventor)
2010-01-01
Systems and methods are provided for progressive mesh storage and reconstruction using wavelet-encoded height fields. A method for progressive mesh storage includes reading raster height field data, and processing the raster height field data with a discrete wavelet transform to generate wavelet-encoded height fields. In another embodiment, a method for progressive mesh storage includes reading texture map data, and processing the texture map data with a discrete wavelet transform to generate wavelet-encoded texture map fields. A method for reconstructing a progressive mesh from wavelet-encoded height field data includes determining terrain blocks, and a level of detail required for each terrain block, based upon a viewpoint. Triangle strip constructs are generated from vertices of the terrain blocks, and an image is rendered utilizing the triangle strip constructs. Software products that implement these methods are provided.
Multiresolution local tomography in dental radiology using wavelets.
Niinimäki, K; Siltanen, S; Kolehmainen, V
2007-01-01
A Bayesian multiresolution model for local tomography in dental radiology is proposed. In this model a wavelet basis is used to present dental structures and the prior information is modeled in terms of Besov norm penalty. The proposed wavelet-based multiresolution method is used to reduce the number of unknowns in the reconstruction problem by abandoning fine-scale wavelets outside the region of interest (ROI). This multiresolution model allows significant reduction in the number of unknowns without the loss of reconstruction accuracy inside the ROI. The feasibility of the proposed method is tested with two-dimensional (2D) examples using simulated and experimental projection data from dental specimens. PMID:18002604
Dependence and risk assessment for oil prices and exchange rate portfolios: A wavelet based approach
NASA Astrophysics Data System (ADS)
Aloui, Chaker; Jammazi, Rania
2015-10-01
In this article, we propose a wavelet-based approach to accommodate the stylized facts and complex structure of financial data, caused by frequent and abrupt changes of markets and noises. Specifically, we show how the combination of both continuous and discrete wavelet transforms with traditional financial models helps improve portfolio's market risk assessment. In the empirical stage, three wavelet-based models (wavelet-EGARCH with dynamic conditional correlations, wavelet-copula, and wavelet-extreme value) are considered and applied to crude oil price and US dollar exchange rate data. Our findings show that the wavelet-based approach provides an effective and powerful tool for detecting extreme moments and improving the accuracy of VaR and Expected Shortfall estimates of oil-exchange rate portfolios after noise is removed from the original data.
Wavelet based free-form deformations for nonrigid registration
NASA Astrophysics Data System (ADS)
Sun, Wei; Niessen, Wiro J.; Klein, Stefan
2014-03-01
In nonrigid registration, deformations may take place on the coarse and fine scales. For the conventional B-splines based free-form deformation (FFD) registration, these coarse- and fine-scale deformations are all represented by basis functions of a single scale. Meanwhile, wavelets have been proposed as a signal representation suitable for multi-scale problems. Wavelet analysis leads to a unique decomposition of a signal into its coarse- and fine-scale components. Potentially, this could therefore be useful for image registration. In this work, we investigate whether a wavelet-based FFD model has advantages for nonrigid image registration. We use a B-splines based wavelet, as defined by Cai and Wang.1 This wavelet is expressed as a linear combination of B-spline basis functions. Derived from the original B-spline function, this wavelet is smooth, differentiable, and compactly supported. The basis functions of this wavelet are orthogonal across scales in Sobolev space. This wavelet was previously used for registration in computer vision, in 2D optical flow problems,2 but it was not compared with the conventional B-spline FFD in medical image registration problems. An advantage of choosing this B-splines based wavelet model is that the space of allowable deformation is exactly equivalent to that of the traditional B-spline. The wavelet transformation is essentially a (linear) reparameterization of the B-spline transformation model. Experiments on 10 CT lung and 18 T1-weighted MRI brain datasets show that wavelet based registration leads to smoother deformation fields than traditional B-splines based registration, while achieving better accuracy.
Bieleck, T.; Song, L.M.; Yau, S.S.T.; Kwong, M.K.
1995-07-01
The concepts of random wavelet transforms and discrete random wavelet transforms are introduced. It is shown that these transforms can lead to simultaneous compression and de-noising of signals that have been corrupted with fractional noises. Potential applications of algebraic geometric coding theory to encode the ensuing data are also discussed.
Nonstationary Dynamics Data Analysis with Wavelet-SVD Filtering
NASA Technical Reports Server (NTRS)
Brenner, Marty; Groutage, Dale; Bessette, Denis (Technical Monitor)
2001-01-01
Nonstationary time-frequency analysis is used for identification and classification of aeroelastic and aeroservoelastic dynamics. Time-frequency multiscale wavelet processing generates discrete energy density distributions. The distributions are processed using the singular value decomposition (SVD). Discrete density functions derived from the SVD generate moments that detect the principal features in the data. The SVD standard basis vectors are applied and then compared with a transformed-SVD, or TSVD, which reduces the number of features into more compact energy density concentrations. Finally, from the feature extraction, wavelet-based modal parameter estimation is applied.
Manchanda, P.; Meenakshi
2009-07-02
Recently Manchanda, Meenakshi and Siddiqi have studied Haar-Vilenkin wavelet and a special type of non-uniform multiresolution analysis. Haar-Vilenkin wavelet is a generalization of Haar wavelet. Motivated by the paper of Gabardo and Nashed we have introduced a class of multiresolution analysis extending the concept of classical multiresolution analysis. We present here a resume of these results. We hope that applications of these concepts to some significant real world problems could be found.
A 2-D orientation-adaptive prediction filter in lifting structures for image coding.
Gerek, Omer N; Cetin, A Enis
2006-01-01
Lifting-style implementations of wavelets are widely used in image coders. A two-dimensional (2-D) edge adaptive lifting structure, which is similar to Daubechies 5/3 wavelet, is presented. The 2-D prediction filter predicts the value of the next polyphase component according to an edge orientation estimator of the image. Consequently, the prediction domain is allowed to rotate +/-45 degrees in regions with diagonal gradient. The gradient estimator is computationally inexpensive with additional costs of only six subtractions per lifting instruction, and no multiplications are required. PMID:16435541
Characterization and simulation of gunfire with wavelets
Smallwood, D.O.
1998-09-01
Gunfire is used as an example to show how the wavelet transform can be used to characterize and simulate nonstationary random events when an ensemble of events is available. The response of a structure to nearby firing of a high-firing rate gun has been characterized in several ways as a nonstationary random process. The methods all used some form of the discrete fourier transform. The current paper will explore a simpler method to describe the nonstationary random process in terms of a wavelet transform. As was done previously, the gunfire record is broken up into a sequence of transient waveforms each representing the response to the firing of a single round. The wavelet transform is performed on each of these records. The mean and standard deviation of the resulting wavelet coefficients describe the composite characteristics of the entire waveform. It is shown that the distribution of the wavelet coefficients is approximately Gaussian with a nonzero mean and that the standard deviation of the coefficients at different times and levels are approximately independent. The gunfire is simulated by generating realizations of records of a single-round firing by computing the inverse wavelet transform from Gaussian random coefficients with the same mean and standard deviation as those estimated from the previously discussed gunfire record. The individual realizations are then assembled into a realization of a time history of many rounds firing. A second-order correction of the probability density function (pdf) is accomplished with a zero memory nonlinear (ZMNL) function. The method is straightforward, easy to implement, and produces a simulated record very much like the original measured gunfire record.
Wavelet Analyses and Applications
ERIC Educational Resources Information Center
Bordeianu, Cristian C.; Landau, Rubin H.; Paez, Manuel J.
2009-01-01
It is shown how a modern extension of Fourier analysis known as wavelet analysis is applied to signals containing multiscale information. First, a continuous wavelet transform is used to analyse the spectrum of a nonstationary signal (one whose form changes in time). The spectral analysis of such a signal gives the strength of the signal in each…
Three-dimensional compression scheme based on wavelet transform
NASA Astrophysics Data System (ADS)
Yang, Wu; Xu, Hui; Liao, Mengyang
1999-03-01
In this paper, a 3D compression method based on separable wavelet transform is discussed in detail. The most commonly used digital modalities generate multiple slices in a single examination, which are normally anatomically or physiologically correlated to each other. 3D wavelet compression methods can achieve more efficient compression by exploring the correlation between slices. The first step is based on a separable 3D wavelet transform. Considering the difference between pixel distances within a slice and those between slices, one biorthogonal Antoninin filter bank is applied within 2D slices and a second biorthogonal Villa4 filter bank on the slice direction. Then, S+P transform is applied in the low-resolution wavelet components and an optimal quantizer is presented after analysis of the quantization noise. We use an optimal bit allocation algorithm, which, instead of eliminating the coefficients of high-resolution components in smooth areas, minimizes the system reconstruction distortion at a given bit-rate. Finally, to remain high coding efficiency and adapt to different properties of each component, a comprehensive entropy coding method is proposed, in which arithmetic coding method is applied in high-resolution components and adaptive Huffman coding method in low-resolution components. Our experimental results are evaluated by several image measures and our 3D wavelet compression scheme is proved to be more efficient than 2D wavelet compression.
The use of wavelet transformations in the solution of two-phase flow problems
Moridis, G.J.; Nikolaou, M.; You, Y.
1995-12-31
In this paper the authors present the use of wavelets to solve the non-linear Partial Differential Equation (PDE) of two-phase flow in one dimension. The wavelet transforms allow a drastically different approach in the discretization of space. In contrast to the traditional trigonometric basis functions, wavelets approximate a function not by cancellation but by placement of wavelets at appropriate locations. When an abrupt change, such as a shock wave or a spike, occurs in a function, only local coefficients in a wavelet approximation will be affected. The unique feature of wavelets is their Multi-Resolution Analysis (MRA) property, which allows seamless investigation at nay spatial resolution. The use of wavelets is tested in the solution of the one-dimensional Buckley-Leverett problem against analytical solutions and solutions obtained from standard numerical models. Two classes of wavelet bases (Daubechies and Chui-Wang) and two methods (Galerkin and collocation) are investigated. The authors determine that the Chui-Wang wavelets and a collection method provide the optimum wavelet solution for this type of problem. Increasing the resolution level improves the accuracy of the solution, but the order of the basis function seems to be far less important. The results indicate that wavelet transforms are an effective and accurate method which does not suffer from oscillations or numerical smearing in the presence of steep fronts.
The use of wavelet transforms in the solution of two-phase flow problems
Moridis, G.J.; Nikolaou, M.; You, Yong
1994-10-01
In this paper we present the use of wavelets to solve the nonlinear Partial Differential.Equation (PDE) of two-phase flow in one dimension. The wavelet transforms allow a drastically different approach in the discretization of space. In contrast to the traditional trigonometric basis functions, wavelets approximate a function not by cancellation but by placement of wavelets at appropriate locations. When an abrupt chance, such as a shock wave or a spike, occurs in a function, only local coefficients in a wavelet approximation will be affected. The unique feature of wavelets is their Multi-Resolution Analysis (MRA) property, which allows seamless investigational any spatial resolution. The use of wavelets is tested in the solution of the one-dimensional Buckley-Leverett problem against analytical solutions and solutions obtained from standard numerical models. Two classes of wavelet bases (Daubechies and Chui-Wang) and two methods (Galerkin and collocation) are investigated. We determine that the Chui-Wang, wavelets and a collocation method provide the optimum wavelet solution for this type of problem. Increasing the resolution level improves the accuracy of the solution, but the order of the basis function seems to be far less important. Our results indicate that wavelet transforms are an effective and accurate method which does not suffer from oscillations or numerical smearing in the presence of steep fronts.
Source Wavelet Phase Extraction
NASA Astrophysics Data System (ADS)
Naghadeh, Diako Hariri; Morley, Christopher Keith
2016-06-01
Extraction of propagation wavelet phase from seismic data can be conducted using first, second, third and fourth-order statistics. Three new methods are introduced, which are: (1) Combination of different moments, (2) Windowed continuous wavelet transform and (3) Maximum correlation with cosine function. To compare different methods synthetic data with and without noise were chosen. Results show that first, second and third order statistics are not able to preserve wavelet phase. Kurtosis can preserve propagation wavelet phase but signal-to-noise ratio can affect the extracted phase using this method. So for data set with low signal-to-noise ratio, it will be unstable. Using a combination of different moments to extract the phase is more robust than applying kurtosis. The improvement occurs because zero phase wavelets with reverse polarities have equal maximum kurtosis values hence the correct wavelet polarity cannot be identified. Zero-phase wavelets with reverse polarities have minimum and maximum values for a combination of different-moments method. These properties enable the technique to handle a finite data segment and to choose the correct wavelet polarity. Also, the existence of different moments can decrease sensitivity to outliers. A windowed continuous wavelet transform is more sensitive to signal-to-noise ratio than the combination of different-moments method, also if the scale for the wavelet is incorrect it will encounter with more problems to extract phase. When the effects of frequency bandwidth, signal-to-noise ratio and analyzing window length are considered, the results of extracting phase information from data without and with noise demonstrate that combination of different-moments is superior to the other methods introduced here.
Directional wavelet based features for colonic polyp classification.
Wimmer, Georg; Tamaki, Toru; Tischendorf, J J W; Häfner, Michael; Yoshida, Shigeto; Tanaka, Shinji; Uhl, Andreas
2016-07-01
In this work, various wavelet based methods like the discrete wavelet transform, the dual-tree complex wavelet transform, the Gabor wavelet transform, curvelets, contourlets and shearlets are applied for the automated classification of colonic polyps. The methods are tested on 8 HD-endoscopic image databases, where each database is acquired using different imaging modalities (Pentax's i-Scan technology combined with or without staining the mucosa), 2 NBI high-magnification databases and one database with chromoscopy high-magnification images. To evaluate the suitability of the wavelet based methods with respect to the classification of colonic polyps, the classification performances of 3 wavelet transforms and the more recent curvelets, contourlets and shearlets are compared using a common framework. Wavelet transforms were already often and successfully applied to the classification of colonic polyps, whereas curvelets, contourlets and shearlets have not been used for this purpose so far. We apply different feature extraction techniques to extract the information of the subbands of the wavelet based methods. Most of the in total 25 approaches were already published in different texture classification contexts. Thus, the aim is also to assess and compare their classification performance using a common framework. Three of the 25 approaches are novel. These three approaches extract Weibull features from the subbands of curvelets, contourlets and shearlets. Additionally, 5 state-of-the-art non wavelet based methods are applied to our databases so that we can compare their results with those of the wavelet based methods. It turned out that extracting Weibull distribution parameters from the subband coefficients generally leads to high classification results, especially for the dual-tree complex wavelet transform, the Gabor wavelet transform and the Shearlet transform. These three wavelet based transforms in combination with Weibull features even outperform the state
Wavelet transformation based watermarking technique for human electrocardiogram (ECG).
Engin, Mehmet; Cidam, Oğuz; Engin, Erkan Zeki
2005-12-01
Nowadays, watermarking has become a technology of choice for a broad range of multimedia copyright protection applications. Watermarks have also been used to embed prespecified data in biomedical signals. Thus, the watermarked biomedical signals being transmitted through communication are resistant to some attacks. This paper investigates discrete wavelet transform based watermarking technique for signal integrity verification in an Electrocardiogram (ECG) coming from four ECG classes for monitoring application of cardiovascular diseases. The proposed technique is evaluated under different noisy conditions for different wavelet functions. Daubechies (db2) wavelet function based technique performs better than those of Biorthogonal (bior5.5) wavelet function. For the beat-to-beat applications, all performance results belonging to four ECG classes are highly moderate. PMID:16235811
Wavelet analysis of electric adjustable speed drive waveforms
Czarkowski, D.; Domijan, A. Jr.
1998-10-01
The three most common adjustable speed drives (ASDs) used in HVAC equipment, namely, pulse-width modulated (PWM) induction drive, brushless-dc drive, and switched-reluctance drive, generate non-periodic and nonstationary electric waveforms with sharp edges and transients. Deficiencies of Fourier transform methods in analysis of such ASD waveforms prompted an application of the wavelet transform. Results of discrete wavelet transform (DWT) analysis of PWM inverter-fed motor waveforms are presented. The best mother wavelet for analysis of the recorded waveforms is selected. Data compression properties of the selected mother wavelet are compared to those of the fast Fourier transform (FFT). Multilevel feature detection of ASD waveforms using the DWT is shown.
Application of wavelet transforms to reservoir data analysis and scaling
Panda, M.N.; Mosher, C.; Chopra, A.K.
1996-12-31
General characterization of physical systems uses two aspects of data analysis methods: decomposition of empirical data to determine model parameters and reconstruction of the image using these characteristic parameters. Spectral methods, involving a frequency based representation of data, usually assume stationarity. These methods, therefore, extract only the average information and hence are not suitable for analyzing data with isolated or deterministic discontinuities, such as faults or fractures in reservoir rocks or image edges in computer vision. Wavelet transforms provide a multiresolution framework for data representation. They are a family of orthogonal basis functions that separate a function or a signal into distinct frequency packets that are localized in the time domain. Thus, wavelets are well suited for analyzing non-stationary data. In other words, a projection of a function or a discrete data set onto a time-frequency space using wavelets shows how the function behaves at different scales of measurement. Because wavelets have compact support, it is easy to apply this transform to large data sets with minimal computations. We apply the wavelet transforms to one-dimensional and two-dimensional permeability data to determine the locations of layer boundaries and other discontinuities. By binning in the time-frequency plane with wavelet packets, permeability structures of arbitrary size are analyzed. We also apply orthogonal wavelets for scaling up of spatially correlated heterogeneous permeability fields.
Semi-orthogonal wavelets for elliptic variational problems
Hardin, D.P.; Roach, D.W.
1998-04-01
In this paper the authors give a construction of wavelets which are (a) semi-orthogonal with respect to an arbitrary elliptic bilinear form a({center_dot},{center_dot}) on the Sobolev space H{sub 0}{sup 1}((0, L)) and (b) continuous and piecewise linear on an arbitrary partition of [0, L]. They illustrate this construction using a model problem. They also construct alpha-orthogonal Battle-Lemarie type wavelets which fully diagonalize the Galerkin discretized matrix for the model problem with domain IR. Finally they describe a hybrid basis consisting of a combination of elements from the semi-orthogonal wavelet basis and the hierarchical Schauder basis. Numerical experiments indicate that this basis leads to robust scalable Galerkin discretizations of the model problem which remain well-conditioned independent of {epsilon}, L, and the refinement level K.
NASA Astrophysics Data System (ADS)
Ng, J.; Kingsbury, N. G.
2004-02-01
This book provides an overview of the theory and practice of continuous and discrete wavelet transforms. Divided into seven chapters, the first three chapters of the book are introductory, describing the various forms of the wavelet transform and their computation, while the remaining chapters are devoted to applications in fluids, engineering, medicine and miscellaneous areas. Each chapter is well introduced, with suitable examples to demonstrate key concepts. Illustrations are included where appropriate, thus adding a visual dimension to the text. A noteworthy feature is the inclusion, at the end of each chapter, of a list of further resources from the academic literature which the interested reader can consult. The first chapter is purely an introduction to the text. The treatment of wavelet transforms begins in the second chapter, with the definition of what a wavelet is. The chapter continues by defining the continuous wavelet transform and its inverse and a description of how it may be used to interrogate signals. The continuous wavelet transform is then compared to the short-time Fourier transform. Energy and power spectra with respect to scale are also discussed and linked to their frequency counterparts. Towards the end of the chapter, the two-dimensional continuous wavelet transform is introduced. Examples of how the continuous wavelet transform is computed using the Mexican hat and Morlet wavelets are provided throughout. The third chapter introduces the discrete wavelet transform, with its distinction from the discretized continuous wavelet transform having been made clear at the end of the second chapter. In the first half of the chapter, the logarithmic discretization of the wavelet function is described, leading to a discussion of dyadic grid scaling, frames, orthogonal and orthonormal bases, scaling functions and multiresolution representation. The fast wavelet transform is introduced and its computation is illustrated with an example using the Haar
Multispectral multisensor image fusion using wavelet transforms
Lemeshewsky, George P.
1999-01-01
Fusion techniques can be applied to multispectral and higher spatial resolution panchromatic images to create a composite image that is easier to interpret than the individual images. Wavelet transform-based multisensor, multiresolution fusion (a type of band sharpening) was applied to Landsat thematic mapper (TM) multispectral and coregistered higher resolution SPOT panchromatic images. The objective was to obtain increased spatial resolution, false color composite products to support the interpretation of land cover types wherein the spectral characteristics of the imagery are preserved to provide the spectral clues needed for interpretation. Since the fusion process should not introduce artifacts, a shift invariant implementation of the discrete wavelet transform (SIDWT) was used. These results were compared with those using the shift variant, discrete wavelet transform (DWT). Overall, the process includes a hue, saturation, and value color space transform to minimize color changes, and a reported point-wise maximum selection rule to combine transform coefficients. The performance of fusion based on the SIDWT and DWT was evaluated with a simulated TM 30-m spatial resolution test image and a higher resolution reference. Simulated imagery was made by blurring higher resolution color-infrared photography with the TM sensors' point spread function. The SIDWT based technique produced imagery with fewer artifacts and lower error between fused images and the full resolution reference. Image examples with TM and SPOT 10-m panchromatic illustrate the reduction in artifacts due to the SIDWT based fusion.
NASA Astrophysics Data System (ADS)
Wang, Jin; Ma, Jianyong; Zhou, Changhe
2014-11-01
A 3×3 high divergent 2D-grating with period of 3.842μm at wavelength of 850nm under normal incidence is designed and fabricated in this paper. This high divergent 2D-grating is designed by the vector theory. The Rigorous Coupled Wave Analysis (RCWA) in association with the simulated annealing (SA) is adopted to calculate and optimize this 2D-grating.The properties of this grating are also investigated by the RCWA. The diffraction angles are more than 10 degrees in the whole wavelength band, which are bigger than the traditional 2D-grating. In addition, the small period of grating increases the difficulties of fabrication. So we fabricate the 2D-gratings by direct laser writing (DLW) instead of traditional manufacturing method. Then the method of ICP etching is used to obtain the high divergent 2D-grating.
An Explicitly Correlated Wavelet Method for the Electronic Schroedinger Equation
Bachmayr, Markus
2010-09-30
A discretization for an explicitly correlated formulation of the electronic Schroedinger equation based on hyperbolic wavelets and exponential sum approximations of potentials is described, covering mathematical results as well as algorithmic realization, and discussing in particular the potential of methods of this type for parallel computing.
3D Wavelet-Based Filter and Method
Moss, William C.; Haase, Sebastian; Sedat, John W.
2008-08-12
A 3D wavelet-based filter for visualizing and locating structural features of a user-specified linear size in 2D or 3D image data. The only input parameter is a characteristic linear size of the feature of interest, and the filter output contains only those regions that are correlated with the characteristic size, thus denoising the image.
Implemented Wavelet Packet Tree based Denoising Algorithm in Bus Signals of a Wearable Sensorarray
NASA Astrophysics Data System (ADS)
Schimmack, M.; Nguyen, S.; Mercorelli, P.
2015-11-01
This paper introduces a thermosensing embedded system with a sensor bus that uses wavelets for the purposes of noise location and denoising. From the principle of the filter bank the measured signal is separated in two bands, low and high frequency. The proposed algorithm identifies the defined noise in these two bands. With the Wavelet Packet Transform as a method of Discrete Wavelet Transform, it is able to decompose and reconstruct bus input signals of a sensor network. Using a seminorm, the noise of a sequence can be detected and located, so that the wavelet basis can be rearranged. This particularly allows for elimination of any incoherent parts that make up unavoidable measuring noise of bus signals. The proposed method was built based on wavelet algorithms from the WaveLab 850 library of the Stanford University (USA). This work gives an insight to the workings of Wavelet Transformation.
Periodized Daubechies wavelets
Restrepo, J.M.; Leaf, G.K.; Schlossnagle, G.
1996-03-01
The properties of periodized Daubechies wavelets on [0,1] are detailed and counterparts which form a basis for L{sup 2}(R). Numerical examples illustrate the analytical estimates for convergence and demonstrated by comparison with Fourier spectral methods the superiority of wavelet projection methods for approximations. The analytical solution to inner products of periodized wavelets and their derivatives, which are known as connection coefficients, is presented, and their use ius illustrated in the approximation of two commonly used differential operators. The periodization of the connection coefficients in Galerkin schemes is presented in detail.
MAGNUM-2D computer code: user's guide
England, R.L.; Kline, N.W.; Ekblad, K.J.; Baca, R.G.
1985-01-01
Information relevant to the general use of the MAGNUM-2D computer code is presented. This computer code was developed for the purpose of modeling (i.e., simulating) the thermal and hydraulic conditions in the vicinity of a waste package emplaced in a deep geologic repository. The MAGNUM-2D computer computes (1) the temperature field surrounding the waste package as a function of the heat generation rate of the nuclear waste and thermal properties of the basalt and (2) the hydraulic head distribution and associated groundwater flow fields as a function of the temperature gradients and hydraulic properties of the basalt. MAGNUM-2D is a two-dimensional numerical model for transient or steady-state analysis of coupled heat transfer and groundwater flow in a fractured porous medium. The governing equations consist of a set of coupled, quasi-linear partial differential equations that are solved using a Galerkin finite-element technique. A Newton-Raphson algorithm is embedded in the Galerkin functional to formulate the problem in terms of the incremental changes in the dependent variables. Both triangular and quadrilateral finite elements are used to represent the continuum portions of the spatial domain. Line elements may be used to represent discrete conduits. 18 refs., 4 figs., 1 tab.
NASA Technical Reports Server (NTRS)
Kempel, Leo C.
1992-01-01
Wavelets are an exciting new topic in applied mathematics and signal processing. This paper will provide a brief review of wavelets which are also known as families of functions with an emphasis on interpretation rather than rigor. We will derive an indirect use of wavelets for the solution of integral equations based techniques adapted from image processing. Examples for resistive strips will be given illustrating the effect of these techniques as well as their promise in reducing dramatically the requirement in order to solve an integral equation for large bodies. We also will present a direct implementation of wavelets to solve an integral equation. Both methods suggest future research topics and may hold promise for a variety of uses in computational electromagnetics.
Yun, Jong Pil; Jeon, Yong-Ju; Choi, Doo-chul; Kim, Sang Woo
2012-05-01
We propose a new defect detection algorithm for scale-covered steel wire rods. The algorithm incorporates an adaptive wavelet filter that is designed on the basis of lattice parameterization of orthogonal wavelet bases. This approach offers the opportunity to design orthogonal wavelet filters via optimization methods. To improve the performance and the flexibility of wavelet design, we propose the use of the undecimated discrete wavelet transform, and separate design of column and row wavelet filters but with a common cost function. The coefficients of the wavelet filters are optimized by the so-called univariate dynamic encoding algorithm for searches (uDEAS), which searches the minimum value of a cost function designed to maximize the energy difference between defects and background noise. Moreover, for improved detection accuracy, we propose an enhanced double-threshold method. Experimental results for steel wire rod surface images obtained from actual steel production lines show that the proposed algorithm is effective. PMID:22561939
The discrete Kalman filtering approach for seismic signals deconvolution
Kurniadi, Rizal; Nurhandoko, Bagus Endar B.
2012-06-20
Seismic signals are a convolution of reflectivity and seismic wavelet. One of the most important stages in seismic data processing is deconvolution process; the process of deconvolution is inverse filters based on Wiener filter theory. This theory is limited by certain modelling assumptions, which may not always valid. The discrete form of the Kalman filter is then used to generate an estimate of the reflectivity function. The main advantage of Kalman filtering is capability of technique to handling continually time varying models and has high resolution capabilities. In this work, we use discrete Kalman filter that it was combined with primitive deconvolution. Filtering process works on reflectivity function, hence the work flow of filtering is started with primitive deconvolution using inverse of wavelet. The seismic signals then are obtained by convoluting of filtered reflectivity function with energy waveform which is referred to as the seismic wavelet. The higher frequency of wavelet gives smaller wave length, the graphs of these results are presented.
Classification of mammographic microcalcifications using wavelets
NASA Astrophysics Data System (ADS)
Chitre, Yateen S.; Dhawan, Atam P.; Moskowitz, Myron; Sarwal, Alok; Bonasso, Christine; Narayan, Suresh B.
1995-05-01
Breast cancer is the leading cause of death among women. Breast cancer can be detected earlier by mammography than any other non-invasive examination. About 30% to 50% of breast cancers demonstrate tiny granulelike deposits of calcium called microcalcifications. It is difficult to distinguish between benign and malignant cases based on an examination of calcification regions, especially in hard-to-diagnose cases. We investigate the potential of using energy and entropy features computed from wavelet packets for their correlation with malignancy. Two types of Daubechies discrete filters were used as prototype wavelets. The energy and entropy features were computed for 128 benign and 63 malignant cases and analyzed using a multivariate cluster analysis and a univariate statistical analysis to reduce the feature set to a `five best set of features.' The efficacy of the reduced feature set to discriminate between the malignant and benign categories was evaluated using different multilayer perceptron architectures. The multilayer perceptron was trained using the backpropagation algorithm for various training and test set sizes. For each case 40 partitions of the data set were used to set up the training and test sets. The performance of the features was evaluated by computing the best area under the relative operating characteristic (ROC) curve and the average area under the ROC curve. The performance of the features computed from the wavelet packets was compared to a second set of features consisting of the wavelet packet features, image structure features and cluster features. The classification results are encouraging and indicate the potential of using features derived from wavelet packets in discriminating microcalcification regions into benign and malignant categories.
NASA Astrophysics Data System (ADS)
Mukhopadhyay, Sabyasachi; Das, Nandan K.; Pradhan, Asima; Ghosh, Nirmalya; Panigrahi, Prasanta K.
2014-02-01
The objective of the present work is to diagnose pre-cancer by wavelet transform and multi-fractal de-trended fluctuation analysis of DIC images of normal and different grades of cancer tissues. Our DIC imaging and fluctuation analysis methods (Discrete and continuous wavelet transform, MFDFA) confirm the ability to diagnose and detect the early stage of cancer in cervical tissue.
Lagrange wavelets for signal processing.
Shi, Z; Wei, G W; Kouri, D J; Hoffman, D K; Bao, Z
2001-01-01
This paper deals with the design of interpolating wavelets based on a variety of Lagrange functions, combined with novel signal processing techniques for digital imaging. Halfband Lagrange wavelets, B-spline Lagrange wavelets and Gaussian Lagrange (Lagrange distributed approximating functional (DAF)) wavelets are presented as specific examples of the generalized Lagrange wavelets. Our approach combines the perceptually dependent visual group normalization (VGN) technique and a softer logic masking (SLM) method. These are utilized to rescale the wavelet coefficients, remove perceptual redundancy and obtain good visual performance for digital image processing. PMID:18255493
Wavelet-based analysis of circadian behavioral rhythms.
Leise, Tanya L
2015-01-01
The challenging problems presented by noisy biological oscillators have led to the development of a great variety of methods for accurately estimating rhythmic parameters such as period and amplitude. This chapter focuses on wavelet-based methods, which can be quite effective for assessing how rhythms change over time, particularly if time series are at least a week in length. These methods can offer alternative views to complement more traditional methods of evaluating behavioral records. The analytic wavelet transform can estimate the instantaneous period and amplitude, as well as the phase of the rhythm at each time point, while the discrete wavelet transform can extract the circadian component of activity and measure the relative strength of that circadian component compared to those in other frequency bands. Wavelet transforms do not require the removal of noise or trend, and can, in fact, be effective at removing noise and trend from oscillatory time series. The Fourier periodogram and spectrogram are reviewed, followed by descriptions of the analytic and discrete wavelet transforms. Examples illustrate application of each method and their prior use in chronobiology is surveyed. Issues such as edge effects, frequency leakage, and implications of the uncertainty principle are also addressed. PMID:25662453
Biomedical image and signal de-noising using dual tree complex wavelet transform
NASA Astrophysics Data System (ADS)
Rizi, F. Yousefi; Noubari, H. Ahmadi; Setarehdan, S. K.
2011-10-01
Dual tree complex wavelet transform(DTCWT) is a form of discrete wavelet transform, which generates complex coefficients by using a dual tree of wavelet filters to obtain their real and imaginary parts. The purposes of de-noising are reducing noise level and improving signal to noise ratio (SNR) without distorting the signal or image. This paper proposes a method for removing white Gaussian noise from ECG signals and biomedical images. The discrete wavelet transform (DWT) is very valuable in a large scope of de-noising problems. However, it has limitations such as oscillations of the coefficients at a singularity, lack of directional selectivity in higher dimensions, aliasing and consequent shift variance. The complex wavelet transform CWT strategy that we focus on in this paper is Kingsbury's and Selesnick's dual tree CWT (DTCWT) which outperforms the critically decimated DWT in a range of applications, such as de-noising. Each complex wavelet is oriented along one of six possible directions, and the magnitude of each complex wavelet has a smooth bell-shape. In the final part of this paper, we present biomedical image and signal de-noising by the means of thresholding magnitude of the wavelet coefficients.
Analysis and removing noise from speech using wavelet transform
NASA Astrophysics Data System (ADS)
Tomala, Karel; Voznak, Miroslav; Partila, Pavol; Rezac, Filip; Safarik, Jakub
2013-05-01
The paper discusses the use of Discrete Wavelet Transform (DWT) and Stationary Wavelet Transform (SWT) wavelet in removing noise from voice samples and evaluation of its impact on speech quality. One significant part of Quality of Service (QoS) in communication technology is the speech quality assessment. However, this part is seriously overlooked as telecommunication providers often focus on increasing network capacity, expansion of services offered and their enforcement in the market. Among the fundamental factors affecting the transmission properties of the communication chain is noise, either at the transmitter or the receiver side. A wavelet transform (WT) is a modern tool for signal processing. One of the most significant areas in which wavelet transforms are used is applications designed to suppress noise in signals. To remove noise from the voice sample in our experiment, we used the reference segment of the voice which was distorted by Gaussian white noise. An evaluation of the impact on speech quality was carried out by an intrusive objective algorithm Perceptual Evaluation of Speech Quality (PESQ). DWT and SWT transformation was applied to voice samples that were devalued by Gaussian white noise. Afterwards, we determined the effectiveness of DWT and SWT by means of objective algorithm PESQ. The decisive criterion for determining the quality of a voice sample once the noise had been removed was Mean Opinion Score (MOS) which we obtained in PESQ. The contribution of this work lies in the evaluation of efficiency of wavelet transformation to suppress noise in voice samples.
Directional dual-tree complex wavelet packet transform.
Serbes, Gorkem; Aydin, Nizamettin; Gulcur, Halil Ozcan
2013-01-01
Doppler ultrasound systems, which are widely used in cardiovascular disorders detection, have quadrature format outputs. Various types of algorithms were described in literature to process quadrature Doppler signals (QDS), such as phasing filter technique (PFT), fast Fourier transform method, frequency domain Hilbert transform method and complex continuous wavelet transform. However for the discrete wavelet transform (DWT) case, which becomes a common method for processing QDSs, there was not a direct method to recover flow direction from quadrature signals. Traditionally, to process QDSs with DWT, firstly directional signals have to be extracted and later two DWTs must be applied. Although there exists a complex DWT algorithm called dual tree complex discrete wavelet transform (DTCWT), it does not provide directional signal decoding during analysis because of the unwanted energy leaks into its negative frequency bands. Modified DTCWT, which is a combination of PFT and DTCWT, has the capability of extracting directional information while decomposing QDSs into different frequency bands, but it uses an additional Hilbert transform filter and it increases the computational complexity of whole transform. Discrete wavelet packet transform (DWPT), which is a generalization of the ordinary DWT allowing subband analysis without the constraint of dyadic decomposition, can perform an adaptive decomposition of the frequency axis. In this study, a novel complex DWPT, which maps directional information while processing QDSs, is proposed. The success of proposed method will be measured by using simulated quadrature signals. PMID:24110370
Wavelet decomposition-based efficient face liveness detection
NASA Astrophysics Data System (ADS)
Moniruzzaman, Md.; Alam, Mohammad S.
2016-04-01
Existing face recognition systems are susceptible to spoofing attacks. So, Face liveness detection is a pivotal part for reliable face recognition, which has recently acknowledged vast attention. In this paper we propose a wavelet decomposition based face liveness recognition system using an energy calculation technique. Live faces contain high energy components compared to fake or printed image. In this paper, we calculate energy components of live face as well as fake face using discrete wavelet decomposition method. We analyze percentage of energy at different levels as well as for different wavelet basis function. We also analyze percentage of energy at different RGB bands and efficient face liveness detection method has been proposed. Discrete wavelet representation has been used to calculate decomposed energy components. Moreover, it provides differentiation of several spatial orientations as well as average and detailed information which are missing in the fake faces. This technique provides excellent discrimination capability when compared to the previously reported works based on the discrete Fourier transform and n-dimensional Fourier transform operations. To verify the proposed approach, we tested the performance using various face antispoofing datasets such as university of south Alabama (UFAD), and MSU face antispoofing dataset which incorporates different types of attacks. The test results obtained using the proposed technique shows better performance compared to existing techniques.
Wavelet-RX anomaly detection for dual-band forward-looking infrared imagery.
Mehmood, Asif; Nasrabadi, Nasser M
2010-08-20
This paper describes a new wavelet-based anomaly detection technique for a dual-band forward-looking infrared (FLIR) sensor consisting of a coregistered longwave (LW) with a midwave (MW) sensor. The proposed approach, called the wavelet-RX (Reed-Xiaoli) algorithm, consists of a combination of a two-dimensional (2D) wavelet transform and a well-known multivariate anomaly detector called the RX algorithm. In our wavelet-RX algorithm, a 2D wavelet transform is first applied to decompose the input image into uniform subbands. A subband-image cube is formed by concatenating together a number of significant subbands (high-energy subbands). The RX algorithm is then applied to the subband-image cube obtained from a wavelet decomposition of the LW or MW sensor data. In the case of the dual band, the RX algorithm is applied to a subband-image cube constructed by concatenating together the high-energy subbands of the LW and MW subband-image cubes. Experimental results are presented for the proposed wavelet-RX and the classical constant false alarm rate (CFAR) algorithm for detecting anomalies (targets) in a single broadband FLIR (LW or MW) or in a coregistered dual-band FLIR sensor. The results show that the proposed wavelet-RX algorithm outperforms the classical CFAR detector for both single-band and dual-band FLIR sensors. PMID:20733634
Energy Science and Technology Software Center (ESTSC)
2004-08-01
AnisWave2D is a 2D finite-difference code for a simulating seismic wave propagation in fully anisotropic materials. The code is implemented to run in parallel over multiple processors and is fully portable. A mesh refinement algorithm has been utilized to allow the grid-spacing to be tailored to the velocity model, avoiding the over-sampling of high-velocity materials that usually occurs in fixed-grid schemes.
Lung tissue classification using wavelet frames.
Depeursinge, Adrien; Sage, Daniel; Hidki, Asmâa; Platon, Alexandra; Poletti, Pierre-Alexandre; Unser, Michael; Müller, Henning
2007-01-01
We describe a texture classification system that identifies lung tissue patterns from high-resolution computed tomography (HRCT) images of patients affected with interstitial lung diseases (ILD). This pattern recognition task is part of an image-based diagnostic aid system for ILDs. Five lung tissue patterns (healthy, emphysema, ground glass, fibrosis and microdules) selected from a multimedia database are classified using the overcomplete discrete wavelet frame decompostion combined with grey-level histogram features. The overall multiclass accuracy reaches 92.5% of correct matches while combining the two types of features, which are found to be complementary. PMID:18003452
Image coding by way of wavelets
NASA Technical Reports Server (NTRS)
Shahshahani, M.
1993-01-01
The application of two wavelet transforms to image compression is discussed. It is noted that the Haar transform, with proper bit allocation, has performance that is visually superior to an algorithm based on a Daubechies filter and to the discrete cosine transform based Joint Photographic Experts Group (JPEG) algorithm at compression ratios exceeding 20:1. In terms of the root-mean-square error, the performance of the Haar transform method is basically comparable to that of the JPEG algorithm. The implementation of the Haar transform can be achieved in integer arithmetic, making it very suitable for applications requiring real-time performance.
Stationary wavelet transform for fault detection in rotating machinery
NASA Astrophysics Data System (ADS)
Seker, Serhat; Karatoprak, Erinc; Kayran, A. H.; Senguler, Tayfun
2007-09-01
This research presents a different fault diagnostic approach using the Stationary Wavelet Transform (SWT) as an alternative method to Discrete Wavelet Transform (DWT). In this sense, it is aimed to find potential defects, which exist in healthy motor bearings as manufacturing defects as compared to the faulty case. This approach extracts the origin of the bearing damage that develops during the aging process. In this manner, the advantage of the SWT over the DWT is emphasized. Hence, it can be introduced as a new approach for condition monitoring studies in rotating machineries like the induction motors.
Numerical Evaluation of 2D Ground States
NASA Astrophysics Data System (ADS)
Kolkovska, Natalia
2016-02-01
A ground state is defined as the positive radial solution of the multidimensional nonlinear problem
Wavelet based hierarchical coding scheme for radar image compression
NASA Astrophysics Data System (ADS)
Sheng, Wen; Jiao, Xiaoli; He, Jifeng
2007-12-01
This paper presents a wavelet based hierarchical coding scheme for radar image compression. Radar signal is firstly quantized to digital signal, and reorganized as raster-scanned image according to radar's repeated period frequency. After reorganization, the reformed image is decomposed to image blocks with different frequency band by 2-D wavelet transformation, each block is quantized and coded by the Huffman coding scheme. A demonstrating system is developed, showing that under the requirement of real time processing, the compression ratio can be very high, while with no significant loss of target signal in restored radar image.
NASA Astrophysics Data System (ADS)
Cheng, Kai-jen; Dill, Jeffrey
2013-05-01
In this paper, a lossless to lossy transform based image compression of hyperspectral images based on Integer Karhunen-Loève Transform (IKLT) and Integer Discrete Wavelet Transform (IDWT) is proposed. Integer transforms are used to accomplish reversibility. The IKLT is used as a spectral decorrelator and the 2D-IDWT is used as a spatial decorrelator. The three-dimensional Binary Embedded Zerotree Wavelet (3D-BEZW) algorithm efficiently encodes hyperspectral volumetric image by implementing progressive bitplane coding. The signs and magnitudes of transform coefficients are encoded separately. Lossy and lossless compressions of signs are implemented by conventional EZW algorithm and arithmetic coding respectively. The efficient 3D-BEZW algorithm is applied to code magnitudes. Further compression can be achieved using arithmetic coding. The lossless and lossy compression performance is compared with other state of the art predictive and transform based image compression methods on Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) images. Results show that the 3D-BEZW performance is comparable to predictive algorithms. However, its computational cost is comparable to transform- based algorithms.
NASA Astrophysics Data System (ADS)
Katouzian, Amin; Baseri, Babak; Konofagou, Elisa E.; Laine, Andrew F.
2008-03-01
Intravascular ultrasound (IVUS) has been proven a reliable imaging modality that is widely employed in cardiac interventional procedures. It can provide morphologic as well as pathologic information on the occluded plaques in the coronary arteries. In this paper, we present a new technique using wavelet packet analysis that differentiates between blood and non-blood regions on the IVUS images. We utilized the multi-channel texture segmentation algorithm based on the discrete wavelet packet frames (DWPF). A k-mean clustering algorithm was deployed to partition the extracted textural features into blood and non-blood in an unsupervised fashion. Finally, the geometric and statistical information of the segmented regions was used to estimate the closest set of pixels to the lumen border and a spline curve was fitted to the set. The presented algorithm may be helpful in delineating the lumen border automatically and more reliably prior to the process of plaque characterization, especially with 40 MHz transducers, where appearance of the red blood cells renders the border detection more challenging, even manually. Experimental results are shown and they are quantitatively compared with manually traced borders by an expert. It is concluded that our two dimensional (2-D) algorithm, which is independent of the cardiac and catheter motions performs well in both in-vivo and in-vitro cases.
NASA Astrophysics Data System (ADS)
Ng, Desmond; Wong, Fu Tian; Withayachumnankul, Withawat; Findlay, David; Ferguson, Bradley; Abbott, Derek
2007-12-01
In this work we investigate new feature extraction algorithms on the T-ray response of normal human bone cells and human osteosarcoma cells. One of the most promising feature extraction methods is the Discrete Wavelet Transform (DWT). However, the classification accuracy is dependant on the specific wavelet base chosen. Adaptive wavelets circumvent this problem by gradually adapting to the signal to retain optimum discriminatory information, while removing redundant information. Using adaptive wavelets, classification accuracy, using a quadratic Bayesian classifier, of 96.88% is obtained based on 25 features. In addition, the potential of using rational wavelets rather than the standard dyadic wavelets in classification is explored. The advantage it has over dyadic wavelets is that it allows a better adaptation of the scale factor according to the signal. An accuracy of 91.15% is obtained through rational wavelets with 12 coefficients using a Support Vector Machine (SVM) as the classifier. These results highlight adaptive and rational wavelets as an efficient feature extraction method and the enormous potential of T-rays in cancer detection.
2d PDE Linear Symmetric Matrix Solver
Energy Science and Technology Software Center (ESTSC)
1983-10-01
ICCG2 (Incomplete Cholesky factorized Conjugate Gradient algorithm for 2d symmetric problems) was developed to solve a linear symmetric matrix system arising from a 9-point discretization of two-dimensional elliptic and parabolic partial differential equations found in plasma physics applications, such as resistive MHD, spatial diffusive transport, and phase space transport (Fokker-Planck equation) problems. These problems share the common feature of being stiff and requiring implicit solution techniques. When these parabolic or elliptic PDE''s are discretized withmore » finite-difference or finite-element methods,the resulting matrix system is frequently of block-tridiagonal form. To use ICCG2, the discretization of the two-dimensional partial differential equation and its boundary conditions must result in a block-tridiagonal supermatrix composed of elementary tridiagonal matrices. The incomplete Cholesky conjugate gradient algorithm is used to solve the linear symmetric matrix equation. Loops are arranged to vectorize on the Cray1 with the CFT compiler, wherever possible. Recursive loops, which cannot be vectorized, are written for optimum scalar speed. For matrices lacking symmetry, ILUCG2 should be used. Similar methods in three dimensions are available in ICCG3 and ILUCG3. A general source containing extensions and macros, which must be processed by a pre-compiler to obtain the standard FORTRAN source, is provided along with the standard FORTRAN source because it is believed to be more readable. The pre-compiler is not included, but pre-compilation may be performed by a text editor as described in the UCRL-88746 Preprint.« less
2d PDE Linear Asymmetric Matrix Solver
Energy Science and Technology Software Center (ESTSC)
1983-10-01
ILUCG2 (Incomplete LU factorized Conjugate Gradient algorithm for 2d problems) was developed to solve a linear asymmetric matrix system arising from a 9-point discretization of two-dimensional elliptic and parabolic partial differential equations found in plasma physics applications, such as plasma diffusion, equilibria, and phase space transport (Fokker-Planck equation) problems. These equations share the common feature of being stiff and requiring implicit solution techniques. When these parabolic or elliptic PDE''s are discretized with finite-difference or finite-elementmore » methods, the resulting matrix system is frequently of block-tridiagonal form. To use ILUCG2, the discretization of the two-dimensional partial differential equation and its boundary conditions must result in a block-tridiagonal supermatrix composed of elementary tridiagonal matrices. A generalization of the incomplete Cholesky conjugate gradient algorithm is used to solve the matrix equation. Loops are arranged to vectorize on the Cray1 with the CFT compiler, wherever possible. Recursive loops, which cannot be vectorized, are written for optimum scalar speed. For problems having a symmetric matrix ICCG2 should be used since it runs up to four times faster and uses approximately 30% less storage. Similar methods in three dimensions are available in ICCG3 and ILUCG3. A general source, containing extensions and macros, which must be processed by a pre-compiler to obtain the standard FORTRAN source, is provided along with the standard FORTRAN source because it is believed to be more readable. The pre-compiler is not included, but pre-compilation may be performed by a text editor as described in the UCRL-88746 Preprint.« less
Wavelets on Planar Tesselations
Bertram, M.; Duchaineau, M.A.; Hamann, B.; Joy, K.I.
2000-02-25
We present a new technique for progressive approximation and compression of polygonal objects in images. Our technique uses local parameterizations defined by meshes of convex polygons in the plane. We generalize a tensor product wavelet transform to polygonal domains to perform multiresolution analysis and compression of image regions. The advantage of our technique over conventional wavelet methods is that the domain is an arbitrary tessellation rather than, for example, a uniform rectilinear grid. We expect that this technique has many applications image compression, progressive transmission, radiosity, virtual reality, and image morphing.
Electromagnetic spatial coherence wavelets.
Castaneda, Roman; Garcia-Sucerquia, Jorge
2006-01-01
The recently introduced concept of spatial coherence wavelets is generalized to describe the propagation of electromagnetic fields in the free space. For this aim, the spatial coherence wavelet tensor is introduced as an elementary amount, in terms of which the formerly known quantities for this domain can be expressed. It allows for the analysis of the relationship between the spatial coherence properties and the polarization state of the electromagnetic wave. This approach is completely consistent with the recently introduced unified theory of coherence and polarization for random electromagnetic beams, but it provides further insight about the causal relationship between the polarization states at different planes along the propagation path. PMID:16478063
Li, Jingsong; Yu, Benli; Fischer, Horst
2015-04-01
This paper presents a novel methodology-based discrete wavelet transform (DWT) and the choice of the optimal wavelet pairs to adaptively process tunable diode laser absorption spectroscopy (TDLAS) spectra for quantitative analysis, such as molecular spectroscopy and trace gas detection. The proposed methodology aims to construct an optimal calibration model for a TDLAS spectrum, regardless of its background structural characteristics, thus facilitating the application of TDLAS as a powerful tool for analytical chemistry. The performance of the proposed method is verified using analysis of both synthetic and observed signals, characterized with different noise levels and baseline drift. In terms of fitting precision and signal-to-noise ratio, both have been improved significantly using the proposed method. PMID:25741689
NASA Astrophysics Data System (ADS)
Shoaib, Muhammad; Shamseldin, Asaad Y.; Melville, Bruce W.; Khan, Mudasser Muneer
2016-04-01
In order to predict runoff accurately from a rainfall event, the multilayer perceptron type of neural network models are commonly used in hydrology. Furthermore, the wavelet coupled multilayer perceptron neural network (MLPNN) models has also been found superior relative to the simple neural network models which are not coupled with wavelet. However, the MLPNN models are considered as static and memory less networks and lack the ability to examine the temporal dimension of data. Recurrent neural network models, on the other hand, have the ability to learn from the preceding conditions of the system and hence considered as dynamic models. This study for the first time explores the potential of wavelet coupled time lagged recurrent neural network (TLRNN) models for runoff prediction using rainfall data. The Discrete Wavelet Transformation (DWT) is employed in this study to decompose the input rainfall data using six of the most commonly used wavelet functions. The performance of the simple and the wavelet coupled static MLPNN models is compared with their counterpart dynamic TLRNN models. The study found that the dynamic wavelet coupled TLRNN models can be considered as alternative to the static wavelet MLPNN models. The study also investigated the effect of memory depth on the performance of static and dynamic neural network models. The memory depth refers to how much past information (lagged data) is required as it is not known a priori. The db8 wavelet function is found to yield the best results with the static MLPNN models and with the TLRNN models having small memory depths. The performance of the wavelet coupled TLRNN models with large memory depths is found insensitive to the selection of the wavelet function as all wavelet functions have similar performance.
The effects of wavelet compression on Digital Elevation Models (DEMs)
Oimoen, M.J.
2004-01-01
This paper investigates the effects of lossy compression on floating-point digital elevation models using the discrete wavelet transform. The compression of elevation data poses a different set of problems and concerns than does the compression of images. Most notably, the usefulness of DEMs depends largely in the quality of their derivatives, such as slope and aspect. Three areas extracted from the U.S. Geological Survey's National Elevation Dataset were transformed to the wavelet domain using the third order filters of the Daubechies family (DAUB6), and were made sparse by setting 95 percent of the smallest wavelet coefficients to zero. The resulting raster is compressible to a corresponding degree. The effects of the nulled coefficients on the reconstructed DEM are noted as residuals in elevation, derived slope and aspect, and delineation of drainage basins and streamlines. A simple masking technique also is presented, that maintains the integrity and flatness of water bodies in the reconstructed DEM.
ECG Signal Analysis and Arrhythmia Detection using Wavelet Transform
NASA Astrophysics Data System (ADS)
Kaur, Inderbir; Rajni, Rajni; Marwaha, Anupma
2016-06-01
Electrocardiogram (ECG) is used to record the electrical activity of the heart. The ECG signal being non-stationary in nature, makes the analysis and interpretation of the signal very difficult. Hence accurate analysis of ECG signal with a powerful tool like discrete wavelet transform (DWT) becomes imperative. In this paper, ECG signal is denoised to remove the artifacts and analyzed using Wavelet Transform to detect the QRS complex and arrhythmia. This work is implemented in MATLAB software for MIT/BIH Arrhythmia database and yields the sensitivity of 99.85 %, positive predictivity of 99.92 % and detection error rate of 0.221 % with wavelet transform. It is also inferred that DWT outperforms principle component analysis technique in detection of ECG signal.
A Wavelet-Based Methodology for Grinding Wheel Condition Monitoring
Liao, T. W.; Ting, C.F.; Qu, Jun; Blau, Peter Julian
2007-01-01
Grinding wheel surface condition changes as more material is removed. This paper presents a wavelet-based methodology for grinding wheel condition monitoring based on acoustic emission (AE) signals. Grinding experiments in creep feed mode were conducted to grind alumina specimens with a resinoid-bonded diamond wheel using two different conditions. During the experiments, AE signals were collected when the wheel was 'sharp' and when the wheel was 'dull'. Discriminant features were then extracted from each raw AE signal segment using the discrete wavelet decomposition procedure. An adaptive genetic clustering algorithm was finally applied to the extracted features in order to distinguish different states of grinding wheel condition. The test results indicate that the proposed methodology can achieve 97% clustering accuracy for the high material removal rate condition, 86.7% for the low material removal rate condition, and 76.7% for the combined grinding conditions if the base wavelet, the decomposition level, and the GA parameters are properly selected.
On 2D bisection method for double eigenvalue problems
Ji, X.
1996-06-01
The two-dimensional bisection method presented in (SIAM J. Matrix Anal. Appl. 13(4), 1085 (1992)) is efficient for solving a class of double eigenvalue problems. This paper further extends the 2D bisection method of full matrix cases and analyses its stability. As in a single parameter case, the 2D bisection method is very stable for the tridiagonal matrix triples satisfying the symmetric-definite condition. Since the double eigenvalue problems arise from two-parameter boundary value problems, an estimate of the discretization error in eigenpairs is also given. Some numerical examples are included. 42 refs., 1 tab.
Dual tree fractional quaternion wavelet transform for disparity estimation.
Kumar, Sanoj; Kumar, Sanjeev; Sukavanam, Nagarajan; Raman, Balasubramanian
2014-03-01
This paper proposes a novel phase based approach for computing disparity as the optical flow from the given pair of consecutive images. A new dual tree fractional quaternion wavelet transform (FrQWT) is proposed by defining the 2D Fourier spectrum upto a single quadrant. In the proposed FrQWT, each quaternion wavelet consists of a real part (a real DWT wavelet) and three imaginary parts that are organized according to the quaternion algebra. First two FrQWT phases encode the shifts of image features in the absolute horizontal and vertical coordinate system, while the third phase has the texture information. The FrQWT allowed a multi-scale framework for calculating and adjusting local disparities and executing phase unwrapping from coarse to fine scales with linear computational efficiency. PMID:24388356
The wavelet/scalar quantization compression standard for digital fingerprint images
Bradley, J.N.; Brislawn, C.M.
1994-04-01
A new digital image compression standard has been adopted by the US Federal Bureau of Investigation for use on digitized gray-scale fingerprint images. The algorithm is based on adaptive uniform scalar quantization of a discrete wavelet transform image decomposition and is referred to as the wavelet/scalar quantization standard. The standard produces archival quality images at compression ratios of around 20:1 and will allow the FBI to replace their current database of paper fingerprint cards with digital imagery.
NASA Astrophysics Data System (ADS)
Mayor, Louise
2016-05-01
Graphene might be the most famous example, but there are other 2D materials and compounds too. Louise Mayor explains how these atomically thin sheets can be layered together to create flexible “van der Waals heterostructures”, which could lead to a range of novel applications.
NASA Astrophysics Data System (ADS)
Vivaldi, Franco
2015-12-01
The concept of resonance has been instrumental to the study of Hamiltonian systems with divided phase space. One can also define such systems over discrete spaces, which have a finite or countable number of points, but in this new setting the notion of resonance must be re-considered from scratch. I review some recent developments in the area of arithmetic dynamics which outline some salient features of linear and nonlinear stable (elliptic) orbits over a discrete space, and also underline the difficulties that emerge in their analysis.
NASA Astrophysics Data System (ADS)
Vivaldi, Franco
The concept of resonance has been instrumental to the study of Hamiltonian systems with divided phase space. One can also define such systems over discrete spaces, which have a finite or countable number of points, but in this new setting the notion of resonance must be re-considered from scratch. I review some recent developments in the area of arithmetic dynamics which outline some salient features of linear and nonlinear stable (elliptic) orbits over a discrete space, and also underline the difficulties that emerge in their analysis.
Security of Color Image Data Designed by Public-Key Cryptosystem Associated with 2D-DWT
NASA Astrophysics Data System (ADS)
Mishra, D. C.; Sharma, R. K.; Kumar, Manish; Kumar, Kuldeep
2014-08-01
In present times the security of image data is a major issue. So, we have proposed a novel technique for security of color image data by public-key cryptosystem or asymmetric cryptosystem. In this technique, we have developed security of color image data using RSA (Rivest-Shamir-Adleman) cryptosystem with two-dimensional discrete wavelet transform (2D-DWT). Earlier proposed schemes for security of color images designed on the basis of keys, but this approach provides security of color images with the help of keys and correct arrangement of RSA parameters. If the attacker knows about exact keys, but has no information of exact arrangement of RSA parameters, then the original information cannot be recovered from the encrypted data. Computer simulation based on standard example is critically examining the behavior of the proposed technique. Security analysis and a detailed comparison between earlier developed schemes for security of color images and proposed technique are also mentioned for the robustness of the cryptosystem.
Application of wavelet transforms in terahertz spectroscopy of rough surface targets
NASA Astrophysics Data System (ADS)
Arbab, M. Hassan; Winebrenner, Dale P.; Thorsos, Eric I.; Chen, Antao
2010-02-01
Previously, it has been shown that scattering of terahertz waves by surface roughness of a target can alter the terahertz absorption spectrum and thus obscure the detection of some chemicals in both transmission and reflection geometries. In this paper it is demonstrated that by employing Maximal Overlap Discrete Wavelet Transform (MODWT) coefficients, wavelet-based methods can be used to retrieve spectroscopic information from a broadband terahertz signal reflected from a rough surface target. It is concluded that while the commonly used direct frequency domain deconvolution method fails to accurately characterize and detect the resonance in the dielectric constant of rough surface lactose pellets, wavelet techniques were able to successfully identify such features.
Gopalan, K.; Gopalsami, N.; Bakhtiari, S.; Raptis, A.C.
1995-07-01
This paper reports on wavelet-based decomposition methods and neural networks for remote monitoring of airborne chemicals using millimeter wave spectroscopy. Because of instrumentation noise and the presence of untargeted chemicals, direct decomposition of the spectra requires a large number of training data and yields low accuracy. A neural network trained with features obtained from a discrete wavelet transform is demonstrated to have better decomposition with faster training time. Results based on simulated and experimental spectra are presented to show the efficacy of the wavelet-based methods.
SILC: a new Planck internal linear combination CMB temperature map using directional wavelets
NASA Astrophysics Data System (ADS)
Rogers, Keir K.; Peiris, Hiranya V.; Leistedt, Boris; McEwen, Jason D.; Pontzen, Andrew
2016-08-01
We present new clean maps of the cosmic microwave background (CMB) temperature anisotropies (as measured by Planck) constructed with a novel internal linear combination (ILC) algorithm using directional, scale-discretized wavelets - scale-discretized, directional wavelet ILC or Scale-discretised, directional wavelet Internal Linear Combination (SILC). Directional wavelets, when convolved with signals on the sphere, can separate the anisotropic filamentary structures which are characteristic of both the CMB and foregrounds. Extending previous component separation methods, which use the frequency, spatial and harmonic signatures of foregrounds to separate them from the cosmological background signal, SILC can additionally use morphological information in the foregrounds and CMB to better localize the cleaning algorithm. We test the method on Planck data and simulations, demonstrating consistency with existing component separation algorithms, and discuss how to optimize the use of morphological information by varying the number of directional wavelets as a function of spatial scale. We find that combining the use of directional and axisymmetric wavelets depending on scale could yield higher quality CMB temperature maps. Our results set the stage for the application of SILC to polarization anisotropies through an extension to spin wavelets.
Parallel algorithms for 2-D cylindrical transport equations of Eigenvalue problem
Wei, J.; Yang, S.
2013-07-01
In this paper, aimed at the neutron transport equations of eigenvalue problem under 2-D cylindrical geometry on unstructured grid, the discrete scheme of Sn discrete ordinate and discontinuous finite is built, and the parallel computation for the scheme is realized on MPI systems. Numerical experiments indicate that the designed parallel algorithm can reach perfect speedup, it has good practicality and scalability. (authors)
A study of stationarity in time series by using wavelet transform
NASA Astrophysics Data System (ADS)
Dghais, Amel Abdoullah Ahmed; Ismail, Mohd Tahir
2014-07-01
In this work the core objective is to apply discrete wavelet transform (DWT) functions namely Haar, Daubechies, Symmlet, Coiflet and discrete approximation of the meyer wavelets in non-stationary financial time series data from US stock market (DJIA30). The data consists of 2048 daily data of closing index starting from December 17, 2004 until October 23, 2012. From the unit root test the results show that the data is non stationary in the level. In order to study the stationarity of a time series, the autocorrelation function (ACF) is used. Results indicate that, Haar function is the lowest function to obtain noisy series as compared to Daubechies, Symmlet, Coiflet and discrete approximation of the meyer wavelets. In addition, the original data after decomposition by DWT is less noisy series than decomposition by DWT for return time series.
Baby universes and fractal structure of 2d gravity
NASA Astrophysics Data System (ADS)
Thorleifsson, Gudmar
1994-04-01
We extract the string susceptibility exponent γstr by measuring the distribution of baby universes on surfaces in the case of various matter fields coupled to discrete 2d quantum gravity. For c <= 1 the results are in good agreement with the KPZ-formula, if logarithmic corrections are taken into account for c = 1. For c > 1 it is not as clear how to extract γstr but universality with respect to c is observed in the fractal structure.