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.
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.
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
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.
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.
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
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.
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.
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.
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.
Data compression by wavelet transforms
NASA Technical Reports Server (NTRS)
Shahshahani, M.
1992-01-01
A wavelet transform algorithm is applied to image compression. It is observed that the algorithm does not suffer from the blockiness characteristic of the DCT-based algorithms at compression ratios exceeding 25:1, but the edges do not appear as sharp as they do with the latter method. Some suggestions for the improved performance of the wavelet transform method are presented.
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.
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.
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
A Mellin transform approach to wavelet analysis
NASA Astrophysics Data System (ADS)
Alotta, Gioacchino; Di Paola, Mario; Failla, Giuseppe
2015-11-01
The paper proposes a fractional calculus approach to continuous wavelet analysis. Upon introducing a Mellin transform expression of the mother wavelet, it is shown that the wavelet transform of an arbitrary function f(t) can be given a fractional representation involving a suitable number of Riesz integrals of f(t), and corresponding fractional moments of the mother wavelet. This result serves as a basis for an original approach to wavelet analysis of linear systems under arbitrary excitations. In particular, using the proposed fractional representation for the wavelet transform of the excitation, it is found that the wavelet transform of the response can readily be computed by a Mellin transform expression, with fractional moments obtained from a set of algebraic equations whose coefficient matrix applies for any scale a of the wavelet transform. Robustness and computationally efficiency of the proposed approach are shown in the paper.
General inversion formulas for wavelet transforms
NASA Astrophysics Data System (ADS)
Holschneider, Matthias
1993-09-01
This article is the continuation of a series of articles about group theory and wavelet analysis [A. Grossmann, J. Morlet, and T. Paul, J. Math. Phys. 26, 2473 (1985)]. As is well-known in the case of the afine group, the reconstruction wavelet and the analyzing wavelet need not be identic. In this article it is shown that this holds for arbitrary groups. In addition it is shown that even for nonadmissible analyzing wavelets the wavelet transform may be inverted. Accordingly the image of the wavelet transform can be characterized by many different reproducing kernels.
Staring 2-D hadamard transform spectral imager
Gentry, Stephen M.; Wehlburg, Christine M.; Wehlburg, Joseph C.; Smith, Mark W.; Smith, Jody L.
2006-02-07
A staring imaging system inputs a 2D spatial image containing multi-frequency spectral information. This image is encoded in one dimension of the image with a cyclic Hadamarid S-matrix. The resulting image is detecting with a spatial 2D detector; and a computer applies a Hadamard transform to recover the encoded image.
Optical wavelet transform for fingerprint identification
NASA Astrophysics Data System (ADS)
MacDonald, Robert P.; Rogers, Steven K.; Burns, Thomas J.; Fielding, Kenneth H.; Warhola, Gregory T.; Ruck, Dennis W.
1994-03-01
The Federal Bureau of Investigation (FBI) has recently sanctioned a wavelet fingerprint image compression algorithm developed for reducing storage requirements of digitized fingerprints. This research implements an optical wavelet transform of a fingerprint image, as the first step in an optical fingerprint identification process. Wavelet filters are created from computer- generated holograms of biorthogonal wavelets, the same wavelets implemented in the FBI algorithm. Using a detour phase holographic technique, a complex binary filter mask is created with both symmetry and linear phase. The wavelet transform is implemented with continuous shift using an optical correlation between binarized fingerprints written on a Magneto-Optic Spatial Light Modulator and the biorthogonal wavelet filters. A telescopic lens combination scales the transformed fingerprint onto the filters, providing a means of adjusting the biorthogonal wavelet filter dilation continuously. The wavelet transformed fingerprint is then applied to an optical fingerprint identification process. Comparison between normal fingerprints and wavelet transformed fingerprints shows improvement in the optical identification process, in terms of rotational invariance.
Entangled Husimi Distribution and Complex Wavelet Transformation
NASA Astrophysics Data System (ADS)
Hu, Li-Yun; Fan, Hong-Yi
2010-05-01
Similar in spirit to the preceding work (Int. J. Theor. Phys. 48:1539, 2009) where the relationship between wavelet transformation and Husimi distribution function is revealed, we study this kind of relationship to the entangled case. We find that the optical complex wavelet transformation can be used to study the entangled Husimi distribution function in phase space theory of quantum optics. We prove that, up to a Gaussian function, the entangled Husimi distribution function of a two-mode quantum state | ψ> is just the modulus square of the complex wavelet transform of e^{-\\vert η \\vert 2/2} with ψ( η) being the mother wavelet.
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.
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.
Reservoir characterization using wavelet transforms
NASA Astrophysics Data System (ADS)
Rivera Vega, Nestor
Automated detection of geological boundaries and determination of cyclic events controlling deposition can facilitate stratigraphic analysis and reservoir characterization. This study applies the wavelet transformation, a recent advance in signal analysis techniques, to interpret cyclicity, determine its controlling factors, and detect zone boundaries. We tested the cyclostratigraphic assessments using well log and core data from a well in a fluvio-eolian sequence in the Ormskirk Sandstone, Irish Sea. The boundary detection technique was tested using log data from 10 wells in the Apiay field, Colombia. We processed the wavelet coefficients for each zone of the Ormskirk Formation and determined the wavelengths of the strongest cyclicities. Comparing these periodicities with Milankovitch cycles, we found a strong correspondence of the two. This suggests that climate exercised an important control on depositional cyclicity, as had been concluded in previous studies of the Ormskirk Sandstone. The wavelet coefficients from the log data in the Apiay field were combined to form features. These vectors were used in conjunction with pattern recognition techniques to perform detection in 7 boundaries. For the upper two units, the boundary was detected within 10 feet of their actual depth, in 90% of the wells. The mean detection performance in the Apiay field is 50%. We compared our method with other traditional techniques which do not focus on selecting optimal features for boundary identification. Those methods resulted in detection performances of 40% for the uppermost boundary, which lag behind the 90% performance of our method. Automated determination of geologic boundaries will expedite studies, and knowledge of the controlling deposition factors will enhance stratigraphic and reservoir characterization models. We expect that automated boundary detection and cyclicity analysis will prove to be valuable and time-saving methods for establishing correlations and their
Fan, Hong-Yi; Lu, Hai-Liang
2007-03-01
The Einstein-Podolsky-Rosen entangled state representation is applied to studying the admissibility condition of mother wavelets for complex wavelet transforms, which leads to a family of new mother wavelets. Mother wavelets thus are classified as the Hermite-Gaussian type for real wavelet transforms and the Laguerre-Gaussian type for the complex case. PMID:17392919
Wavelet transforms for optical pulse analysis.
Vázquez, Javier Molina; Mazilu, Michael; Miller, Alan; Galbraith, Ian
2005-12-01
An exploration of wavelet transforms for ultrashort optical pulse characterization is given. Some of the most common wavelets are examined to determine the advantages of using the causal quasi-wavelet suggested in Proceedings of the LEOS 15th Annual Meeting (IEEE, 2002), Vol. 2, p. 592, in terms of pulse analysis and, in particular, chirp extraction. Owing to its ability to distinguish between past and future pulse information, the causal quasi-wavelet is found to be highly suitable for optical pulse characterization. PMID:16396051
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 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.
Mining wavelet transformed boiler data sets
NASA Astrophysics Data System (ADS)
Letsche, Terry Lee
Accurate combustion models provide information that allows increased boiler efficiency optimization, saving money and resources while reducing waste. Boiler combustion processes are noted for being complex, nonstationary and nonlinear. While numerous methods have been used to model boiler processes, data driven approaches reflect actual operating conditions within a particular boiler and do not depend on idealized, complex, or expensive empirical models. Boiler and combustion processes vary in time, requiring a denoising technique that preserves the temporal and frequency nature of the data. Moving average, a common technique, smoothes data---low frequency noise is not removed. This dissertation examines models built with wavelet denoising techniques that remove low and high frequency noise in both time and frequency domains. The denoising process has a number of parameters, including choice of wavelet, threshold value, level of wavelet decomposition, and disposition of attributes that appear to be significant at multiple thresholds. A process is developed to experimentally evaluate the predictive accuracy of these models and compares this result against two benchmarks. The first research hypothesis compares the performance of these wavelet denoised models to the model generated from the original data. The second research hypothesis compares the performance of the models generated with this denoising approach to the most effective model generated from a moving average process. In both experiments it was determined that the Daubechies 4 wavelet was a better choice than the more typically chosen Haar wavelet, wavelet packet decomposition outperforms other levels of wavelet decomposition, and discarding all but the lowest threshold repeating attributes produces superior results. The third research hypothesis examined using a two-dimensional wavelet transform on the data. Another parameter for handling the boundary condition was introduced. In the two-dimensional case
Image encryption using the fractional wavelet transform
NASA Astrophysics Data System (ADS)
Vilardy, Juan M.; Useche, J.; Torres, C. O.; Mattos, L.
2011-01-01
In this paper a technique for the coding of digital images is developed using Fractional Wavelet Transform (FWT) and random phase masks (RPMs). The digital image to encrypt is transformed with the FWT, after the coefficients resulting from the FWT (Approximation, Details: Horizontal, vertical and diagonal) are multiplied each one by different RPMs (statistically independent) and these latest results is applied an Inverse Wavelet Transform (IWT), obtaining the encrypted digital image. The decryption technique is the same encryption technique in reverse sense. This technique provides immediate advantages security compared to conventional techniques, in this technique the mother wavelet family and fractional orders associated with the FWT are additional keys that make access difficult to information to an unauthorized person (besides the RPMs used), thereby the level of encryption security is extraordinarily increased. In this work the mathematical support for the use of the FWT in the computational algorithm for the encryption is also developed.
Wavelet transform in electrocardiography--data compression.
Provazník, I; Kozumplík, J
1997-06-01
An application of the wavelet transform to electrocardiography is described in the paper. The transform is used as a first stage of a lossy compression algorithm for efficient coding of rest ECG signals. The proposed technique is based on the decomposition of the ECG signal into a set of basic functions covering the time-frequency domain. Thus, non-stationary character of ECG data is considered. Some of the time-frequency signal components are removed because of their low influence to signal characteristics. Resulting components are efficiently coded by quantization, composition into a sequence of coefficients and compression by a run-length coder and a entropic Huffman coder. The proposed wavelet-based compression algorithm can compress data to average code length about 1 bit/sample. The algorithm can be also implemented to a real-time processing system when wavelet transform is computed by fast linear filters described in the paper. PMID:9291025
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.
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
Information retrieval system utilizing wavelet transform
Brewster, Mary E.; Miller, Nancy E.
2000-01-01
A method for automatically partitioning an unstructured electronically formatted natural language document into its sub-topic structure. Specifically, the document is converted to an electronic signal and a wavelet transform is then performed on the signal. The resultant signal may then be used to graphically display and interact with the sub-topic structure of the document.
Wavelet transforms for detecting microcalcifications in mammograms
Strickland, R.N.; Hahn, H.I.
1996-04-01
Clusters of fine, granular microcalcifications in mammograms may be an early sign of disease. Individual grains are difficult to detect and segment due to size and shape variability and because the background mammogram texture is typically inhomogeneous. The authors develop a two-stage method based on wavelet transforms for detecting and segmenting calcifications. The first stage is based on an undecimated wavelet transform, which is simply the conventional filter bank implementation without downsampling, so that the low-low (LL), low-high (LH), high-low (HL), and high-high (HH) sub-bands remain at full size. Detection takes place in HH and the combination LH + HL. Four octaves are compared with two inter-octave voices for finer scale resolution. By appropriate selection of the wavelet basis the detection of microcalcifications in the relevant size range can be nearly optimized. In fact, the filters which transform the input image into HH and LH + HL are closely related to prewhitening matched filters for detecting Gaussian objects (idealized microcalcifications) in two common forms of Markov (background) noise. The second stage is designed to overcome the limitations of the simplistic Gaussian assumption and provides an accurate segmentation of calcification boundaries. Detected pixel sites in HH and LH + HL are dilated then weighted before computing the inverse wavelet transform. Individual microcalcifications are greatly enhanced in the output image, to the point where straightforward thresholding can be applied to segment them. FROC curves are computed from tests using a freely distributed database of digitized mammograms.
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.
Undecimated Wavelet Transforms for Image De-noising
Gyaourova, A; Kamath, C; Fodor, I K
2002-11-19
A few different approaches exist for computing undecimated wavelet transform. In this work we construct three undecimated schemes and evaluate their performance for image noise reduction. We use standard wavelet based de-noising techniques and compare the performance of our algorithms with the original undecimated wavelet transform, as well as with the decimated wavelet transform. The experiments we have made show that our algorithms have better noise removal/blurring ratio.
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.
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.
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
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
Time sequence image analysis of positron emission tomography using wavelet transformation.
Hsu, Chih-Yu; Lai, Yeong-Lin; Chen, Chih-Cheng; Lee, Yu-Tzu; Tseng, Kuo-Kun; Lai, Yeong-Kang; Zheng, Chun-Yi; Jheng, Huai-Cian
2015-01-01
This paper presents the time sequence image analysis technique of positron emission tomography (PET) using a wavelet transformation method. The abdominal cavity of a person taking [18F]Fluoro-2-deoxy-2-D-glucose (18F-FDG) was scanned by the dynamic PET. The organ selection with dynamic PET images was conducted by the wavelet transformation to implement automatic selection of the region of interest (ROI). The image segmentation was carried out by the processes of sampling, wavelet transformation, erosion, dilation, and superimposition. Wavelet constructed image (WCI) contours were created by sampling 512 images from 1960 consecutive dynamic sequence PET images. The image segmentation technology developed can help doctors automatically select ROI, accurately identify lesion locations of organs, and thus effectively reduce human operation time and errors. PMID:26578275
Hyperspectral trace gas detection using the wavelet packet transform
NASA Astrophysics Data System (ADS)
Salvador, Mark Z.; Resmini, Ronald G.; Gomez, Richard B.
2008-04-01
A method for trace gas detection in hyperspectral data is demonstrated using the wavelet packet transform. This new method, the Wavelet Packet Subspace (WPS), applies the wavelet packet transform and selects a best basis for pattern matching. The wavelet packet transform is an extension of the wavelet transform, which fully decomposes a signal into a library of wavelet packet bases. Application of the wavelet packet transform to hyperspectral data for the detection of trace gases takes advantage of the ability of the wavelet transform to locate spectral features in both scale and location. By analyzing the wavelet packet tree of specific gas, nodes of the tree are selected which represent an orthogonal best basis. The best basis represents the significant spectral features of that gas. This is then used to identify pixels in the scene using existing matching algorithms such as spectral angle or matched filter. Using data from the Airborne Hyperspectral Imager (AHI), this method is compared to traditional matched filter detection methods. Initial results demonstrate a promising wavelet packet subspace technique for hyperspectral trace gas detection applications.
Spike detection using the continuous wavelet transform.
Nenadic, Zoran; Burdick, Joel W
2005-01-01
This paper combines wavelet transforms with basic detection theory to develop a new unsupervised method for robustly detecting and localizing spikes in noisy neural recordings. The method does not require the construction of templates, or the supervised setting of thresholds. We present extensive Monte Carlo simulations, based on actual extracellular recordings, to show that this technique surpasses other commonly used methods in a wide variety of recording conditions. We further demonstrate that falsely detected spikes corresponding to our method resemble actual spikes more than the false positives of other techniques such as amplitude thresholding. Moreover, the simplicity of the method allows for nearly real-time execution. PMID:15651566
Embedded wavelet packet transform technique for texture compression
NASA Astrophysics Data System (ADS)
Li, Jin; Cheng, Po-Yuen; Kuo, C.-C. Jay
1995-09-01
A highly efficient texture compression scheme is proposed in this research. With this scheme, energy compaction of texture images is first achieved by the wavelet packet transform, and an embedding approach is then adopted for the coding of the wavelet packet transform coefficients. By comparing the proposed algorithm with the JPEG standard, FBI wavelet/scalar quantization standard and the EZW scheme with extensive experimental results, we observe a significant improvement in the rate-distortion performance and visual quality.
Continuous wavelet transform in quantum field theory
NASA Astrophysics Data System (ADS)
Altaisky, M. V.; Kaputkina, N. E.
2013-07-01
We describe the application of the continuous wavelet transform to calculation of the Green functions in quantum field theory: scalar ϕ4 theory, quantum electrodynamics, and quantum chromodynamics. The method of continuous wavelet transform in quantum field theory, presented by Altaisky [Phys. Rev. D 81, 125003 (2010)] for the scalar ϕ4 theory, consists in substitution of the local fields ϕ(x) by those dependent on both the position x and the resolution a. The substitution of the action S[ϕ(x)] by the action S[ϕa(x)] makes the local theory into a nonlocal one and implies the causality conditions related to the scale a, the region causality [J. D. Christensen and L. Crane, J. Math. Phys. (N.Y.) 46, 122502 (2005)]. These conditions make the Green functions G(x1,a1,…,xn,an)=⟨ϕa1(x1)…ϕan(xn)⟩ finite for any given set of regions by means of an effective cutoff scale A=min(a1,…,an).
Improved Compression of Wavelet-Transformed Images
NASA Technical Reports Server (NTRS)
Kiely, Aaron; Klimesh, Matthew
2005-01-01
A recently developed data-compression method is an adaptive technique for coding quantized wavelet-transformed data, nominally as part of a complete image-data compressor. Unlike some other approaches, this method admits a simple implementation and does not rely on the use of large code tables. A common data compression approach, particularly for images, is to perform a wavelet transform on the input data, and then losslessly compress a quantized version of the wavelet-transformed data. Under this compression approach, it is common for the quantized data to include long sequences, or runs, of zeros. The new coding method uses prefixfree codes for the nonnegative integers as part of an adaptive algorithm for compressing the quantized wavelet-transformed data by run-length coding. In the form of run-length coding used here, the data sequence to be encoded is parsed into strings consisting of some number (possibly 0) of zeros, followed by a nonzero value. The nonzero value and the length of the run of zeros are encoded. For a data stream that contains a sufficiently high frequency of zeros, this method is known to be more effective than using a single variable length code to encode each symbol. The specific prefix-free codes used are from two classes of variable-length codes: a class known as Golomb codes, and a class known as exponential-Golomb codes. The codes within each class are indexed by a single integer parameter. The present method uses exponential-Golomb codes for the lengths of the runs of zeros, and Golomb codes for the nonzero values. The code parameters within each code class are determined adaptively on the fly as compression proceeds, on the basis of statistics from previously encoded values. In particular, a simple adaptive method has been devised to select the parameter identifying the particular exponential-Golomb code to use. The method tracks the average number of bits used to encode recent runlengths, and takes the difference between this average
Medical image fusion by wavelet transform modulus maxima
NASA Astrophysics Data System (ADS)
Guihong, Qu; Dali, Zhang; Pingfan, Yan
2001-08-01
Medical image fusion has been used to derive useful information from multimodality medical image data. In this research, we propose a novel method for multimodality medical image fusion. Using wavelet transform, we achieved a fusion scheme. Afusion rule is proposed and used for calculating the wavelet transformation modulus maxima of input images at different bandwidths and levels. To evaluate the fusion result, a metric based on mutual information (MI) is presented for measuring fusion effect. The performances of other two methods of image fusion based on wavelet transform are briefly described for comparison. The experiment results demonstrate the effectiveness of the fusion scheme.
Coresident sensor fusion and compression using the wavelet transform
Yocky, D.A.
1996-03-11
Imagery from coresident sensor platforms, such as unmanned aerial vehicles, can be combined using, multiresolution decomposition of the sensor images by means of the two-dimensional wavelet transform. The wavelet approach uses the combination of spatial/spectral information at multiple scales to create a fused image. This can be done in both an ad hoc or model-based approach. We compare results from commercial ``fusion`` software and the ad hoc, wavelet approach. Results show the wavelet approach outperforms the commercial algorithms and also supports efficient compression of the fused image.
NASA Astrophysics Data System (ADS)
Arvind, Pratul
2012-11-01
The ability to identify and classify all ten types of faults in a distribution system is an important task for protection engineers. Unlike transmission system, distribution systems have a complex configuration and are subjected to frequent faults. In the present work, an algorithm has been developed for identifying all ten types of faults in a distribution system by collecting current samples at the substation end. The samples are subjected to wavelet packet transform and artificial neural network in order to yield better classification results. A comparison of results between wavelet transform and wavelet packet transform is also presented thereby justifying the feature extracted from wavelet packet transform yields promising results. It should also be noted that current samples are collected after simulating a 25kv distribution system in PSCAD software.
Complex Wavelet Transform of the Two-mode Quantum States
NASA Astrophysics Data System (ADS)
Song, Jun; Zhou, Jun; Yuan, Hao; He, Rui; Fan, Hong-Yi
2016-08-01
By employing the bipartite entangled state representation and the technique of integration within an ordered product of operators, the classical complex wavelet transform of a complex signal function can be recast to a matrix element of the squeezing-displacing operator U 2( μ, σ) between the mother wavelet vector < ψ| and the two-mode quantum state vector | f> to be transformed. < ψ| U 2( μ, σ)| f> can be considered as the spectrum for analyzing the two-mode quantum state | f>. In this way, for some typical two-mode quantum states, such as two-mode coherent state and two-mode Fock state, we derive the complex wavelet transform spectrum and carry out the numerical calculation. This kind of wavelet-transform spectrum can be used to recognize quantum states.
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.
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.
An Adaptive Digital Image Watermarking Algorithm Based on Morphological Haar Wavelet Transform
NASA Astrophysics Data System (ADS)
Huang, Xiaosheng; Zhao, Sujuan
At present, much more of the wavelet-based digital watermarking algorithms are based on linear wavelet transform and fewer on non-linear wavelet transform. In this paper, we propose an adaptive digital image watermarking algorithm based on non-linear wavelet transform--Morphological Haar Wavelet Transform. In the algorithm, the original image and the watermark image are decomposed with multi-scale morphological wavelet transform respectively. Then the watermark information is adaptively embedded into the original image in different resolutions, combining the features of Human Visual System (HVS). The experimental results show that our method is more robust and effective than the ordinary wavelet transform algorithms.
Early detection of rogue waves by the wavelet transforms
NASA Astrophysics Data System (ADS)
Bayındır, Cihan
2016-01-01
We discuss the possible advantages of using the wavelet transform over the Fourier transform for the early detection of rogue waves. We show that the triangular wavelet spectra of the rogue waves can be detected at early stages of the development of rogue waves in a chaotic wave field. Compared to the Fourier spectra, the wavelet spectra are capable of detecting not only the emergence of a rogue wave but also its possible spatial (or temporal) location. Due to this fact, wavelet transform is also capable of predicting the characteristic distances between successive rogue waves. Therefore multiple simultaneous breaking of the successive rogue waves on ships or on the offshore structures can be predicted and avoided by smart designs and operations.
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.
Combining Wavelet Transform and Hidden Markov Models for ECG Segmentation
NASA Astrophysics Data System (ADS)
Andreão, Rodrigo Varejão; Boudy, Jérôme
2006-12-01
This work aims at providing new insights on the electrocardiogram (ECG) segmentation problem using wavelets. The wavelet transform has been originally combined with a hidden Markov models (HMMs) framework in order to carry out beat segmentation and classification. A group of five continuous wavelet functions commonly used in ECG analysis has been implemented and compared using the same framework. All experiments were realized on the QT database, which is composed of a representative number of ambulatory recordings of several individuals and is supplied with manual labels made by a physician. Our main contribution relies on the consistent set of experiments performed. Moreover, the results obtained in terms of beat segmentation and premature ventricular beat (PVC) detection are comparable to others works reported in the literature, independently of the type of the wavelet. Finally, through an original concept of combining two wavelet functions in the segmentation stage, we achieve our best performances.
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).
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.
Topology-Preserving Rigid Transformation of 2D Digital Images.
Ngo, Phuc; Passat, Nicolas; Kenmochi, Yukiko; Talbot, Hugues
2014-02-01
We provide conditions under which 2D digital images preserve their topological properties under rigid transformations. We consider the two most common digital topology models, namely dual adjacency and well-composedness. This paper leads to the proposal of optimal preprocessing strategies that ensure the topological invariance of images under arbitrary rigid transformations. These results and methods are proved to be valid for various kinds of images (binary, gray-level, label), thus providing generic and efficient tools, which can be used in particular in the context of image registration and warping. PMID:26270925
Novel signal shape descriptors through wavelet transforms and dimensionality reduction
NASA Astrophysics Data System (ADS)
Hughes, Nicholas P.; Tarassenko, Lionel
2003-11-01
The wavelet transform is a powerful tool for capturing the joint time-frequency characteristics of a signal. However, the resulting wavelet coefficients are typically high-dimensional, since at each time sample the wavelet transform is evaluated at a number of distinct scales. Unfortunately, modelling these coefficients can be problematic because of the large number of parameters needed to capture the dependencies between different scales. In this paper we investigate the use of algorithms from the field of dimensionality reduction to extract informative and compact descriptions of shape from wavelet coefficients. These low-dimensional shape descriptors lead to models that are governed by only a small number of parameters and can be learnt successfully from limited amounts of data. The validity of our approach is demonstrated on the task of automatically segmenting an electrocardiogram signal into its constituent waveform features.
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
NASA Astrophysics Data System (ADS)
Hu, Li-Yun; Fan, Hong-Yi
2010-07-01
In a preceding letter (2007 Opt. Lett. 32 554) we propose complex continuous wavelet transforms and found Laguerre-Gaussian mother wavelets family. In this work we present the inversion formula and Parseval theorem for complex continuous wavelet transform by virtue of the entangled state representation, which makes the complex continuous wavelet transform theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.
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.
Color graph based wavelet transform with perceptual information
NASA Astrophysics Data System (ADS)
Malek, Mohamed; Helbert, David; Carré, Philippe
2015-09-01
We propose a numerical strategy to define a multiscale analysis for color and multicomponent images based on the representation of data on a graph. Our approach consists of computing the graph of an image using the psychovisual information and analyzing it by using the spectral graph wavelet transform. We suggest introducing color dimension into the computation of the weights of the graph and using the geodesic distance as a mean of distance measurement. We thus have defined a wavelet transform based on a graph with perceptual information by using the CIELab color distance. This new representation is illustrated with denoising and inpainting applications. Overall, by introducing psychovisual information in the graph computation for the graph wavelet transform, we obtain very promising results. Thus, results in image restoration highlight the interest of the appropriate use of color information.
Using wavelet transforms in gearbox vibration monitoring data
Badi, M.N.M.; Engin, S.N.; Esat, I.I.
1996-12-31
Gearbox vibration signals are composed of transient changes and they are non-stationary (i.e. their spectra change with time). In a mechanical system consisting of various rotating parts, different components contribute to the overall vibration signals at different times and with different levels. Thus, if a signal analysis method used as an alternative to the standard methods can localize the information on the time axis, it can be possible to determine the approximate location of the fault or damage. Hence further techniques have to be developed such that the localized information in the time domain can be mapped to the frequency domain. Wavelet transforms which is an adjustable windowed analysis method have been used to compensate for the inadequate information provided by other signal analysis methods used before. In order to get more meaningful interpretation of the data mean-square wavelet contour maps were used. These maps show how the mean-square value of the signal is distributed between wavelet levels. Mesh diagrams are then generated for those maps for two different types of wavelet transforms which are dilation wavelets and harmonic wavelets.
Video text localization using wavelet and shearlet transforms
NASA Astrophysics Data System (ADS)
Banerjee, Purnendu; Chaudhuri, B. B.
2013-12-01
Text in video is useful and important in indexing and retrieving the video documents efficiently and accurately. In this paper, we present a new method of text detection using a combined dictionary consisting of wavelets and a recently introduced transform called shearlets. Wavelets provide optimally sparse expansion for point-like structures and shearlets provide optimally sparse expansions for curve-like structures. By combining these two features we have computed a high frequency sub-band to brighten the text part. Then K-means clustering is used for obtaining text pixels from the Standard Deviation (SD) of combined coefficient of wavelets and shearlets as well as the union of wavelets and shearlets features. Text parts are obtained by grouping neighboring regions based on geometric properties of the classified output frame of unsupervised K-means classification. The proposed method tested on a standard as well as newly collected database shows to be superior to some of the existing methods.
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
Doppler radar fall activity detection using the wavelet transform.
Su, Bo Yu; Ho, K C; Rantz, Marilyn J; Skubic, Marjorie
2015-03-01
We propose in this paper the use of Wavelet transform (WT) to detect human falls using a ceiling mounted Doppler range control radar. The radar senses any motions from falls as well as nonfalls due to the Doppler effect. The WT is very effective in distinguishing the falls from other activities, making it a promising technique for radar fall detection in nonobtrusive inhome elder care applications. The proposed radar fall detector consists of two stages. The prescreen stage uses the coefficients of wavelet decomposition at a given scale to identify the time locations in which fall activities may have occurred. The classification stage extracts the time-frequency content from the wavelet coefficients at many scales to form a feature vector for fall versus nonfall classification. The selection of different wavelet functions is examined to achieve better performance. Experimental results using the data from the laboratory and real inhome environments validate the promising and robust performance of the proposed detector. PMID:25376033
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.
Compressed-domain video segmentation using wavelet transformation
NASA Astrophysics Data System (ADS)
Yu, Hong H.
1999-10-01
Video segmentation is an important first step towards automatic video indexing, retrieval, editing, and etc. However, the 'large' property of video makes it hard to handle in real time. To fulfill the goal of real-time processing, several factors need to be considered. First of all, indexing video directly in the compressed-domain offers the advantages of fast processing upon efficient storage. Secondly, extracting simple features with fast algorithms is no doubt helpful in speeding up the process. The questions are what kind of simple feature can characterize the changing statistics and what kind of algorithm can provide such feature with fast executability. In this paper, we propose a new automatic video segmentation scheme that utilizes wavelet transformation based on the following consideration: wavelet is a nice tool for subband decomposition, it encodes both frequency and spatial information; more over, it is easy to program and fast to execute. In the last decade or so, wavelet transform is emerged to image/video signal processing for analyzing functions at different levels of details. In particular, wavelet, as a tool, has been widely used in the area of image compression. In image compression, it is possible to recover a fairly accurate representation of the image by saving the few largest wavelet coefficients (and throwing away part or all of the smaller coefficients). By using this property, we extract a discrimination signature of each image from a few large coefficients for each color channel. The system works on the compressed video that does not require full decoding of the video and performs a wavelet transformation on the extracted video data. The signature (as feature) is extracted from the wavelet coefficients to characterize the changing statistics of shot transitions. Cuts, fades, and dissolve are detected based on the analysis of the changing statistics curve.
Iterative image coding with overcomplete complex wavelet transforms
NASA Astrophysics Data System (ADS)
Kingsbury, Nick G.; Reeves, Tanya
2003-06-01
Overcomplete transforms, such as the Dual-Tree Complex Wavelet Transform, can offer more flexible signal representations than critically-sampled transforms such as the Discrete Wavelet Transform. However the process of selecting the optimal set of coefficients to code is much more difficult because many different sets of transform coefficients can represent the same decoded image. We show that large numbers of transform coefficients can be set to zero without much reconstruction quality loss by forcing compensatory changes in the remaining coefficients. We develop a system for achieving these coding aims of coefficient elimination and compensation, based on iterative projection of signals between the image domain and transform domain with a non-linear process (e.g.~centre-clipping or quantization) applied in the transform domain. The convergence properties of such non-linear feedback loops are discussed and several types of non-linearity are proposed and analyzed. The compression performance of the overcomplete scheme is compared with that of the standard Discrete Wavelet Transform, both objectively and subjectively, and is found to offer advantages of up to 0.65 dB in PSNR and significant reduction in visibility of some types of coding artifacts.
Optical asymmetric image encryption using gyrator wavelet transform
NASA Astrophysics Data System (ADS)
Mehra, Isha; Nishchal, Naveen K.
2015-11-01
In this paper, we propose a new optical information processing tool termed as gyrator wavelet transform to secure a fully phase image, based on amplitude- and phase-truncation approach. The gyrator wavelet transform constitutes four basic parameters; gyrator transform order, type and level of mother wavelet, and position of different frequency bands. These parameters are used as encryption keys in addition to the random phase codes to the optical cryptosystem. This tool has also been applied for simultaneous compression and encryption of an image. The system's performance and its sensitivity to the encryption parameters, such as, gyrator transform order, and robustness has also been analyzed. It is expected that this tool will not only update current optical security systems, but may also shed some light on future developments. The computer simulation results demonstrate the abilities of the gyrator wavelet transform as an effective tool, which can be used in various optical information processing applications, including image encryption, and image compression. Also this tool can be applied for securing the color image, multispectral, and three-dimensional images.
Detection of Orthoimage Mosaicking Seamlines by Means of Wavelet Transform
NASA Astrophysics Data System (ADS)
Pyka, K.
2016-06-01
The detection of orthoimage mosaicking seamlines by means of wavelet transform was examined. Radiometric alignment was omitted, giving priority to the issue of seamlines which bypass locations where there is a parallax between orthoimages. The importance of this issue is particularly relevant for images with very high resolution. In order to create a barrier image between orthoimages, the redundant wavelet transform variant known as MODWT-MRA was used. While more computationally complex than the frequently used DWT, it enables very good multiresolution edge detection. An IT prototype was developed on the basis of the described concept, and several cases of seamline detection were tested on the basis of data with a resolution of 10 cm to 1 m. The correct seamline location was obtained for each test case. This result opens the door to future expansion of the radiometric alignment method, which is also based on wavelets.
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.
NASA Astrophysics Data System (ADS)
Hou, Ying
2009-10-01
In this paper, a hyperspectral image lossy coder using three-dimensional Embedded ZeroBlock Coding (3D EZBC) algorithm based on Karhunen-Loève transform (KLT) and wavelet transform (WT) is proposed. This coding scheme adopts 1D KLT as spectral decorrelator and 2D WT as spatial decorrelator. Furthermore, the computational complexity and the coding performance of the low-complexity KLT are compared and evaluated. In comparison with several stateof- the-art coding algorithms, experimental results indicate that our coder can achieve better lossy compression performance.
NASA Astrophysics Data System (ADS)
Wang, Chun-Hsiung; Hsu, Kuan-Yu; Lee, Chih-Kung
2016-03-01
A real-time three-dimensional surface profile metrology system was implemented by integrating Fourier Transform (FT) based algorithms to convert interference intensity fringes to wrapped frequency phase maps and then to unwrapped phase maps. The revival of this field can find its roots in recognizing the development of high-resolution high-speed CCD/CMOS over the years. Two-dimensional Continuous Wavelet Transform (2D-CWT), which possesses the ability to construct daughter wavelets of good time and frequency localization according to different fringes conditions from a characteristic mother wavelet, was implemented with an attempt to reduce redundant fitting process of ordinary Short Time Fourier Transform (STFT), also known as Windowed Fourier Transform (WFT), and therefore to accelerate the FT-related algorithms needed. Implemented with the efficient wavelet construction process by using 2D-CWT, Electronic Speckle Pattern Interferometer (ESPI) was adopted to take advantage of this new process. Different from using several phase shifting steps before to solve the direction ambiguity, which takes time to capture multiple intensity maps during measurement, the phase maps needed were retrieved from a single frame interference fringes. It is to be noted that this one-image interference fringe was captured by having a pre-introduced spatial carrier frequency embedded within the experimental setup so as to remove the directional ambiguity. 2D-CWT dealing with different signal-to-noise ratios was also designed by selecting wavelet parameters properly, which is expected to achieve higher accuracy and faster processing speed. For phase unwrapping, Poisson's equation with Neumann boundary condition was solved by using FFT. The benefit of using 2D-CWTs with different wavelets as compared to WFT was demonstrated experimentally.
Application of the wavelet transform for speech processing
NASA Technical Reports Server (NTRS)
Maes, Stephane
1994-01-01
Speaker identification and word spotting will shortly play a key role in space applications. An approach based on the wavelet transform is presented that, in the context of the 'modulation model,' enables extraction of speech features which are used as input for the classification process.
Wavelet steerability and the higher-order Riesz transform.
Unser, Michael; Van De Ville, Dimitri
2010-03-01
Our main goal in this paper is to set the foundations of a general continuous-domain framework for designing steerable, reversible signal transformations (a.k.a. frames) in multiple dimensions ( d >or= 2). To that end, we introduce a self-reversible, Nth-order extension of the Riesz transform. We prove that this generalized transform has the following remarkable properties: shift-invariance, scale-invariance, inner-product preservation, and steerability. The pleasing consequence is that the transform maps any primary wavelet frame (or basis) of [Formula: see text] into another "steerable" wavelet frame, while preserving the frame bounds. The concept provides a functional counterpart to Simoncelli's steerable pyramid whose construction was primarily based on filterbank design. The proposed mechanism allows for the specification of wavelets with any order of steerability in any number of dimensions; it also yields a perfect reconstruction filterbank algorithm. We illustrate the method with the design of a novel family of multidimensional Riesz-Laplace wavelets that essentially behave like the N th-order partial derivatives of an isotropic Gaussian kernel. PMID:20031498
A Secret Image Sharing Method Using Integer Wavelet Transform
NASA Astrophysics Data System (ADS)
Huang, Chin-Pan; Li, Ching-Chung
2007-12-01
A new image sharing method, based on the reversible integer-to-integer (ITI) wavelet transform and Shamir's [InlineEquation not available: see fulltext.] threshold scheme is presented, that provides highly compact shadows for real-time progressive transmission. This method, working in the wavelet domain, processes the transform coefficients in each subband, divides each of the resulting combination coefficients into [InlineEquation not available: see fulltext.] shadows, and allows recovery of the complete secret image by using any [InlineEquation not available: see fulltext.] or more shadows [InlineEquation not available: see fulltext.]. We take advantages of properties of the wavelet transform multiresolution representation, such as coefficient magnitude decay and excellent energy compaction, to design combination procedures for the transform coefficients and processing sequences in wavelet subbands such that small shadows for real-time progressive transmission are obtained. Experimental results demonstrate that the proposed method yields small shadow images and has the capabilities of real-time progressive transmission and perfect reconstruction of secret images.
High Speed 2D Hadamard Transform Spectral Imager
WEHLBURG, JOSEPH C.; WEHLBURG, CHRISTINE M.; SMITH, JODY L.; SPAHN, OLGA B.; SMITH, MARK W.; BONEY, CRAIG M.
2003-02-01
Hadamard Transform Spectrometer (HTS) approaches share the multiplexing advantages found in Fourier transform spectrometers. Interest in Hadamard systems has been limited due to data storage/computational limitations and the inability to perform accurate high order masking in a reasonable amount of time. Advances in digital micro-mirror array (DMA) technology have opened the door to implementing an HTS for a variety of applications including fluorescent microscope imaging and Raman imaging. A Hadamard transform spectral imager (HTSI) for remote sensing offers a variety of unique capabilities in one package such as variable spectral and temporal resolution, no moving parts (other than the micro-mirrors) and vibration tolerance. Two approaches to for 2D HTS systems have been investigated in this LDRD. The first approach involves dispersing the incident light, encoding the dispersed light then recombining the light. This method is referred to as spectral encoding. The other method encodes the incident light then disperses the encoded light. The second technique is called spatial encoding. After creating optical designs for both methods the spatial encoding method was selected as the method that would be implemented because the optical design was less costly to implement.
Bayesian Wavelet Shrinkage of the Haar-Fisz Transformed Wavelet Periodogram
2015-01-01
It is increasingly being realised that many real world time series are not stationary and exhibit evolving second-order autocovariance or spectral structure. This article introduces a Bayesian approach for modelling the evolving wavelet spectrum of a locally stationary wavelet time series. Our new method works by combining the advantages of a Haar-Fisz transformed spectrum with a simple, but powerful, Bayesian wavelet shrinkage method. Our new method produces excellent and stable spectral estimates and this is demonstrated via simulated data and on differenced infant electrocardiogram data. A major additional benefit of the Bayesian paradigm is that we obtain rigorous and useful credible intervals of the evolving spectral structure. We show how the Bayesian credible intervals provide extra insight into the infant electrocardiogram data. PMID:26381141
Bayesian Wavelet Shrinkage of the Haar-Fisz Transformed Wavelet Periodogram.
Nason, Guy; Stevens, Kara
2015-01-01
It is increasingly being realised that many real world time series are not stationary and exhibit evolving second-order autocovariance or spectral structure. This article introduces a Bayesian approach for modelling the evolving wavelet spectrum of a locally stationary wavelet time series. Our new method works by combining the advantages of a Haar-Fisz transformed spectrum with a simple, but powerful, Bayesian wavelet shrinkage method. Our new method produces excellent and stable spectral estimates and this is demonstrated via simulated data and on differenced infant electrocardiogram data. A major additional benefit of the Bayesian paradigm is that we obtain rigorous and useful credible intervals of the evolving spectral structure. We show how the Bayesian credible intervals provide extra insight into the infant electrocardiogram data. PMID:26381141
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.
Sequential damage detection based on the continuous wavelet transform
NASA Astrophysics Data System (ADS)
Liao, Yizheng; Balafas, Konstantinos; Rajagopal, Ram; Kiremidjian, Anne S.
2015-03-01
This paper presents a sequential structural damage detection algorithm that is based on a statistical model for the wavelet transform of the structural responses. The detector uses the coefficients of the wavelet model and does not require prior knowledge of the structural properties. Principal Component Analysis is applied to select and extract the most sensitive features from the wavelet coefficients as the damage sensitive features. The damage detection algorithm is validated using the simulation data collected from a four-story steel moment frame. Various features have been explored and the detection algorithm was able to identify damage. Additionally, we show that for a desired probability of false alarm, the proposed detector is asymptotically optimal on the expected delay.
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.
Analysis of Tibet NM Data with Wavelet Transform Method
NASA Astrophysics Data System (ADS)
Tang, Y. Q.; Lu, H.; Hu H. B.; Tan, Y. H.; Zhang, J. L.; Le, G. M.; Labaciren; Meng, X. R.; Yuan, A. F.; Miyasaka, H.; Shimoda, S.; Yamada, Sakamoto, E.; Munakata, K.; Yuda, T.; Tibet NM Collaboration
2003-07-01
The China-Japan coop erative Tibet neutron monitor(90.53°E,30.11° N,4300 m a.s.l.)b egan to work in October 1998.Now we have about 4 years data covering the 23rd solar maximum period.This is a work on correlative study of solar activity and cosmic ray intensity(CRI) by means of wavelet transform method,which is more sensitive to detect sharp variation points of CRI than Fourier transform method,these points represent modulation to cosmic rays of solar activities,esp ecially CME, which is thought as the main source of geomagnetic storm. After analysis,we find that CRI can provide some precursory imformation of CME.So CRI data can predict geomagnetic storm by wavelet transform analysis.
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.
Evaluating Interpersonal Synchrony: Wavelet Transform Toward an Unstructured Conversation
Fujiwara, Ken; Daibo, Ikuo
2016-01-01
This study examined whether interpersonal synchrony could be extracted using spectrum analysis (i.e., wavelet transform) in an unstructured conversation. Sixty-two female undergraduates were randomly paired and they engaged in a 6-min unstructured conversation. Interpersonal synchrony was evaluated by calculating the cross-wavelet coherence of the time-series movement data, extracted using a video-image analysis software. The existence of synchrony was tested using a pseudo-synchrony paradigm. In addition, the frequency at which the synchrony occurred and the distribution of the relative phase was explored. The results showed that the value of cross-wavelet coherence was higher in the experimental participant pairs than in the pseudo pairs. Further, the coherence value was higher in the frequency band under 0.5 Hz. These results support the validity of evaluating interpersonal synchron Behavioral mimicry and interpersonal syyby using wavelet transform even in an unstructured conversation. However, the role of relative phase was not clear; there was no significant difference between each relative-phase region. The theoretical contribution of these findings to the area of interpersonal coordination is discussed. PMID:27148125
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
Damage Identification in Beam Structure using Spatial Continuous Wavelet Transform
NASA Astrophysics Data System (ADS)
Janeliukstis, R.; Rucevskis, S.; Wesolowski, M.; Kovalovs, A.; Chate, A.
2015-11-01
In this paper the applicability of spatial continuous wavelet transform (CWT) technique for damage identification in the beam structure is analyzed by application of different types of wavelet functions and scaling factors. The proposed method uses exclusively mode shape data from the damaged structure. To examine limitations of the method and to ascertain its sensitivity to noisy experimental data, several sets of simulated data are analyzed. Simulated test cases include numerical mode shapes corrupted by different levels of random noise as well as mode shapes with different number of measurement points used for wavelet transform. A broad comparison of ability of different wavelet functions to detect and locate damage in beam structure is given. Effectiveness and robustness of the proposed algorithms are demonstrated experimentally on two aluminum beams containing single mill-cut damage. The modal frequencies and the corresponding mode shapes are obtained via finite element models for numerical simulations and by using a scanning laser vibrometer with PZT actuator as vibration excitation source for the experimental study.
Noise reduction in ultrasonic NDT using undecimated wavelet transforms.
Pardo, E; San Emeterio, J L; Rodriguez, M A; Ramos, A
2006-12-22
Translation-invariant wavelet processing is applied to grain noise reduction in ultrasonic non-destructive testing of materials. In particular, the undecimated wavelet transform (UWT), which is essentially a discrete wavelet transform (DWT) that avoids decimation, is used. Two different UWT processors have been specifically developed for that purpose, based on two UWT implementation schemes: the "à trous" algorithm and the cycle-spinning scheme. The performance of these two UWT processors is compared with that of a classical DWT processor, by using synthetic grain noise registers and experimental pulse-echo NDT traces. The synthetic ultrasonic traces have been generated by an own-developed frequency-domain model that includes frequency dependence in both material attenuation and scattering. The experimental ultrasonic traces have been obtained by inspecting a piece of carbon-fiber reinforced plastic composite in which we have mechanized artificial flaws. Decomposition level-dependent thresholds, which are suitable for correlated noise, are specifically determined in all cases. Soft thresholding, Daubechies db6 mother wavelet and the three well-known threshold selection rules, Universal, Minimax and SURE, are applied to the different decomposition levels. The performance of the different de-noising procedures for single echo detection has been comparatively evaluated in terms of signal-to-noise ratio enhancement. PMID:16797651
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
On the determination of box dimensions by means of wavelet transforms
Rasmussen, H.O. )
1993-05-01
Wavelet transforms decompose square-integrable functions in terms of translated and scaled versions of an [open quotes]analyzing wavelet,[close quotes] a square-integrable function. The wavelet coefficients used for this decomposition are formed by convoluting the original function with translated and scaled versions of the analyzing wavelet. In this work, sufficient conditions are established for the determination of box dimensions of graphs from the decrease of the corresponding wavelet transforms. As an application, wavelet Weierstrass functions are constructed. 10 refs.
Missile flutter experiment and data analysis using wavelet transform
NASA Astrophysics Data System (ADS)
Yu, Kaiping; Ye, Jiyuan; Zou, Jingxiang; Yang, Bingyuan; Yang, Hua
2004-01-01
A modal parameter identification method of impulse response function, based on a modulated Gaussian wavelet transform, is presented. The factors influencing the identification accuracy and the required conditions of using this parameter identification method are discussed. Numerical verification of the proposed method is presented for several two-degree-of-freedom examples. A wind tunnel flutter experiment on a wing model of missiles is introduced. The data set from the flutter test is analyzed by using the proposed wavelet transform method. The first two order modal parameters of the wing model are identified, and then the critical dynamic stress is predicted by using the flutter stability parameter method. Finally, the results are compared with the results of FFT analysis.
Structural transformation in monolayer materials: a 2D to 1D transformation.
Momeni, Kasra; Attariani, Hamed; LeSar, Richard A
2016-07-20
Reducing the dimensions of materials to atomic scales results in a large portion of atoms being at or near the surface, with lower bond order and thus higher energy. At such scales, reduction of the surface energy and surface stresses can be the driving force for the formation of new low-dimensional nanostructures, and may be exhibited through surface relaxation and/or surface reconstruction, which can be utilized for tailoring the properties and phase transformation of nanomaterials without applying any external load. Here we used atomistic simulations and revealed an intrinsic structural transformation in monolayer materials that lowers their dimension from 2D nanosheets to 1D nanostructures to reduce their surface and elastic energies. Experimental evidence of such transformation has also been revealed for one of the predicted nanostructures. Such transformation plays an important role in bi-/multi-layer 2D materials. PMID:27388501
Multisensensor Multitemporal Data Fusion Using Wavelet Transform
NASA Astrophysics Data System (ADS)
Ghannam, S.; Awadallah, M.; Abbott, A. L.; Wynne, R. H.
2014-11-01
Interest in data fusion, for remote-sensing applications, continues to grow due to the increasing importance of obtaining data in high resolution both spatially and temporally. Applications that will benefit from data fusion include ecosystem disturbance and recovery assessment, ecological forecasting, and others. This paper introduces a novel spatiotemporal fusion approach, the wavelet-based Spatiotemporal Adaptive Data Fusion Model (WSAD-FM). This new technique is motivated by the popular STARFM tool, which utilizes lower-resolution MODIS imagery to supplement Landsat scenes using a linear model. The novelty of WSAD-FM is twofold. First, unlike STARFM, this technique does not predict an entire new image in one linear step, but instead decomposes input images into separate "approximation" and "detail" parts. The different portions are fed into a prediction model that limits the effects of linear interpolation among images. Low-spatial-frequency components are predicted by a weighted mixture of MODIS images and low-spatial-frequency components of Landsat images that are neighbors in the temporal domain. Meanwhile, high-spatialfrequency components are predicted by a weighted average of high-spatial-frequency components of Landsat images alone. The second novelty is that the method has demonstrated good performance using only one input Landsat image and a pair of MODIS images. The technique has been tested using several Landsat and MODIS images for a study area from Central North Carolina (WRS-2 path/row 16/35 in Landsat and H/V11/5 in MODIS), acquired in 2001. NDVI images that were calculated from the study area were used as input to the algorithm. The technique was tested experimentally by predicting existing Landsat images, and we obtained R2 values in the range 0.70 to 0.92 for estimated Landsat images in the red band, and 0.62 to 0.89 for estimated NDVI images.
Remote Sensing Image Fusion Using Ica and Optimized Wavelet Transform
NASA Astrophysics Data System (ADS)
Hnatushenko, V. V.; Vasyliev, V. V.
2016-06-01
In remote-sensing image processing, fusion (pan-sharpening) is a process of merging high-resolution panchromatic and lower resolution multispectral (MS) imagery to create a single high-resolution color image. Many methods exist to produce data fusion results with the best possible spatial and spectral characteristics, and a number have been commercially implemented. However, the pan-sharpening image produced by these methods gets the high color distortion of spectral information. In this paper, to minimize the spectral distortion we propose a remote sensing image fusion method which combines the Independent Component Analysis (ICA) and optimization wavelet transform. The proposed method is based on selection of multiscale components obtained after the ICA of images on the base of their wavelet decomposition and formation of linear forms detailing coefficients of the wavelet decomposition of images brightness distributions by spectral channels with iteratively adjusted weights. These coefficients are determined as a result of solving an optimization problem for the criterion of maximization of information entropy of the synthesized images formed by means of wavelet reconstruction. Further, reconstruction of the images of spectral channels is done by the reverse wavelet transform and formation of the resulting image by superposition of the obtained images. To verify the validity, the new proposed method is compared with several techniques using WorldView-2 satellite data in subjective and objective aspects. In experiments we demonstrated that our scheme provides good spectral quality and efficiency. Spectral and spatial quality metrics in terms of RASE, RMSE, CC, ERGAS and SSIM are used in our experiments. These synthesized MS images differ by showing a better contrast and clarity on the boundaries of the "object of interest - the background". The results show that the proposed approach performs better than some compared methods according to the performance metrics.
Classification of Transient Phenomena in Distribution System using wavelet Transform
NASA Astrophysics Data System (ADS)
Sedighi, Alireza
2014-05-01
An efficient procedure for classification of transient phenomena in distribution systems is proposed in this paper. The proposed method has been applied to classify some transient phenomena such as inrush current, load switching, capacitor switching and single phase to ground fault. The new scheme is based on wavelet transform algorithm. All of the events for feature extraction and test are simulated using Electro Magnetic Transient Program (EMTP). Results show high accuracy of proposed method.
Addison, Paul S
2015-08-01
A novel method of identifying stable phase coupling behavior of two signals within the wavelet transform time-frequency plane is presented. The technique employs the cross-wavelet transform to provide a map of phase coupling followed by synchrosqueezing to collect the stable phase regime information. The resulting synchrosqueezed cross-wavelet transform method (Synchro-CrWT) is illustrated using a synthetic signal and then applied to the analysis of the relationship between biosignals used in the analysis of cerebral autoregulation function. PMID:26737649
Low-memory-usage image coding with line-based wavelet transform
NASA Astrophysics Data System (ADS)
Ye, Linning; Guo, Jiangling; Nutter, Brian; Mitra, Sunanda
2011-02-01
When compared to the traditional row-column wavelet transform, the line-based wavelet transform can achieve significant memory savings. However, the design of an image codec using the line-based wavelet transform is an intricate task because of the irregular order in which the wavelet coefficients are generated. The independent block coding feature of JPEG2000 makes it work effectively with the line-based wavelet transform. However, with wavelet tree-based image codecs, such as set partitioning in hierarchical trees, the memory usage of the codecs does not realize significant advantage with the line-based wavelet transform because many wavelet coefficients must be buffered before the coding starts. In this paper, the line-based wavelet transform was utilized to facilitate backward coding of wavelet trees (BCWT). Although the BCWT algorithm is a wavelet tree-based algorithm, its coding order differs from that of the traditional wavelet tree-based algorithms, which allows the proposed line-based image codec to become more memory efficient than other line-based image codecs, including line-based JPEG2000, while still offering comparable rate distortion performance and much lower system complexity.
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
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.
Automated transformation-invariant shape recognition through wavelet multiresolution
NASA Astrophysics Data System (ADS)
Brault, Patrice; Mounier, Hugues
2001-12-01
We present here new results in Wavelet Multi-Resolution Analysis (W-MRA) applied to shape recognition in automatic vehicle driving applications. Different types of shapes have to be recognized in this framework. They pertain to most of the objects entering the sensors field of a car. These objects can be road signs, lane separation lines, moving or static obstacles, other automotive vehicles, or visual beacons. The recognition process must be invariant to global, affine or not, transformations which are : rotation, translation and scaling. It also has to be invariant to more local, elastic, deformations like the perspective (in particular with wide angle camera lenses), and also like deformations due to environmental conditions (weather : rain, mist, light reverberation) or optical and electrical signal noises. To demonstrate our method, an initial shape, with a known contour, is compared to the same contour altered by rotation, translation, scaling and perspective. The curvature computed for each contour point is used as a main criterion in the shape matching process. The original part of this work is to use wavelet descriptors, generated with a fast orthonormal W-MRA, rather than Fourier descriptors, in order to provide a multi-resolution description of the contour to be analyzed. In such way, the intrinsic spatial localization property of wavelet descriptors can be used and the recognition process can be speeded up. The most important part of this work is to demonstrate the potential performance of Wavelet-MRA in this application of shape recognition.
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)
Harikumar, Rajaguru; Vijayakumar, Thangavel
2014-12-01
The objective of this paper is to compare the performance of singular value decomposition (SVD), expectation maximization (EM), and modified expectation maximization (MEM) as the postclassifiers for classifications of the epilepsy risk levels obtained from extracted features through wavelet transforms and morphological filters from electroencephalogram (EEG) signals. The code converter acts as a level one classifier. The seven features such as energy, variance, positive and negative peaks, spike and sharp waves, events, average duration, and covariance are extracted from EEG signals. Out of which four parameters like positive and negative peaksand spike and sharp waves, events and average duration are extracted using Haar, dB2, dB4, and Sym 8 wavelet transforms with hard and soft thresholding methods. The above said four features are also extracted through morphological filters. Then, the performance of the code converter and classifiers are compared based on the parameters such as performance index (PI) and quality value (QV).The performance index and quality value of code converters are at low value of 33.26% and 12.74, respectively. The highest PI of 98.03% and QV of 23.82 are attained at dB2 wavelet with hard thresholding method for SVD classifier. All the postclassifiers are settled at PI value of more than 90% at QV of 20.
Wavelet transform analysis of chromatin texture changes during heat shock.
Herbomel, G; Grichine, A; Fertin, A; Delon, A; Vourc'h, C; Souchier, C; Usson, Y
2016-06-01
Texture analysis can be a useful tool to investigate the organization of chromatin. Approaches based on multiscale analysis and in particular the 'à trou' wavelet analysis has already been used for microscopy (Olivo Marin). In order to analyse texture changes, the statistical properties of the wavelet coefficient images were summarized by the first four statistical orders: mean, standard deviation, skewness and kurtosis of the coefficient image histogram. The 'à trou' transform provided a representation of the wavelet coefficients and texture parameters with the same statistical robustness throughout the scale spaces. It was applied for quantifying chromatin texture and heat-induced chromatin changes in living cells. We investigated the changes by both laser scanning and spinning disk confocal microscopies and compared the texture parameters before and after increasing duration of heat shock exposure (15 min, 30 min and 1 h). Furthermore, as activation of the heat shock response also correlates with a rapid localization of HSF1 within a few nuclear structures termed nuclear stress bodies (nSBs), we compared the dynamics of nSBs formation with that of textural changes during 1 h of continuous heat shock. Next, we studied the recovery phase following a 1-h heat shock. Significant differences were observed, particularly affecting the perinucleolar region, even for the shortest heat shock time affecting mostly the skewness and standard deviation. Furthermore, progressive changes could be observed according to the duration of heat shock, mostly affecting fine details (pixel-wise changes) as revealed by the parameters, obtained from the first- and second-order wavelet coefficients. 'A trou' wavelet texture analysis provided a sensitive and efficient tool to investigate minute changes of chromatin. PMID:26694695
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.
Elastic Wave Propagation in Concrete and Continuous Wavelet Transform
Chiang, C.-H.; Gi, Y.-F.; Pan, C.-L.; Cheng, C.-C.
2005-04-09
Elastic wave methods, such as the ultrasonic pulse velocity and the impact echo, are often subject to multiple reflections at the boundaries of various constituents of concrete. Current study aims to improve the feature identification of elastic wave propagation due to buried objects in concrete slabs and cylinders. Embedded steel reinforcement, steel and PVC tubes, wooden disks, and rubber spheres are tested. The received signals are analyzed using continuous wavelet transform. As a result, signals are decomposed into distinctive frequency bands with transient information preserved. The interpretation of multiple reflections at different boundary conditions thus becomes more straightforward. Features related to reflections from steel bar, PVC tube, and steel tube can be readily identified in the magnitude plot of wavelet coefficients. Vibration modes of the concrete slab corresponding to different buried objects can also be separated based on corresponding time duration.
Elastic Wave Propagation in Concrete and Continuous Wavelet Transform
NASA Astrophysics Data System (ADS)
Chiang, Chih-Hung; Gi, Yu-Fung; Pan, Chi-Ling; Cheng, Chia-Chi
2005-04-01
Elastic wave methods, such as the ultrasonic pulse velocity and the impact echo, are often subject to multiple reflections at the boundaries of various constituents of concrete. Current study aims to improve the feature identification of elastic wave propagation due to buried objects in concrete slabs and cylinders. Embedded steel reinforcement, steel and PVC tubes, wooden disks, and rubber spheres are tested. The received signals are analyzed using continuous wavelet transform. As a result, signals are decomposed into distinctive frequency bands with transient information preserved. The interpretation of multiple reflections at different boundary conditions thus becomes more straightforward. Features related to reflections from steel bar, PVC tube, and steel tube can be readily identified in the magnitude plot of wavelet coefficients. Vibration modes of the concrete slab corresponding to different buried objects can also be separated based on corresponding time duration.
Dating the age of admixture via wavelet transform analysis of genome-wide data.
Pugach, Irina; Matveyev, Rostislav; Wollstein, Andreas; Kayser, Manfred; Stoneking, Mark
2011-01-01
We describe a PCA-based genome scan approach to analyze genome-wide admixture structure, and introduce wavelet transform analysis as a method for estimating the time of admixture. We test the wavelet transform method with simulations and apply it to genome-wide SNP data from eight admixed human populations. The wavelet transform method offers better resolution than existing methods for dating admixture, and can be applied to either SNP or sequence data from humans or other species. PMID:21352535
Dating the age of admixture via wavelet transform analysis of genome-wide data
2011-01-01
We describe a PCA-based genome scan approach to analyze genome-wide admixture structure, and introduce wavelet transform analysis as a method for estimating the time of admixture. We test the wavelet transform method with simulations and apply it to genome-wide SNP data from eight admixed human populations. The wavelet transform method offers better resolution than existing methods for dating admixture, and can be applied to either SNP or sequence data from humans or other species. PMID:21352535
Sensor signals monitoring and control using wavelets transform representation algorithm
NASA Astrophysics Data System (ADS)
Paul, Okuwobi I.; Lu, Yonghua
2015-03-01
The usefulness of wavelet transforms has been compared and contrasted to Fourier transforms. Most importantly, wavelets transform provide a much needed alternative to Fourier transform for certain application such as pattern based monitoring and control. Effort has been made to provide a technique to extract essential trends from process signals and provide a compact representation. The effectiveness of a signal processing technique depends to a large extent on the nature of the signals involved. On technique that works for specific signal trends might not be effective in dealing with other signal trends. More so in pre-processing stage, signal extension has been identified as the critical factor influencing signal representation and retention of trends. This paper introduce a new algorithm in solving the present problems in sensor signal monitoring and control. The New Extension Technique (NET) was introduced, which provide an accurate wavelet decomposition irrespective of the nature of the signal. This method uses a statistical approach to provide a good approximation of the signal outside the boundaries of the signal depending on signal trends at the boundaries. Different statistical approaches were adopted for this purpose and four new extension methods were also introduced in order to ascertain which extension methods provide a reliable extension for all cases. The concept behind these methods is the same, since the signal samples close to the boundary are considered and a mean value is determined. The procedure for determining this mean value differs for each of these four methods; NET A, NET B, NET C, and NET D. The signal is then extended by making it symmetric with respect to that mean value and then inverting it.
Fusion of PET and CT images using wavelet transform.
Shalchian, Bahareh; Rajabi, Hossein; Soltanian-zadeh, Hamid
2009-01-01
While information about anatomy is available in CT images, information about physiology and metabolism is available in PET images. To integrate both information, the two images are fused. Image fusion methods include simple methods like pixel averaging and sophisticated methods like wavelet transformation. An advantage of using wavelet transformation is that it preserves significant parts of each image. After creating lesions of 10, 8, 6 mm in a NURBS (non-uniform rational B-splines) based cardiac torso (NCAT) phantom, PET images were simulated using SimSET simulator. Attenuation maps of the activity phantom were used as CT images. Each of the PET and CT images was divided into an approximation image and three detailed images by the wavelet transform. The corresponding transformed images generated from the PET and CT images were fused in nine different ways to generate composite images, which were compared to the original images. The basis of comparison is the lesion-to-tissue contrast in the fused image in comparison to the lesion-to-tissue contrast in the original PET and CT images. Our results showed that except for one method, the lesion-to-tissue contrast in the fused image was higher than that of the CT images. In the first six methods, the lesion-to-tissue contrast in the fused image was less than the contrast, in the PET image. In the other three methods, the contrast in the fused image was higher than in the PET image. This was true in cases of 10, 8, 6 mm lesions. In conclusion, we have show that the approximation image produced a better ultimate image and that the lesion-to-tissue contrast in the fused image was also better than that of the original PET and CT images. This is because the approximation image is comprised of fundamental information of the signal (low frequency) that directly affects the image contrast. PMID:19936335
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.
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
Quantum computation of multifractal exponents through the quantum wavelet transform
Garcia-Mata, Ignacio; Giraud, Olivier; Georgeot, Bertrand
2009-05-15
We study the use of the quantum wavelet transform to extract efficiently information about the multifractal exponents for multifractal quantum states. We show that, combined with quantum simulation algorithms, it enables to build quantum algorithms for multifractal exponents with a polynomial gain compared to classical simulations. Numerical results indicate that a rough estimate of fractality could be obtained exponentially fast. Our findings are relevant, e.g., for quantum simulations of multifractal quantum maps and of the Anderson model at the metal-insulator transition.
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.
CT image retrieval using dual tree complex wavelet packet transform
NASA Astrophysics Data System (ADS)
Kokare, Manesh
2010-02-01
In this paper, novel method based on Dual Tree Complex Wavelet Packet Transform (DT-CWPT) to analyze texture of Computer Tomography (CT) images and extract the corresponding feature vectors for content based medical image retrieval is proposed. This is mainly because of DT-CWPT characterizes textural property of CT images in better way. The feature vectors of CT images are extracted by measuring energy and standard deviation of DT-CWPT subband. These features are used to facilitate content based medical image retrieval (CBMIR).The proposed method outperforms than existing available methods.
Givehchi, Alireza; Bender, Andreas; Glen, Robert C
2006-01-01
The effect of multitarget dependent descriptor transformation on classification performance is explored in this work. To this end decision trees as well as neural net QSAR in combination with PLS were applied to predict the activity class of 5HT3 ligands, angiotensin converting enzyme inhibitors, 3-hydroxyl-3-methyl glutaryl coenzyme A reductase inhibitors, platelet activating factor antagonists, and thromboxane A2 antagonists. Physicochemical descriptors calculated by MOE and fragment-based descriptors (MOLPRINT 2D) were employed to generate descriptor vectors. In a subsequent step the physicochemical descriptor vectors were transformed to a lower dimensional space using multitarget dependent descriptor transformation. Cross-validation of the original physicochemical descriptors in combination with decision trees and neural net QSAR as well as cross-validation of PLS multitarget transformed descriptors with neural net QSAR were performed. For comparison this was repeated using fragment-based descriptors in combination with decision trees. PMID:16711727
NASA Astrophysics Data System (ADS)
Widjaja, Joewono
2015-11-01
A new method is proposed for recognizing noise corrupted low-contrast retinal images that employs joint wavelet transform correlator with compressed reference and target. Noise robustness is achieved by correlating wavelet-transformed retinal target and reference images. Simulation results show that besides being robust to noise, its recognition performance can become independent upon compression qualities when low spatial-frequency components of joint power spectrum are enhanced by appropriately dilated wavelet filter.
Measuring Heart Filling Propagation Velocity using the Cross Wavelet Transform
NASA Astrophysics Data System (ADS)
Niebel, Casandra; Ohara, Takahiro; Vlachos, Pavlos; Little, William
2011-11-01
During early diastole, a pressure gradient is formed across the mitral valve as the left ventricle (LV) relaxes, forcing blood from the left atrium into the LV. This process generates a rapid filling wave and creates an unsteady flow environment within the LV. A continuous wavelet transform is capable of dealing with non-stationary and noisy signals and is therefore ideal for measuring the wave speed of the early diastole rapid filling wave. This wave speed, or propagation velocity (Vp), is used clinically to evaluate diastolic function and is conventionally measured from a Color M-Mode (CMM) echocardiogram. A CMM scan gives a spatiotemporal map of the blood velocity in the left ventricle and is used to visualize flow patterns and manually measure the Vp. In this work, a moving cross wavelet transform is used to measure the phase shift between consecutive time steps in a CMM echocardiogram, providing a more robust and repeatable measurement of Vp, less sensitive to noise, aliasing boundaries, and user inputs.
Identification of formation interfaces by using wavelet and Fourier transforms
NASA Astrophysics Data System (ADS)
Mukherjee, Bappa; Srivardhan, V.; Roy, P. N. S.
2016-05-01
The identification of formation interfaces is of prime importance from well log data. The interfaces are not clearly discernible due to the presence of high and low frequency noise in the log response. Accurate bed boundary information is very crucial in hydrocarbon exploration and the problem has received considerable attention and many techniques have been proposed. Frequency spectrum based filtering techniques aids us in interpretation, but usually leads to inaccurate amplification of unwanted components of the log response. Wavelet transform is very effective in denoising the log response and can be carried out to filter low and high frequency components of signal. The use of Fourier and Wavelet transform in denoising the log data for obtaining formation interfaces is demonstrated in this work. The feasibility of the proposed technique is tested so that it can be used in the industry to decipher formation interfaces. The work flow is demonstrated by testing on wells belonging to the Upper Assam Basin, which are self-potential, gamma ray, and resistivity log responses.
Adaptive segmentation of wavelet transform coefficients for video compression
NASA Astrophysics Data System (ADS)
Wasilewski, Piotr
2000-04-01
This paper presents video compression algorithm suitable for inexpensive real-time hardware implementation. This algorithm utilizes Discrete Wavelet Transform (DWT) with the new Adaptive Spatial Segmentation Algorithm (ASSA). The algorithm was designed to obtain better or similar decompressed video quality in compare to H.263 recommendation and MPEG standard using lower computational effort, especially at high compression rates. The algorithm was optimized for hardware implementation in low-cost Field Programmable Gate Array (FPGA) devices. The luminance and chrominance components of every frame are encoded with 3-level Wavelet Transform with biorthogonal filters bank. The low frequency subimage is encoded with an ADPCM algorithm. For the high frequency subimages the new Adaptive Spatial Segmentation Algorithm is applied. It divides images into rectangular blocks that may overlap each other. The width and height of the blocks are set independently. There are two kinds of blocks: Low Variance Blocks (LVB) and High Variance Blocks (HVB). The positions of the blocks and the values of the WT coefficients belonging to the HVB are encoded with the modified zero-tree algorithms. LVB are encoded with the mean value. Obtained results show that presented algorithm gives similar or better quality of decompressed images in compare to H.263, even up to 5 dB in PSNR measure.
Remotely sensed image compression based on wavelet transform
NASA Technical Reports Server (NTRS)
Kim, Seong W.; Lee, Heung K.; Kim, Kyung S.; Choi, Soon D.
1995-01-01
In this paper, we present an image compression algorithm that is capable of significantly reducing the vast amount of information contained in multispectral images. The developed algorithm exploits the spectral and spatial correlations found in multispectral images. The scheme encodes the difference between images after contrast/brightness equalization to remove the spectral redundancy, and utilizes a two-dimensional wavelet transform to remove the spatial redundancy. the transformed images are then encoded by Hilbert-curve scanning and run-length-encoding, followed by Huffman coding. We also present the performance of the proposed algorithm with the LANDSAT MultiSpectral Scanner data. The loss of information is evaluated by PSNR (peak signal to noise ratio) and classification capability.
Electroencephalographic compression based on modulated filter banks and wavelet transform.
Bazán-Prieto, Carlos; Cárdenas-Barrera, Julián; Blanco-Velasco, Manuel; Cruz-Roldán, Fernando
2011-01-01
Due to the large volume of information generated in an electroencephalographic (EEG) study, compression is needed for storage, processing or transmission for analysis. In this paper we evaluate and compare two lossy compression techniques applied to EEG signals. It compares the performance of compression schemes with decomposition by filter banks or wavelet Packets transformation, seeking the best value for compression, best quality and more efficient real time implementation. Due to specific properties of EEG signals, we propose a quantization stage adapted to the dynamic range of each band, looking for higher quality. The results show that the compressor with filter bank performs better than transform methods. Quantization adapted to the dynamic range significantly enhances the quality. PMID:22255966
Hyperspectral image compression using bands combination wavelet transformation
NASA Astrophysics Data System (ADS)
Wang, Wenjie; Zhao, Zhongming; Zhu, Haiqing
2009-10-01
Hyperspectral imaging technology is the foreland of the remote sensing development in the 21st century and is one of the most important focuses of the remote sensing domain. Hyperspectral images can provide much more information than multispectral images do and can solve many problems which can't be solved by multispectral imaging technology. However this advantage is at the cost of massy quantity of data that brings difficulties of images' process, storage and transmission. Research on hyperspectral image compression method has important practical significance. This paper intends to do some improvement of the famous KLT-WT-2DSPECK (Karhunen-Loeve transform+ wavelet transformation+ two-dimensional set partitioning embedded block compression) algorithm and advances KLT + bands combination 2DWT + 2DSPECK algorithm. Experiment proves that this method is effective.
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.
Analysis of Satellite Drag Coefficient Based on Wavelet Transform
NASA Astrophysics Data System (ADS)
Liu, Wei; Wang, Ronglan; Liu, Siqing
Abstract: Drag coefficient sequence was obtained by solving Tiangong1 continuous 55days GPS orbit data with different arc length. The same period solar flux f10.7 and geomagnetic index Ap ap series were high and low frequency multi-wavelet decomposition. Statistical analysis results of the layers sliding correlation between space environmental parameters and decomposition of Cd, showed that the satellite drag coefficient sequence after wavelet decomposition and the corresponding level of f10.7 Ap sequence with good lag correlation. It also verified that the Cd prediction is feasible. Prediction residuals of Cd with different regression models and different sample length were analysed. The results showed that the case was best when setting sample length 20 days and f10.7 regression model were used. It also showed that NRLMSIS-00 model's response in the region of 350km (Tiangong's altitude) and low-middle latitude (Tiangong's inclination) is excessive in ascent stage of geomagnetic activity Ap and is inadequate during fall off segment. Additionally, the low-frequency decomposition components NRLMSIS-00 model's response is appropriate in f10.7 rising segment. High frequency decomposition section, Showed NRLMSIS-00 model's response is small-scale inadequate during f10.7 ascent segment and is reverse in decline of f10.7. Finally, the potential use of a summary and outlook were listed; This method has an important reference value to improve the spacecraft orbit prediction accuracy. Key words: wavelet transform; drag coefficient; lag correlation; Tiangong1;space environment
Xu, Yonghong; Li, Xingxing; Zhao, Yong
2013-10-01
In this paper, a new method combining wavelet packet transform and multivariate multiscale entropy for the classification of epilepsy EEG signals is introduced. Firstly, the original EEG signals are decomposed at multi-scales with the wavelet packet transform, and the wavelet packet coefficients of the required frequency bands are extracted. Secondly, the wavelet packet coefficients are processed with multivariate multiscale entropy algorithm. Finally, the EEG data are classified by support vector machines (SVM). The experimental results on the international public Bonn epilepsy EEG dataset show that the proposed method can efficiently extract epileptic features and the accuracy of classification result is satisfactory. PMID:24459973
The application study of wavelet packet transformation in the de-noising of dynamic EEG data.
Li, Yifeng; Zhang, Lihui; Li, Baohui; Wei, Xiaoyang; Yan, Guiding; Geng, Xichen; Jin, Zhao; Xu, Yan; Wang, Haixia; Liu, Xiaoyan; Lin, Rong; Wang, Quan
2015-01-01
This paper briefly describes the basic principle of wavelet packet analysis, and on this basis introduces the general principle of wavelet packet transformation for signal den-noising. The dynamic EEG data under +Gz acceleration is made a de-noising treatment by using wavelet packet transformation, and the de-noising effects with different thresholds are made a comparison. The study verifies the validity and application value of wavelet packet threshold method for the de-noising of dynamic EEG data under +Gz acceleration. PMID:26405863
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
ECG signals denoising using wavelet transform and independent component analysis
NASA Astrophysics Data System (ADS)
Liu, Manjin; Hui, Mei; Liu, Ming; Dong, Liquan; Zhao, Zhu; Zhao, Yuejin
2015-08-01
A method of two channel exercise electrocardiograms (ECG) signals denoising based on wavelet transform and independent component analysis is proposed in this paper. First of all, two channel exercise ECG signals are acquired. We decompose these two channel ECG signals into eight layers and add up the useful wavelet coefficients separately, getting two channel ECG signals with no baseline drift and other interference components. However, it still contains electrode movement noise, power frequency interference and other interferences. Secondly, we use these two channel ECG signals processed and one channel signal constructed manually to make further process with independent component analysis, getting the separated ECG signal. We can see the residual noises are removed effectively. Finally, comparative experiment is made with two same channel exercise ECG signals processed directly with independent component analysis and the method this paper proposed, which shows the indexes of signal to noise ratio (SNR) increases 21.916 and the root mean square error (MSE) decreases 2.522, proving the method this paper proposed has high reliability.
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
Texture Analysis of Medical Images Using the Wavelet Transform
NASA Astrophysics Data System (ADS)
Fernández, Margarita; Mavilio, Adriana
2002-08-01
Texture analysis of images can contribute to a better interpretation of medical images. This type of analysis provides not only qualitative but also quantitative information about tissue affection degree. In this work an algorithm is developed which uses the wavelet transform to carry out the supervised segmentation of echographic images corresponding to injured Achilles tendon of athletes. To construct the pattern, the image corresponding to healthy tendon tissue of the athlete, is taken as a reference based upon the duplicity of this structure. Texture features are calculated on the expansion wavelet coefficients of the images. The Mahalanobis distance between texture samples of the injured tissue and pattern texture is computed and used as the discriminating function. It is concluded that this distance, after appropriate medical calibrations, can offer quantitative information about the injury degree in every point along the damaged tissue. Further, its behavior along the segmented image can serve as a measure of the degree of change in tissue properties. The parameter, similarity degree, is defined and obtained by taking into account the correlation between distance histograms for the healthy tissue and the damaged one. It is also shown that this parameter, when properly calibrated, can offer a quantitative global evaluation of the state of the injured tissue.
NASA Astrophysics Data System (ADS)
Xu, Luopeng; Dan, Youquan; Wang, Qingyuan
2015-10-01
The continuous wavelet transform (CWT) introduces an expandable spatial and frequency window which can overcome the inferiority of localization characteristic in Fourier transform and windowed Fourier transform. The CWT method is widely applied in the non-stationary signal analysis field including optical 3D shape reconstruction with remarkable performance. In optical 3D surface measurement, the performance of CWT for optical fringe pattern phase reconstruction usually depends on the choice of wavelet function. A large kind of wavelet functions of CWT, such as Mexican Hat wavelet, Morlet wavelet, DOG wavelet, Gabor wavelet and so on, can be generated from Gauss wavelet function. However, so far, application of the Gauss wavelet transform (GWT) method (i.e. CWT with Gauss wavelet function) in optical profilometry is few reported. In this paper, the method using GWT for optical fringe pattern phase reconstruction is presented first and the comparisons between real and complex GWT methods are discussed in detail. The examples of numerical simulations are also given and analyzed. The results show that both the real GWT method along with a Hilbert transform and the complex GWT method can realize three-dimensional surface reconstruction; and the performance of reconstruction generally depends on the frequency domain appearance of Gauss wavelet functions. For the case of optical fringe pattern of large phase variation with position, the performance of real GWT is better than that of complex one due to complex Gauss series wavelets existing frequency sidelobes. Finally, the experiments are carried out and the experimental results agree well with our theoretical analysis.
Multi-frequency fringe projection profilometry based on wavelet transform.
Jiang, Chao; Jia, Shuhai; Dong, Jun; Lian, Qin; Li, Dichen
2016-05-30
Based on wavelet transforms (WTs), an alternative multi-frequency fringe projection profilometry is described. Fringe patterns with multiple frequencies are projected onto an object and the reflected patterns are recorded digitally. Phase information for every pattern is calculated by identifying the ridge that appears in WT results. Distinct from the phase unwrapping process, a peak searching algorithm is applied to obtain object height from the phases of the different frequency for a single point on the object. Thus, objects with large discontinuities can be profiled. In comparing methods, the height profiles obtained from the WTs have lower noise and higher measurement accuracy. Although measuring times are similar, the proposed method offers greater reliability. PMID:27410063
Ho, Derek; Kim, Sanghoon; Drake, Tyler K.; Eldridge, Will J.; Wax, Adam
2014-01-01
We present a fast approach for size determination of spherical scatterers using the continuous wavelet transform of the angular light scattering profile to address the computational limitations of previously developed sizing techniques. The potential accuracy, speed, and robustness of the algorithm were determined in simulated models of scattering by polystyrene beads and cells. The algorithm was tested experimentally on angular light scattering data from polystyrene bead phantoms and MCF-7 breast cancer cells using a 2D a/LCI system. Theoretical sizing of simulated profiles of beads and cells produced strong fits between calculated and actual size (r2 = 0.9969 and r2 = 0.9979 respectively), and experimental size determinations were accurate to within one micron. PMID:25360350
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.
An overview of the quantum wavelet transform, focused on earth science applications
NASA Astrophysics Data System (ADS)
Shehab, O.; LeMoigne, J.; Lomonaco, S.; Halem, M.
2015-12-01
Registering the images from the MODIS system and the OCO-2 satellite is currently being done by classical image registration techniques. One such technique is wavelet transformation. Besides image registration, wavelet transformation is also used in other areas of earth science, for example, processinga and compressing signal variation, etc. In this talk, we investigate the applicability of few quantum wavelet transformation algorithms to perform image registration on the MODIS and OCO-2 data. Most of the known quantum wavelet transformation algorithms are data agnostic. We investigate their applicability in transforming Flexible Representation for Quantum Images. Similarly, we also investigate the applicability of the algorithms in signal variation analysis. We also investigate the transformation of the models into pseudo-boolean functions to implement them on commercially available quantum annealing computers, such as the D-Wave computer located at NASA Ames.
NASA Astrophysics Data System (ADS)
Kulesh, M.; Holschneider, M.
2007-12-01
Surface wave propagation in heterogeneous media can provide a valuable source of information about the subsurface structure and its elastic properties. The processing of experimental seismic data sets related to the surface waves is computationally expensive and requires sophisticated techniques in order to infer the physical properties and structure of the subsurface from the bulk of available information. Most of the previous studies related to these problems are based on Fourier analysis. However, the frequency- dependent measurements, or time-frequency analysis offer additional insight and performance in any applications where Fourier techniques have been used. This analysis consists of examining the variation of the frequency content of a signal with time and is particularly suitable in geophysical applications. The continuous wavelet transform gives a suitable general framework for solving these types of problems; this approach is powerful and elegant, but is not the only available for the practical applications. Other methods such as the Gabor transform, the S-transform or bilinear transforms can be used as well. The relative performance of time-frequency analysis from different approaches is primarily controlled by the frequency resolution capability. To perform the time-frequency analysis of digital seismic data, we propose in this contribution a new free software package developed by the authors and based on the continuous wavelet transform. This package allows to perform the direct and inverse continuous wavelet transform, 2C and 3C polarization analysis and filtering, modeling the dispersed and attenuated wave propagation in the time-frequency domain and optimization in signal and wavelet domains. The aim of these operations is to extract polarization properties, velocities and attenuation parameters from a seismogram. The novelty of this package is that we incorporate the continuous wavelet transform into the library where the kernel is the time
Interactive transmission of spectrally wavelet-transformed hyperspectral images
NASA Astrophysics Data System (ADS)
Monteagudo-Pereira, José Lino; Bartrina-Rapesta, Joan; Aulí-Llinàs, Francesc; Serra-Sagristà, Joan; Zabala, Alaitz; Pons, Xavier
2008-08-01
The size of images used in remote sensing scenarios has constantly increased in the last years. Remote sensing images are not only stored, but also processed and transmitted, raising the need for more resources and bandwidth. On another side, hyperspectral remote sensing images have a large number of components with a significant inter-component redundancy, which is usually taken into account by many image coding systems to improve the coding performance. The main approaches used to decorrelate the spectral dimension are the Karhunen Loeve-Transform and the Discrete Wavelet Transform (DWT). This paper is focused on DWT decorrelators because they have a lower computational complexity, and because they provide interesting features such as component and resolution scalability and progressive transmission. Influence of the spectral transform is investigated, considering the DWT kernel applied and the number of decomposition levels. In addition, a JPIP compliant application, CADI, is introduced. It may be useful to test new protocols, techniques, or coding systems, without requiring significant changes on the application. CADI can be run in most computer platforms and devices thanks to the use of JAVA and the configuration of a light-version, suitable for devices with constrained resources.
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.
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)
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
3D segmentation of prostate ultrasound images using wavelet transform
NASA Astrophysics Data System (ADS)
Akbari, Hamed; Yang, Xiaofeng; Halig, Luma V.; Fei, Baowei
2011-03-01
The current definitive diagnosis of prostate cancer is transrectal ultrasound (TRUS) guided biopsy. However, the current procedure is limited by using 2D biopsy tools to target 3D biopsy locations. This paper presents a new method for automatic segmentation of the prostate in three-dimensional transrectal ultrasound images, by extracting texture features and by statistically matching geometrical shape of the prostate. A set of Wavelet-based support vector machines (WSVMs) are located and trained at different regions of the prostate surface. The WSVMs capture texture priors of ultrasound images for classification of the prostate and non-prostate tissues in different zones around the prostate boundary. In the segmentation procedure, these W-SVMs are trained in three sagittal, coronal, and transverse planes. The pre-trained W-SVMs are employed to tentatively label each voxel around the surface of the model as a prostate or non-prostate voxel by the texture matching. The labeled voxels in three planes after post-processing is overlaid on a prostate probability model. The probability prostate model is created using 10 segmented prostate data. Consequently, each voxel has four labels: sagittal, coronal, and transverse planes and one probability label. By defining a weight function for each labeling in each region, each voxel is labeled as a prostate or non-prostate voxel. Experimental results by using real patient data show the good performance of the proposed model in segmenting the prostate from ultrasound images.
NASA Astrophysics Data System (ADS)
Nenna, V.; Pidlisecky, A.
2012-12-01
As mapping of groundwater resources with airborne electromagnetics expands into more urban areas, it is increasingly important to identify sources of cultural noise in acquired data sets. A number of methods have been proposed to reduce the impact of cultural coupling on acquired data. While intense local calibration to increase the signal to noise ratio has been used, most often in practice, the transients associated with these noise sources are manually identified and filtered out during data processing. This can be a challenging task, particularly as datasets grow large (e.g. up to terabytes of data). In response to this, we propose a method for identifying noise in airborne electromagnetic data based on a spatial application of the continuous wavelet transform (CWT). We apply a continuous wavelet transform to three airborne electromagnetic surveys collected in the Edmonton-Calgary Corridor as part of a groundwater inventory sponsored by the Alberta Geological Survey and Environment Alberta. The three surveys consist of 210 flightlines covering approximately 18 000 linear kilometers with roughly 13 m sounding spacing. B-field and dB/dt data from a three-component 20-channel GeoTEM multicoil system, were recorded at 5 on-time and 15 off-time channels with a total measurement time of 16.664 ms per sounding. The nominal height of vertical axis transmitter was 120 m; the current pulse was 670 A, and the pulse-width was 4.045 ms. Wavelet transforms are localized in time and frequency, similar to a windowed Fourier transform, and are used to identify dominant frequencies within a signal as a function of time or space. While there are a number of options for wavelet functions, we convolve a Morlet wavelet with the data signal at 120 distance scales on a logarithmic scale from 0.1 to 30 km. We calculate the CWT along each flightline for all off-time channels. We then calculate the wavelet power normalized by the data variance, and bin results into 4 bins of spatial
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.
Fast Fourier and Wavelet Transforms for Wavefront Reconstruction in Adaptive Optics
Dowla, F U; Brase, J M; Olivier, S S
2000-07-28
Wavefront reconstruction techniques using the least-squares estimators are computationally quite expensive. We compare wavelet and Fourier transforms techniques in addressing the computation issues of wavefront reconstruction in adaptive optics. It is shown that because the Fourier approach is not simply a numerical approximation technique unlike the wavelet method, the Fourier approach might have advantages in terms of numerical accuracy. However, strictly from a numerical computations viewpoint, the wavelet approximation method might have advantage in terms of speed. To optimize the wavelet method, a statistical study might be necessary to use the best basis functions or ''approximation tree.''
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.
R-peaks detection based on stationary wavelet transform.
Merah, M; Abdelmalik, T A; Larbi, B H
2015-10-01
Automatic detection of the QRS complexes/R-peaks in an electrocardiogram (ECG) signal is the most important step preceding any kind of ECG processing and analysis. The performance of these systems heavily relies on the accuracy of the QRS detector. The objective of present work is to drive a new robust method based on stationary wavelet transform (SWT) for R-peaks detection. The decimation of the coefficients at each level of the transformation algorithm is omitted, more samples in the coefficient sequences are available and hence a better outlier detection can be performed. Using the information of local maxima, minima and zero crossings of the fourth SWT coefficient detail, the proposed algorithm identifies the significant points for detection and delineation of the QRS complexes, as well as detection and identification of the QRS individual waves peaks of the pre-processed ECG signal. Various experimental results show that the proposed algorithm exhibits reliable QRS detection as well as accurate ECG delineation, achieving excellent performance on different databases, on the MIT-BIH database (Se=99.84%, P=99.88%), on the QT Database (Se=99.94%, P=99.89%) and on MIT-BIH Noise Stress Test Database, (Se=95.30%, P=93.98%). Reliability and accuracy are close to the highest among the ones obtained in other studies. Experiments results being satisfactory, the SWT may represent a novel QRS detection tool, for a robust ECG signal analysis. PMID:26105724
Harmonic wavelets, constant Q transforms, and the cone kernel TFD
NASA Astrophysics Data System (ADS)
Chettri, Samir R.; Ishiwaka, Yuko; Kimura, H.; Nagano, Isamu
1996-03-01
In this research we compare general harmonic wavelet transforms (GHWT), constant Q transforms (CQT) and the Cone kernel time-frequency distribution (CKTFD) for the analysis of musical signals. The first two consist of a series of band pass filters that have a constant Q (quality), each of which correspond to a semitone interval (or better) in the musical scale. The CKTFD is not a constant Q type transform but belongs to the more general class of bilinear time-frequency distributions with the special property of reducing the (usually) undesirable interference terms common in these types of distributions. Their computation schemes are compared and the advantages of each discussed. All three have a structure that may be easily parallelized. We used the three methods to analyze a musical note (middle C) played on an electric piano. There are subtle differences in the results of the methods. All three quite clearly show the first four harmonics of the musical note (C4). However, the CQT reveals that harmonics higher than four extend in time for almost the entire duration of the note. Neither the GHWT nor the CKTFD show harmonics higher than four for the entire length of the signal, though they do reveal them (i.e., frequencies higher than 1024 Hz.) at the initiation of the note. The power spectrum of the signal does reveal harmonics from one through four as having most of the power but harmonics five through ten are also revealed. Unfortunately, the time variation of the signal cannot be extracted from the power spectrum hence the use of time-frequency or time-scale diagrams. Aside from musical applications, such methods would be useful for t-f analysis of vibrating machinery.
"NONLINEAR DYNAMIC SYSTEMS RESPONSE TO NON-STATIONARY EXCITATION USING THE WAVELET TRANSFORM"
SPANOS, POL D.
2006-01-15
The objective of this research project has been the development of techniques for estimating the power spectra of stochastic processes using wavelet transform, and the development of related techniques for determining the response of linear/nonlinear systems to excitations which are described via the wavelet transform. Both of the objectives have been achieved, and the research findings have been disseminated in papers in archival journals and technical conferences.
Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates.
Dovlo, Edem; Baddour, Natalie
2015-01-01
The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: •The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms.•The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform.•The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time. PMID:26150988
Clifford Continuous Wavelet Transforms in Ll{sub 0,2} and Ll{sub 0,3}
Bernstein, S.
2008-09-01
We consider Clifford-valued functions defined on R{sup n}. From the viewpoint of square integrable group representations a continuous wavelet transform is an irreducible continuous unitary representation of the affin group on the real line but also on R{sup n}. We will demonstrate that different Clifford continuous wavelet transforms can be obtained inside the calculus with similar properties than the real valued transform. Nevertheless, the Clifford wavelet transform is neither just a special vector transform nor just a wavelet transform applied to each component of the Clifford-valued function.
Identification of diesel front sound source based on continuous wavelet transform.
Hao, Zhi-yong; Han, Jun
2004-09-01
Acoustic signals from diesel engines contain useful information but also include considerable noise components. To extract information for condition monitoring purposes, continuous wavelet transform (CWT) is used for the characterization of engine acoustics. This paper first reviews CWT characteristics represented by short duration transient signals. Wavelet selection and CWT are then implemented and wavelet transform is used to analyze the major sources of the engine front's exterior radiation sound. The research provides a reliable basis for engineering practice to reduce vehicle sound level. Comparison of the identification results of the measured acoustic signals with the identification results of the measured surface vibration showed good agreement. PMID:15323001
Identification of the defective transmission devices using the wavelet transform.
Wang, Bingchen; Omatu, Sigeru; Abe, Toshiro
2005-06-01
In this paper, a system is described that uses the wavelet transform to automatically identify the particular failure mode of a known defective transmission device. The problem of identifying a particular failure mode within a costly failed assembly is of benefit in practical applications. In this system, external acoustic sensors, instead of intrusive vibrometers, are used to record the acoustic data of the operating transmission device. A skilled factory worker, who is unfamiliar with statistical classification, helps to determine the feature vector of the particular failure mode in the feature extraction process. In the automatic identification part, an improved learning vector quantization (LVQ) method with normalizing the inputting feature vectors is proposed to compensate for variations in practical data. Some acoustic data, which are collected from the manufacturing site, are utilized to test the effectiveness of the described identification system. The experimental results show that this system can identify the particular failure mode of a defective transmission device and find out the causes of failure successfully. PMID:15943423
Classification of Histological Images Based on the Stationary Wavelet Transform
NASA Astrophysics Data System (ADS)
Nascimento, M. Z.; Neves, L.; Duarte, S. C.; Duarte, Y. A. S.; Ramos Batista, V.
2015-01-01
Non-Hodgkin lymphomas are of many distinct types, and different classification systems make it difficult to diagnose them correctly. Many of these systems classify lymphomas only based on what they look like under a microscope. In 2008 the World Health Organisation (WHO) introduced the most recent system, which also considers the chromosome features of the lymphoma cells and the presence of certain proteins on their surface. The WHO system is the one that we apply in this work. Herewith we present an automatic method to classify histological images of three types of non-Hodgkin lymphoma. Our method is based on the Stationary Wavelet Transform (SWT), and it consists of three steps: 1) extracting sub-bands from the histological image through SWT, 2) applying Analysis of Variance (ANOVA) to clean noise and select the most relevant information, 3) classifying it by the Support Vector Machine (SVM) algorithm. The kernel types Linear, RBF and Polynomial were evaluated with our method applied to 210 images of lymphoma from the National Institute on Aging. We concluded that the following combination led to the most relevant results: detail sub-band, ANOVA and SVM with Linear and RBF kernels.
Cell classification by moments and continuous wavelet transform methods
Chen, Qian; Fan, Yuan; Udpa, Lalita; Ayres, Virginia M
2007-01-01
Image processing techniques are bringing new insights to biomedical research. The automatic recognition and classification of biomedical objects can enhance work efficiency while identifying new inter-relationships among biological features. In this work, a simple rule-based decision tree classifier is developed to classify typical features of mixed cell types investigated by atomic force microscopy (AFM). A combination of continuous wavelet transform (CWT) and moment-based features are extracted from the AFM data to represent that shape information of different cellular objects at multiple resolution levels. The features are shown to be invariant under operations of translation, rotation, and scaling. The features are then used in a simple rule-based classifier to discriminate between anucleate versus nucleate cell types or to distinguish cells from a fibrous environment such as a tissue scaffold or stint. Since each feature has clear physical meaning, the decision rule of this tree classifier is simple, which makes it very suitable for online processing. Experimental results on AFM data confirm that the performance of this classifier is robust and reliable. PMID:17722546
Wavelet transform analysis of transient signals: the seismogram and the electrocardiogram
Anant, K.S.
1997-06-01
In this dissertation I quantitatively demonstrate how the wavelet transform can be an effective mathematical tool for the analysis of transient signals. The two key signal processing applications of the wavelet transform, namely feature identification and representation (i.e., compression), are shown by solving important problems involving the seismogram and the electrocardiogram. The seismic feature identification problem involved locating in time the P and S phase arrivals. Locating these arrivals accurately (particularly the S phase) has been a constant issue in seismic signal processing. In Chapter 3, I show that the wavelet transform can be used to locate both the P as well as the S phase using only information from single station three-component seismograms. This is accomplished by using the basis function (wave-let) of the wavelet transform as a matching filter and by processing information across scales of the wavelet domain decomposition. The `pick` time results are quite promising as compared to analyst picks. The representation application involved the compression of the electrocardiogram which is a recording of the electrical activity of the heart. Compression of the electrocardiogram is an important problem in biomedical signal processing due to transmission and storage limitations. In Chapter 4, I develop an electrocardiogram compression method that applies vector quantization to the wavelet transform coefficients. The best compression results were obtained by using orthogonal wavelets, due to their ability to represent a signal efficiently. Throughout this thesis the importance of choosing wavelets based on the problem at hand is stressed. In Chapter 5, I introduce a wavelet design method that uses linear prediction in order to design wavelets that are geared to the signal or feature being analyzed. The use of these designed wavelets in a test feature identification application led to positive results. The methods developed in this thesis; the
Forecasting performance of denoising signal by Wavelet and Fourier Transforms using SARIMA model
NASA Astrophysics Data System (ADS)
Ismail, Mohd Tahir; Mamat, Siti Salwana; Hamzah, Firdaus Mohamad; Karim, Samsul Ariffin Abdul
2014-07-01
The goal of this research is to determine the forecasting performance of denoising signal. Monthly rainfall and monthly number of raindays with duration of 20 years (1990-2009) from Bayan Lepas station are utilized as the case study. The Fast Fourier Transform (FFT) and Wavelet Transform (WT) are used in this research to find the denoise signal. The denoise data obtained by Fast Fourier Transform and Wavelet Transform are being analyze by seasonal ARIMA model. The best fitted model is determined by the minimum value of MSE. The result indicates that Wavelet Transform is an effective method in denoising the monthly rainfall and number of rain days signals compared to Fast Fourier Transform.
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.
Application of dual tree complex wavelet transform in tandem mass spectrometry.
Murugesan, Selvaraaju; Tay, David B H; Cooke, Ira; Faou, Pierre
2015-08-01
Mass Spectrometry (MS) is a widely used technique in molecular biology for high throughput identification and sequencing of peptides (and proteins). Tandem mass spectrometry (MS/MS) is a specialised mass spectrometry technique whereby the sequence of peptides can be determined. Preprocessing of the MS/MS data is indispensable before performing any statistical analysis on the data. In this work, preprocessing of MS/MS data is proposed based on the Dual Tree Complex Wavelet Transform (DTCWT) using almost symmetric Hilbert pair of wavelets. After the preprocessing step, the identification of peptides is done using the database search approach. The performance of the proposed preprocessing technique is evaluated by comparing its performance against Discrete Wavelet Transform (DWT) and Stationary Wavelet Transform (SWT). The preprocessing performed using DTCWT identified more peptides compared to DWT and SWT. PMID:26004826
Multiresolution phase retrieval in the fresnel region by use of wavelet transform.
Souvorov, Alexei; Ishikawa, Tetsuya; Kuyumchyan, Armen
2006-02-01
A multiresolution (multiscale) analysis based on wavelet transform is applied to the problem of optical phase retrieval from the intensity measured in the in-line geometry (lens-free). The transport-of-intensity equation and the Fresnel diffraction integral are approximated in terms of a wavelet basis. A solution to the phase retrieval problem can be efficiently found in both cases using the multiresolution concept. Due to the hierarchical nature of wavelet spaces, wavelets are well suited to multiresolution methods that contain multigrid algorithms. Appropriate wavelet bases for the best solution approximation are discussed. The proposed approach reduces the computational complexity and accelerates the convergence of the solution. It is robust and reliable, and successful on both simulated and experimental images obtained with hard x rays. PMID:16477833
Sangeetha, S; Sujatha, C M; Manamalli, D
2014-01-01
In this work, anisotropy of compressive and tensile strength regions of femur trabecular bone are analysed using quaternion wavelet transforms. The normal and abnormal femur trabecular bone radiographic images are considered for this study. The sub-anatomic regions, which include compressive and tensile regions, are delineated using pre-processing procedures. These delineated regions are subjected to quaternion wavelet transforms and statistical parameters are derived from the transformed images. These parameters are correlated with apparent porosity, which is derived from the strength regions. Further, anisotropy is also calculated from the transformed images and is analyzed. Results show that the anisotropy values derived from second and third phase components of quaternion wavelet transform are found to be distinct for normal and abnormal samples with high statistical significance for both compressive and tensile regions. These investigations demonstrate that architectural anisotropy derived from QWT analysis is able to differentiate normal and abnormal samples. PMID:25571265
Zhang, Chang-jiang; Li, Dan-ting; Liang, Jiu-zhen; Cheng, Cun-gui
2007-01-01
Infrared spectra of semen celosiae and semen celosiae cristatae were obtained directly, quickly and accurately by Fourier transform infrared spectroscopy (FTIR) with OMNI sampler. Continuous wavelet transform was used to extrude local region of infrared spectra of semen celosiae and its confusable varieties. The difference of infrared spectra between semen celosiae and semen celosiae cristatae was extruded greatly. Accurate identification rate was improved greatly. Morlet wavelet, which can detect singular values of signal effectively, was selected as the mother wavelet. One-dimensional continuous wavelet transform was implemented for the infrared spectra of semen celosiae and its confusable varieties. The difference between semen celosiae and semen celosiae cristatae was observed at all scales in the wavelet domain. An optimal scale, at which the difference between semen celosiae and semen celosiae cristatae was the most obvious, was selected to identify semen celosiae and semen celosiae cristatae. The results show that it is effective to apply continuous wavelet transform on the basis of FTIR to identify the traditional Chinese medicinal materials, which are the same genus but different species. PMID:17390647
Hyperspectral imaging with wavelet transform for classification of colon tissue biopsy samples
NASA Astrophysics Data System (ADS)
Masood, Khalid
2008-08-01
Automatic classification of medical images is a part of our computerised medical imaging programme to support the pathologists in their diagnosis. Hyperspectral data has found its applications in medical imagery. Its usage is increasing significantly in biopsy analysis of medical images. In this paper, we present a histopathological analysis for the classification of colon biopsy samples into benign and malignant classes. The proposed study is based on comparison between 3D spectral/spatial analysis and 2D spatial analysis. Wavelet textural features in the wavelet domain are used in both these approaches for classification of colon biopsy samples. Experimental results indicate that the incorporation of wavelet textural features using a support vector machine, in 2D spatial analysis, achieve best classification accuracy.
Continuous Wavelet Transform Analysis of Acceleration Signals Measured from a Wave Buoy
Chuang, Laurence Zsu-Hsin; Wu, Li-Chung; Wang, Jong-Hao
2013-01-01
Accelerometers, which can be installed inside a floating platform on the sea, are among the most commonly used sensors for operational ocean wave measurements. To examine the non-stationary features of ocean waves, this study was conducted to derive a wavelet spectrum of ocean waves and to synthesize sea surface elevations from vertical acceleration signals of a wave buoy through the continuous wavelet transform theory. The short-time wave features can be revealed by simultaneously examining the wavelet spectrum and the synthetic sea surface elevations. The in situ wave signals were applied to verify the practicality of the wavelet-based algorithm. We confirm that the spectral leakage and the noise at very-low-frequency bins influenced the accuracies of the estimated wavelet spectrum and the synthetic sea surface elevations. The appropriate thresholds of these two factors were explored. To study the short-time wave features from the wave records, the acceleration signals recorded from an accelerometer inside a discus wave buoy are analysed. The results from the wavelet spectrum show the evidence of short-time nonlinear wave events. Our study also reveals that more surface profiles with higher vertical asymmetry can be found from short-time nonlinear wave with stronger harmonic spectral peak. Finally, we conclude that the algorithms of continuous wavelet transform are practical for revealing the short-time wave features of the buoy acceleration signals. PMID:23966188
Continuous wavelet transform analysis of acceleration signals measured from a wave buoy.
Chuang, Laurence Zsu-Hsin; Wu, Li-Chung; Wang, Jong-Hao
2013-01-01
Accelerometers, which can be installed inside a floating platform on the sea, are among the most commonly used sensors for operational ocean wave measurements. To examine the non-stationary features of ocean waves, this study was conducted to derive a wavelet spectrum of ocean waves and to synthesize sea surface elevations from vertical acceleration signals of a wave buoy through the continuous wavelet transform theory. The short-time wave features can be revealed by simultaneously examining the wavelet spectrum and the synthetic sea surface elevations. The in situ wave signals were applied to verify the practicality of the wavelet-based algorithm. We confirm that the spectral leakage and the noise at very-low-frequency bins influenced the accuracies of the estimated wavelet spectrum and the synthetic sea surface elevations. The appropriate thresholds of these two factors were explored. To study the short-time wave features from the wave records, the acceleration signals recorded from an accelerometer inside a discus wave buoy are analysed. The results from the wavelet spectrum show the evidence of short-time nonlinear wave events. Our study also reveals that more surface profiles with higher vertical asymmetry can be found from short-time nonlinear wave with stronger harmonic spectral peak. Finally, we conclude that the algorithms of continuous wavelet transform are practical for revealing the short-time wave features of the buoy acceleration signals. PMID:23966188
Classification of Spectra of Emission-line Stars Using Feature Extraction Based on Wavelet Transform
NASA Astrophysics Data System (ADS)
Bromová P.; Bařina, D.; Škoda, P.; Vážný, J.; Zendulka, J.
2014-05-01
Our goal is to automatically identify spectra of emission (Be) stars in large archives and classify their types based on a typical shape of the Hα emission line. Due to the length of spectra, of the original data is very time-consuming. In order to lower computational requirements and enhance the separability of the classes, we have to find a reduced representation of spectral features, however conserving most of the original information content. As the Be stars show a number of different shapes of emission lines, it is not easy to construct simple criteria (like e.g. Gaussian fits) to distinguish the emission lines in an automatic manner. We proposed to perform the wavelet transform of the spectra, calculate statistical metrics from the wavelet coefficients, and use them as feature vectors for classification. In this paper, we compare different wavelet transforms, different wavelets, and different statistical metrics in an attempt to identify the best method.
Real Clifford Algebra Cl{sub n,0}, n = 2, 3(mod 4) Wavelet Transform
Hitzer, Eckhard
2009-09-09
We show how for n = 2, 3(mod 4) continuous Clifford (geometric) algebra (GA)Cl{sub n}-valued admissible wavelets can be constructed using the similitude group SIM(n). We strictly aim for real geometric interpretation, and replace the imaginary unit i is an element of C therefore with a GA blade squaring to -1. Consequences due to non-commutativity arise. We express the admissibility condition in terms of a Cl{sub n} Clifford Fourier Transform and then derive a set of important properties such as dilation, translation and rotation covariance, a reproducing kernel, and show how to invert the Clifford wavelet transform. As an example, we introduce Clifford Gabor wavelets. We further invent a generalized Clifford wavelet uncertainty principle.
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.
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)
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
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.
Wavelet transform analysis of truncated fringe patterns in 3-D surface profilometry
NASA Astrophysics Data System (ADS)
Gorthi, Sai Siva; Lolla, Kameswara R.
2005-06-01
Wavelet transform analysis of projected fringe pattern for phase recovery in 3-D shape measurement of objects is investigated. The present communication specifically outlines and evaluates the errors that creep in to the reconstructed profiles when fringe images do not satisfy periodicity. Three specific cases that give raise to non-periodicity of fringe image are simulated and leakage effects caused by each one of them are analyzed with continuous complex Morlet wavelet transform. Same images are analyzed with FFT method to make a comparison of the reconstructed profiles with both methods. Simulation results revealed a significant advantage of wavelet transform profilometry (WTP), that the distortions that arise due to leakage are confined to the locations of discontinuity and do not spread out over the entire projection as in the case of Fourier transform profilometry (FTP).
Research of image enhancement of dental cast based on wavelet transformation
NASA Astrophysics Data System (ADS)
Zhao, Jing; Li, Zhongke; Liu, Xingmiao
2010-10-01
This paper describes a 3D laser scanner for dental cast that realize non-contact deepness measuring. The scanner and the control PC make up of a 3D scan system, accomplish the real time digital of dental cast. Owing to the complexity shape of the dental cast and the random nature of scanned points, the detected feature curves are generally not smooth or not accurate enough for subsequent application. The purpose of this p is to present an algorithm for enhancing the useful points and eliminating the noises. So an image enhancement algorithm based on wavelet transform and fuzzy set theory is presented. Firstly, the multi-scale wavelet transform is adopted to decompose the input image, which extracts the characteristic of multi-scale of the image. Secondly, wavelet threshold is used for image de-noising, and then the traditional fuzzy set theory is improved and applied to enhance the low frequency wavelet coefficients and the high frequency wavelet coefficients of different directions of each scale. Finally, the inverse wavelet transform is applied to synthesis image. A group of experimental results demonstrate that the proposed algorithm is effective for the dental cast image de-noising and enhancement, the edge of the enhanced image is distinct which is good for the subsequent image processing.
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.
Integrated system for image storage, retrieval, and transmission using wavelet transform
NASA Astrophysics Data System (ADS)
Yu, Dan; Liu, Yawen; Mu, Ray Y.; Yang, Shi-Qiang
1998-12-01
Currently, much work has been done in the area of image storage and retrieval. However, the overall performance has been far from practical. A highly integrated wavelet-based image management system is proposed in this paper. By integrating wavelet-based solutions for image compression and decompression, content-based retrieval and progressive transmission, much higher performance can be achieved. The multiresolution nature of the wavelet transform has been proven to be a powerful tool to represent images. The wavelet transform decomposes the image into a set of subimages with different resolutions. From here three solutions for key aspects of image management are reached. The content-based image retrieval (CBIR) features of our system include the color, contour, texture, sample, keyword and topic information of images. The first four features can be naturally extracted from the wavelet transform coefficients. By scoring the similarity of users' requests with images in the database, those who have higher scores are noted and the user receives feedback. Image compression and decompression. Assuming that details at high resolution and diagonal directions are less visible to the human eye, a good compression ratio can be achieved. In each subimage, the wavelet coefficients are vector quantized (VQ), using the LGB algorithm, which is improved in our approach to accelerate the process. Higher compression ratio can be achieved with DPCM and entropy coding method applied together. With YIQ representation, color images can also be effectively compressed. There is a very low load on the network bandwidth by transmitting compressed image data across the network. Progressive transmission is possible by employment of the multiresolution nature of the wavelet, which makes the system respond faster and the user-interface more friendly. The system shows a high overall performance by exploring the excellent features of wavelet, and integrating key aspects of image management. An
NASA Astrophysics Data System (ADS)
Sayadi, Omid; Shamsollahi, Mohammad B.
2007-12-01
We present a new modified wavelet transform, called the multiadaptive bionic wavelet transform (MABWT), that can be applied to ECG signals in order to remove noise from them under a wide range of variations for noise. By using the definition of bionic wavelet transform and adaptively determining both the center frequency of each scale together with the[InlineEquation not available: see fulltext.]-function, the problem of desired signal decomposition is solved. Applying a new proposed thresholding rule works successfully in denoising the ECG. Moreover by using the multiadaptation scheme, lowpass noisy interference effects on the baseline of ECG will be removed as a direct task. The method was extensively clinically tested with real and simulated ECG signals which showed high performance of noise reduction, comparable to those of wavelet transform (WT). Quantitative evaluation of the proposed algorithm shows that the average SNR improvement of MABWT is 1.82 dB more than the WT-based results, for the best case. Also the procedure has largely proved advantageous over wavelet-based methods for baseline wandering cancellation, including both DC components and baseline drifts.
Directional dual-tree complex wavelet packet transforms for processing quadrature signals.
Serbes, Gorkem; Gulcur, Halil Ozcan; Aydin, Nizamettin
2016-03-01
Quadrature signals containing in-phase and quadrature-phase components are used in many signal processing applications in every field of science and engineering. Specifically, Doppler ultrasound systems used to evaluate cardiovascular disorders noninvasively also result in quadrature format signals. In order to obtain directional blood flow information, the quadrature outputs have to be preprocessed using methods such as asymmetrical and symmetrical phasing filter techniques. These resultant directional signals can be employed in order to detect asymptomatic embolic signals caused by small emboli, which are indicators of a possible future stroke, in the cerebral circulation. Various transform-based methods such as Fourier and wavelet were frequently used in processing embolic signals. However, most of the times, the Fourier and discrete wavelet transforms are not appropriate for the analysis of embolic signals due to their non-stationary time-frequency behavior. Alternatively, discrete wavelet packet transform can perform an adaptive decomposition of the time-frequency axis. In this study, directional discrete wavelet packet transforms, which have the ability to map directional information while processing quadrature signals and have less computational complexity than the existing wavelet packet-based methods, are introduced. The performances of proposed methods are examined in detail by using single-frequency, synthetic narrow-band, and embolic quadrature signals. PMID:25388779
Identification of turbulence structures above a forest canopy using a wavelet transform
NASA Technical Reports Server (NTRS)
Turner, B. J.; Leclerc, M. Y.; Gauthier, M.; Moore, K. E.; Fitzjarrald, D. R.
1994-01-01
The wavelet transform is used to identify scales of large coherent structures present in atmospheric turbulence above the subarctic forest at Schefferville. Individual coherent structures contributing to much of the exchange between the forest and the atmosphere are depicted in terms of both scale and location using contour diagrams of wavelet transform coefficients. Three typical case studies of turbulence and flux observations were selected to examine the physical characteristics of these flux-filled events and their evolution with distance away from the forest canopy. A wavelet transform spectral technique is applied to vertical velocity, temperature, and turbulent heat flux data observed over the sparse coniferous forest to extract the relative importance of each scale present in those data series. The scale of turbulence structures in relation with their characteristic spacing is discussed.
[Application of kalman filtering based on wavelet transform in ICP-AES].
Qin, Xia; Shen, Lan-sun
2002-12-01
Kalman filtering is a recursive algorithm, which has been proposed as an attractive alternative to correct overlapping interferences in ICP-AES. However, the noise in ICP-AES contaminates the signal arising from the analyte and hence limits the accuracy of kalman filtering. Wavelet transform is a powerful technique in signal denoising due to its multi-resolution characteristics. In this paper, first, the effect of noise on kalman filtering is discussed. Then we apply the wavelet-transform-based soft-thresholding as the pre-processing of kalman filtering. The simulation results show that the kalman filtering based on wavelet transform can effectively reduce the noise and increase the accuracy of the analysis. PMID:12914186
Noise reduction of FBG sensor signal by using a wavelet transform
NASA Astrophysics Data System (ADS)
Cho, Yo-Han; Song, Minho
2011-05-01
We constructed a FBG (fiber Bragg grating) sensor system based on a fiber-optic Sagnac interferometer. A fiber-optic laser source is used as a strong light source to attain high signal-to-noise ratio. However the unstable output power and coherence noises of the fiber laser made it hard to separate the FBG signals from the interference signals of the fiber coils. To reduce noises and extract FBG sensor signals, we used a Gaussian curve-fitting and a wavelet transform. The wavelet transform is a useful tool for analyzing and denoising output signals. The feasibility of the wavelet transform denoising process is presented with the preliminary experimental results, which showed much better accuracy than the case with only the Gaussian curve-fitting algorithm.
Wavelet Transform for Real-Time Detection of Action Potentials in Neural Signals
Quotb, Adam; Bornat, Yannick; Renaud, Sylvie
2011-01-01
We present a study on wavelet detection methods of neuronal action potentials (APs). Our final goal is to implement the selected algorithms on custom integrated electronics for on-line processing of neural signals; therefore we take real-time computing as a hard specification and silicon area as a price to pay. Using simulated neural signals including APs, we characterize an efficient wavelet method for AP extraction by evaluating its detection rate and its implementation cost. We compare software implementation for three methods: adaptive threshold, discrete wavelet transform (DWT), and stationary wavelet transform (SWT). We evaluate detection rate and implementation cost for detection functions dynamically comparing a signal with an adaptive threshold proportional to its SD, where the signal is the raw neural signal, respectively: (i) non-processed; (ii) processed by a DWT; (iii) processed by a SWT. We also use different mother wavelets and test different data formats to set an optimal compromise between accuracy and silicon cost. Detection accuracy is evaluated together with false negative and false positive detections. Simulation results show that for on-line AP detection implemented on a configurable digital integrated circuit, APs underneath the noise level can be detected using SWT with a well-selected mother wavelet, combined to an adaptive threshold. PMID:21811455
Yang, Zijing; Cai, Ligang; Gao, Lixin; Wang, Huaqing
2012-01-01
A least square method based on data fitting is proposed to construct a new lifting wavelet, together with the nonlinear idea and redundant algorithm, the adaptive redundant lifting transform based on fitting is firstly stated in this paper. By variable combination selections of basis function, sample number and dimension of basis function, a total of nine wavelets with different characteristics are constructed, which are respectively adopted to perform redundant lifting wavelet transforms on low-frequency approximate signals at each layer. Then the normalized lP norms of the new node-signal obtained through decomposition are calculated to adaptively determine the optimal wavelet for the decomposed approximate signal. Next, the original signal is taken for subsection power spectrum analysis to choose the node-signal for single branch reconstruction and demodulation. Experiment signals and engineering signals are respectively used to verify the above method and the results show that bearing faults can be diagnosed more effectively by the method presented here than by both spectrum analysis and demodulation analysis. Meanwhile, compared with the symmetrical wavelets constructed with Lagrange interpolation algorithm, the asymmetrical wavelets constructed based on data fitting are more suitable in feature extraction of fault signal of roller bearings. PMID:22666035
Compressed sensing based on the improved wavelet transform for image processing
NASA Astrophysics Data System (ADS)
Pang, Peng; Gao, Wei; Song, Zongxi; XI, Jiang-bo
2014-09-01
Compressed sensing theory is a new sampling theory that can sample signal in a below sampling rate than the traditional Nyquist sampling theory. Compressed sensing theory that has given a revolutionary solution is a novel sampling and processing theory under the condition that the signal is sparse or compressible. This paper investigates how to improve the theory of CS and its application in imaging system. According to the properties of wavelet transform sub-bands, an improved compressed sensing algorithm based on the single layer wavelet transform was proposed. Based on the feature that the most information was preserved on the low-pass layer after the wavelet transform, the improved compressed sensing algorithm only measured the low-pass wavelet coefficients of the image but preserving the high-pass wavelet coefficients. The signal can be restricted exactly by using the appropriate reconstruction algorithms. The reconstruction algorithm is the key point that most researchers focus on and significant progress has been made. For the reconstruction, in order to improve the orthogonal matching pursuit (OMP) algorithm, increased the iteration layers make sure low-pass wavelet coefficients could be recovered by measurements exactly. Then the image could be reconstructed by using the inverse wavelet transform. Compared the original compressed sensing algorithm, simulation results demonstrated that the proposed algorithm decreased the processed data, signal processed time decreased obviously and the recovered image quality improved to some extent. The PSNR of the proposed algorithm was improved about 2 to 3 dB. Experimental results show that the proposed algorithm exhibits its superiority over other known CS reconstruction algorithms in the literature at the same measurement rates, while with a faster convergence speed.
NASA Astrophysics Data System (ADS)
Gdeisat, Munther; Burton, David; Lilley, Francis; Lalor, Michael; Moore, Chris
2010-04-01
This paper proposes the use of the two-dimensional continuous Paul wavelet transform to extract the phase of spatial carrier fringe patterns. The proposed algorithm has been tested using computer-generated and real fringe patterns, and these tests have demonstrated the suitability of the proposed technique for the phase demodulation of fringe patterns. Additionally, this algorithm is compared to three two-dimensional continuous wavelet algorithms that have figured prominently in the literature, specifically the Morlet, advanced Morlet and fan mother wavelets. This comparison has revealed that the proposed algorithm outperforms the other three mother wavelets in terms of its suitability for extracting the phase of fringe patterns that exhibit large phase variations.
NASA Astrophysics Data System (ADS)
Rosyidi, Sri; Taha, Mohd; Chik, Zamri; Ismail, Amiruddin
2009-09-01
Surface wave method consists of measurement and processing of the dispersive Rayleigh waves recorded from two or more vertical transducers. The dispersive phase data are inverted and the shear wave velocity versus depth is obtained. However, in case of residual soil, the reliable phase spectrum curve is difficult to be produced. Noises from nature and other human-made sources disturb the generated surface wave data. In this paper, a continuous wavelet transform based on mother wavelet of Gaussian Derivative was used to analyze seismic waves in different frequency and time. Time-frequency wavelet spectrum was employed to localize the interested seismic response spectrum of generated surface waves. It can also distinguish the fundamental mode of the surface wave from the higher modes of reflected body waves. The results presented in this paper showed that the wavelet analysis is able to determine reliable surface wave spectrum of sandy clayey residual soil.
Coelho, Clarimar José; Galvão, Roberto K H; de Araújo, Mário César U; Pimentel, Maria Fernanda; da Silva, Edvan Cirino
2003-01-01
A novel strategy for the optimization of wavelet transforms with respect to the statistics of the data set in multivariate calibration problems is proposed. The optimization follows a linear semi-infinite programming formulation, which does not display local maxima problems and can be reproducibly solved with modest computational effort. After the optimization, a variable selection algorithm is employed to choose a subset of wavelet coefficients with minimal collinearity. The selection allows the building of a calibration model by direct multiple linear regression on the wavelet coefficients. In an illustrative application involving the simultaneous determination of Mn, Mo, Cr, Ni, and Fe in steel samples by ICP-AES, the proposed strategy yielded more accurate predictions than PCR, PLS, and nonoptimized wavelet regression. PMID:12767151
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
[Detection of R-wave in Fetal EGG Based on Wavelet Transform and Matched Filtering].
Yan, Wenhong; Jiang, Ning
2015-09-01
By analyzing the characteristics of maternal abdominal ECG (Electrocardiogram), a method based on wavelet transform and matched filtering is proposed to detect the R-wave in fetal EGG (FECG). In this method, the high-frequency coefficients are calculated by using wavelet transform. First, the maternal QRS template is obtained by using the arithmetic mean scheme. Finally, the R-wave of FECG is detected based on matched filtering. The experimental results show that this method can effectively eliminate the noises, such as the maternal ECG signal and baseline drift, enhancing the accuracy of the detection of fetal ECG. PMID:26904869
Diagnosis System Based on Wavelet Transform, Fractal Dimension and Neural Network
NASA Astrophysics Data System (ADS)
El-Ramsisi, Abdallah M.; Khalil, Hassan A.
In this study we introduce a diagnosis system based on wavelet and fractal dimension for diagnose the Heart Mitral Valve Diseases. This study deals with the feature extraction from the Doppler signal waveform at heart mitral valve using ultrasound. Wavelet packet transforms, Fourier transform and Fractal Dimension methods are used for feature extraction from the DHS signals. The back-propagation neural network is used to classify the extracted features. The system has been evaluated in 162 samples that contain 89 normal and 73 abnormal. The results showed that the classification was about 91% for normal and abnormal cases.
Application of the dual-tree complex wavelet transform in biomedical signal denoising.
Wang, Fang; Ji, Zhong
2014-01-01
In biomedical signal processing, Gibbs oscillation and severe frequency aliasing may occur when using the traditional discrete wavelet transform (DWT). Herein, a new denoising algorithm based on the dual-tree complex wavelet transform (DTCWT) is presented. Electrocardiogram (ECG) signals and heart sound signals are denoised based on the DTCWT. The results prove that the DTCWT is efficient. The signal-to-noise ratio (SNR) and the mean square error (MSE) are used to compare the denoising effect. Results of the paired samples t-test show that the new method can remove noise more thoroughly and better retain the boundary and texture of the signal. PMID:24211889
Eyebrows Identity Authentication Based on Wavelet Transform and Support Vector Machines
NASA Astrophysics Data System (ADS)
Jun-bin, CAO; Haitao, Yang; Lili, Ding
In order to study the novel biometric of eyebrow,,this paper presents an Eyebrows identity authentication based on wavelet transform and support vector machines. The features of the eyebrows image are extracted by wavelet transform, and then classifies them based on SVM. Verification results of the experiment on an eyebrow database taken from 100 of self-built personal demonstrate the effectiveness of the system. The system has a lower FAR 0.22%and FRR 28% Therefore, eyebrow recongnition may possibly apply to personal identification.
NASA Astrophysics Data System (ADS)
Zhang, Hongbo; Yi, Xingwen; Chen, Lei; Zhang, Jing; Deng, Mingliang; Qiu, Kun
2012-10-01
As an alternate to fast Fourier transform-based orthogonal frequency-division multiplexing (OFDM), wavelet packet transform (WPT)-based OFDM (WPT-OFDM) does not require cyclic prefix to avoid inter-symbol-interference. The wavelet has many varieties and therefore, it can provide more freedom for system design to suit different applications. We propose a real-valued WPT-OFDM that uses intensity modulation/direct detection. We also conduct an experiment to verify its performance through a 75-km standard single-mode fiber.
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.
Fast multi-scale edge detection algorithm based on wavelet transform
NASA Astrophysics Data System (ADS)
Zang, Jie; Song, Yanjun; Li, Shaojuan; Luo, Guoyun
2011-11-01
The traditional edge detection algorithms have certain noise amplificat ion, making there is a big error, so the edge detection ability is limited. In analysis of the low-frequency signal of image, wavelet analysis theory can reduce the time resolution; under high time resolution for high-frequency signal of the image, it can be concerned about the transient characteristics of the signal to reduce the frequency resolution. Because of the self-adaptive for signal, the wavelet transform can ext ract useful informat ion from the edge of an image. The wavelet transform is at various scales, wavelet transform of each scale provides certain edge informat ion, so called mult i-scale edge detection. Multi-scale edge detection is that the original signal is first polished at different scales, and then detects the mutation of the original signal by the first or second derivative of the polished signal, and the mutations are edges. The edge detection is equivalent to signal detection in different frequency bands after wavelet decomposition. This article is use of this algorithm which takes into account both details and profile of image to detect the mutation of the signal at different scales, provided necessary edge information for image analysis, target recognition and machine visual, and achieved good results.
On the equivalence of moment quantization and continuous wavelet transform analysis
NASA Astrophysics Data System (ADS)
Handy, Carlos R.; Murenzi, Romain
1998-12-01
The space of polynomials maps onto itself under affine transformations, 0305-4470/31/49/012/img1. This suggests that a moment reformulation of continuous wavelet transform (CWT) theory (the affine convolution, 0305-4470/31/49/012/img2, of a signal, or wavefunction, 0305-4470/31/49/012/img3) should lead to significant simplifications in its implementation. We present a comprehensive formalism, with numerical examples, that inextricably links moment quantization (MQ) and CWT theory. For rational fraction potential problems and mother wavelets of the form 0305-4470/31/49/012/img4 (Q(x) an appropriate polynomial), MQ permits a more efficient and accurate (in a pointwise convergent sense) CWT implementation; whereas, CWT broadens the scope of applicability for MQ methods, and is its natural extension when a more global approximation is desired. Our formalism also gives one justification for the empirical superiority manifested by previous MQ studies, as compared with dyadic wavelet reconstruction methods. We implement our formalism in the context of the quartic, sextic and octic anharmonic oscillator potentials, and demonstrate the flexibility of the method by treating both the Mexican hat wavelet transform, as well as that based on the mother wavelet 0305-4470/31/49/012/img5.
A new methodology to map double-cropping croplands based on continuous wavelet transform
NASA Astrophysics Data System (ADS)
Qiu, Bingwen; Zhong, Ming; Tang, Zhenghong; Wang, Chongyang
2014-02-01
Cropping intensity is one of the major factors in crop production and agricultural intensification. A new double-cropping croplands mapping methodology using Moderate Resolution Imaging Spectroradiometer (MODIS) time series datasets through continuous wavelet transform was proposed in this study. This methodology involved four steps. First, daily continuous MODIS Enhanced Vegetation Index (EVI) time series datasets were developed for the study year. Next, the EVI time series datasets were transformed into a two dimensional (time-frequency) wavelet scalogram based on continuous wavelet transform. Third, a feature extraction process was conducted on the wavelet scalogram, where the characteristic spectra were calculated from the wavelet scalogram and the feature peak within two skeleton lines was obtained. Finally, a threshold was determined for feature peak values to discriminate double-cropping croplands within each pixel. The application of the proposed procedure to China's Henan Province in 2010 produced an objective and accurate spatial distribution map, which correlated well with in situ observation data (over 90% agreement). The proposed new methodology efficiently handled complex variability that might be caused by regional variation in climate, management practices, growth peaks by winter weed or winter wheat, and data noise. Therefore, the methodology shows promise for future studies at regional and global scales.
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.
Combining 2D synchrosqueezed wave packet transform with optimization for crystal image analysis
NASA Astrophysics Data System (ADS)
Lu, Jianfeng; Wirth, Benedikt; Yang, Haizhao
2016-04-01
We develop a variational optimization method for crystal analysis in atomic resolution images, which uses information from a 2D synchrosqueezed transform (SST) as input. The synchrosqueezed transform is applied to extract initial information from atomic crystal images: crystal defects, rotations and the gradient of elastic deformation. The deformation gradient estimate is then improved outside the identified defect region via a variational approach, to obtain more robust results agreeing better with the physical constraints. The variational model is optimized by a nonlinear projected conjugate gradient method. Both examples of images from computer simulations and imaging experiments are analyzed, with results demonstrating the effectiveness of the proposed method.
Construction of 2D quasi-periodic Rauzy tiling by similarity transformation
Zhuravlev, V. G.; Maleev, A. V.
2009-05-15
A new approach to constructing self-similar fractal tilings is proposed based on the construction of semigroups generated by a finite set of similarity transformations. The Rauzy tiling-a 2D analog of 1D Fibonacci tiling generated by the golden mean-is used as an example to illustrate this approach. It is shown that the Rauzy torus development and the elementary fractal boundary of Rauzy tiling can be constructed in the form of a set of centers of similarity semigroups generated by two and three similarity transformations, respectively. A centrosymmetric tiling, locally dual to the Rauzy tiling, is constructed for the first time and its parameterization is developed.
NASA Astrophysics Data System (ADS)
Zhou, Nanrun; Li, Haolin; Wang, Di; Pan, Shumin; Zhou, Zhihong
2015-05-01
Most of the existing image encryption techniques bear security risks for taking linear transform or suffer encryption data expansion for adopting nonlinear transformation directly. To overcome these difficulties, a novel image compression-encryption scheme is proposed by combining 2D compressive sensing with nonlinear fractional Mellin transform. In this scheme, the original image is measured by measurement matrices in two directions to achieve compression and encryption simultaneously, and then the resulting image is re-encrypted by the nonlinear fractional Mellin transform. The measurement matrices are controlled by chaos map. The Newton Smoothed l0 Norm (NSL0) algorithm is adopted to obtain the decryption image. Simulation results verify the validity and the reliability of this scheme.
Medical image compression algorithm based on wavelet transform
NASA Astrophysics Data System (ADS)
Chen, Minghong; Zhang, Guoping; Wan, Wei; Liu, Minmin
2005-02-01
With rapid development of electronic imaging and multimedia technology, the telemedicine is applied to modern medical servings in the hospital. Digital medical image is characterized by high resolution, high precision and vast data. The optimized compression algorithm can alleviate restriction in the transmission speed and data storage. This paper describes the characteristics of human vision system based on the physiology structure, and analyses the characteristics of medical image in the telemedicine, then it brings forward an optimized compression algorithm based on wavelet zerotree. After the image is smoothed, it is decomposed with the haar filters. Then the wavelet coefficients are quantified adaptively. Therefore, we can maximize efficiency of compression and achieve better subjective visual image. This algorithm can be applied to image transmission in the telemedicine. In the end, we examined the feasibility of this algorithm with an image transmission experiment in the network.
Wavelet transform approach for fitting financial time series data
NASA Astrophysics Data System (ADS)
Ahmed, Amel Abdoullah; Ismail, Mohd Tahir
2015-10-01
This study investigates a newly developed technique; a combined wavelet filtering and VEC model, to study the dynamic relationship among financial time series. Wavelet filter has been used to annihilate noise data in daily data set of NASDAQ stock market of US, and three stock markets of Middle East and North Africa (MENA) region, namely, Egypt, Jordan, and Istanbul. The data covered is from 6/29/2001 to 5/5/2009. After that, the returns of generated series by wavelet filter and original series are analyzed by cointegration test and VEC model. The results show that the cointegration test affirms the existence of cointegration between the studied series, and there is a long-term relationship between the US, stock markets and MENA stock markets. A comparison between the proposed model and traditional model demonstrates that, the proposed model (DWT with VEC model) outperforms traditional model (VEC model) to fit the financial stock markets series well, and shows real information about these relationships among the stock markets.
AlZubi, Shadi; Islam, Naveed; Abbod, Maysam
2011-01-01
The experimental study presented in this paper is aimed at the development of an automatic image segmentation system for classifying region of interest (ROI) in medical images which are obtained from different medical scanners such as PET, CT, or MRI. Multiresolution analysis (MRA) using wavelet, ridgelet, and curvelet transforms has been used in the proposed segmentation system. It is particularly a challenging task to classify cancers in human organs in scanners output using shape or gray-level information; organs shape changes throw different slices in medical stack and the gray-level intensity overlap in soft tissues. Curvelet transform is a new extension of wavelet and ridgelet transforms which aims to deal with interesting phenomena occurring along curves. Curvelet transforms has been tested on medical data sets, and results are compared with those obtained from the other transforms. Tests indicate that using curvelet significantly improves the classification of abnormal tissues in the scans and reduce the surrounding noise. PMID:21960988
Detection of linear features using a localized radon transform with a wavelet filter
Warrick, A L; Delaney, P A
1999-12-13
One problem of interest to the oceanic engineering community is the detection and enhancement of internal wakes in open water synthetic aperture radar (SAR) images. Internal wakes, which occur when a ship travels in a stratified medium, have a V shape extending from the ship, and a chirp-like feature across each arm. The Radon transform has been applied to the detection and the enhancement problems in internal wake images to account for the linear features while the wavelet transform has been applied to the enhancement problem in internal wake images to account for the chirp-like features. In this paper, a new transform, a localized Radon transform with a wavelet filter (LRTWF), is developed which accounts for both the linear and the chirp-like features of the internal wake. This transform is then incorporated into optimal and sub-optimal detection schemes for images (with these features) which are contaminated by additive Gaussian noise.
Alzubi, Shadi; Islam, Naveed; Abbod, Maysam
2011-01-01
The experimental study presented in this paper is aimed at the development of an automatic image segmentation system for classifying region of interest (ROI) in medical images which are obtained from different medical scanners such as PET, CT, or MRI. Multiresolution analysis (MRA) using wavelet, ridgelet, and curvelet transforms has been used in the proposed segmentation system. It is particularly a challenging task to classify cancers in human organs in scanners output using shape or gray-level information; organs shape changes throw different slices in medical stack and the gray-level intensity overlap in soft tissues. Curvelet transform is a new extension of wavelet and ridgelet transforms which aims to deal with interesting phenomena occurring along curves. Curvelet transforms has been tested on medical data sets, and results are compared with those obtained from the other transforms. Tests indicate that using curvelet significantly improves the classification of abnormal tissues in the scans and reduce the surrounding noise. PMID:21960988
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
CW-THz image contrast enhancement using wavelet transform and Retinex
NASA Astrophysics Data System (ADS)
Chen, Lin; Zhang, Min; Hu, Qi-fan; Huang, Ying-Xue; Liang, Hua-Wei
2015-10-01
To enhance continuous wave terahertz (CW-THz) scanning images contrast and denoising, a method based on wavelet transform and Retinex theory was proposed. In this paper, the factors affecting the quality of CW-THz images were analysed. Second, an approach of combination of the discrete wavelet transform (DWT) and a designed nonlinear function in wavelet domain for the purpose of contrast enhancing was applied. Then, we combine the Retinex algorithm for further contrast enhancement. To evaluate the effectiveness of the proposed method in qualitative and quantitative, it was compared with the adaptive histogram equalization method, the homomorphic filtering method and the SSR(Single-Scale-Retinex) method. Experimental results demonstrated that the presented algorithm can effectively enhance the contrast of CW-THZ image and obtain better visual effect.
NASA Astrophysics Data System (ADS)
Yaseen, Alauldeen S.; Pavlov, Alexey N.; Hramov, Alexander E.
2016-03-01
Speech signal processing is widely used to reduce noise impact in acquired data. During the last decades, wavelet-based filtering techniques are often applied in communication systems due to their advantages in signal denoising as compared with Fourier-based methods. In this study we consider applications of a 1-D double density complex wavelet transform (1D-DDCWT) and compare the results with the standard 1-D discrete wavelet-transform (1DDWT). The performances of the considered techniques are compared using the mean opinion score (MOS) being the primary metric for the quality of the processed signals. A two-dimensional extension of this approach can be used for effective image denoising.
On the use of lossless integer wavelet transforms in medical image segmentation
NASA Astrophysics Data System (ADS)
Nagaraj, Nithin; Mallya, Yogish
2005-04-01
Recent trends in medical image processing involve computationally intensive processing techniques on large data sets, especially for 3D applications such as segmentation, registration, volume rendering etc. Multi-resolution image processing techniques have been used in order to speed-up these methods. However, all well-known techniques currently used in multi-resolution medical image processing rely on using Gaussain-based or other equivalent floating point representations that are lossy and irreversible. In this paper, we study the use of Integer Wavelet Transforms (IWT) to address the issue of lossless representation and reversible reconstruction for such medical image processing applications while still retaining all the benefits which floating-point transforms offer such as high speed and efficient memory usage. In particular, we consider three low-complexity reversible wavelet transforms namely the - Lazy-wavelet, the Haar wavelet or (1,1) and the S+P transform as against the Gaussian filter for multi-resolution speed-up of an automatic bone removal algorithm for abdomen CT Angiography. Perfect-reconstruction integer wavelet filters have the ability to perfectly recover the original data set at any step in the application. An additional advantage with the reversible wavelet representation is that it is suitable for lossless compression for purposes of storage, archiving and fast retrieval. Given the fact that even a slight loss of information in medical image processing can be detrimental to diagnostic accuracy, IWTs seem to be the ideal choice for multi-resolution based medical image segmentation algorithms. These could also be useful for other medical image processing methods.
Exploration of EEG features of Alzheimer's disease using continuous wavelet transform.
Ghorbanian, Parham; Devilbiss, David M; Hess, Terry; Bernstein, Allan; Simon, Adam J; Ashrafiuon, Hashem
2015-09-01
We have developed a novel approach to elucidate several discriminating EEG features of Alzheimer's disease. The approach is based on the use of a variety of continuous wavelet transforms, pairwise statistical tests with multiple comparison correction, and several decision tree algorithms, in order to choose the most prominent EEG features from a single sensor. A pilot study was conducted to record EEG signals from Alzheimer's disease (AD) patients and healthy age-matched control (CTL) subjects using a single dry electrode device during several eyes-closed (EC) and eyes-open (EO) resting conditions. We computed the power spectrum distribution properties and wavelet and sample entropy of the wavelet coefficients time series at scale ranges approximately corresponding to the major brain frequency bands. A predictive index was developed using the results from statistical tests and decision tree algorithms to identify the most reliable significant features of the AD patients when compared to healthy controls. The three most dominant features were identified as larger absolute mean power and larger standard deviation of the wavelet scales corresponding to 4-8 Hz (θ) during EO and lower wavelet entropy of the wavelet scales corresponding to 8-12 Hz (α) during EC, respectively. The fourth reliable set of distinguishing features of AD patients was lower relative power of the wavelet scales corresponding to 12-30 Hz (β) followed by lower skewness of the wavelet scales corresponding to 2-4 Hz (upper δ), both during EO. In general, the results indicate slowing and lower complexity of EEG signal in AD patients using a very easy-to-use and convenient single dry electrode device. PMID:25863694
Li, Fang; Wang, Ji-hua; Lu, An-xiang; Han, Ping
2015-04-01
The concentration of Cr, Cu, Zn, As and Pb in soil was tested by portable X-ray fluorescence spectrometer. Each sample was tested for 3 times, then after using wavelet threshold noise filtering method for denoising and smoothing the spectra, a standard curve for each heavy metal was established according to the standard values of heavy metals in soil and the corresponding counts which was the average of the 3 processed spectra. The signal to noise ratio (SNR), mean square error (MSE) and information entropy (H) were taken to assess the effects of denoising when using wavelet threshold noise filtering method for determining the best wavelet basis and wavelet decomposition level. Some samples with different concentrations and H3 B03 (blank) were chosen to retest this instrument to verify its stability. The results show that: the best denoising result was obtained with the coif3 wavelet basis at the decomposition level of 3 when using the wavelet transform method. The determination coefficient (R2) range of the instrument is 0.990-0.996, indicating that a high degree of linearity was found between the contents of heavy metals in soil and each X-ray fluorescence spectral characteristic peak intensity with the instrument measurement within the range (0-1,500 mg · kg(-1)). After retesting and calculating, the results indicate that all the detection limits of the instrument are below the soil standards at national level. The accuracy of the model has been effectively improved, and the instrument also shows good precision with the practical application of wavelet transform to the establishment and improvement of X-ray fluorescence spectrometer detection model. Thus the instrument can be applied in on-site rapid screening of heavy metal in contaminated soil. PMID:26197612
NASA Astrophysics Data System (ADS)
Andre, Julia; Kiremidjian, Anne; Liao, Yizheng; Georgakis, Christos; Rajagopal, Ram
2016-04-01
Ice accretion on cables of bridge structures poses serious risk to the structure as well as to vehicular traffic when the ice falls onto the road. Detection of ice formation, quantification of the amount of ice accumulated, and prediction of icefalls will increase the safety and serviceability of the structure. In this paper, an ice accretion detection algorithm is presented based on the Continuous Wavelet Transform (CWT). In the proposed algorithm, the acceleration signals obtained from bridge cables are transformed using wavelet method. The damage sensitive features (DSFs) are defined as a function of the wavelet energy at specific wavelet scales. It is found that as ice accretes on the cables, the mass of cable increases, thus changing the wavelet energies. Hence, the DSFs can be used to track the change of cables mass. To validate the proposed algorithm, we use the data collected from a laboratory experiment conducted at the Technical University of Denmark (DTU). In this experiment, a cable was placed in a wind tunnel as ice volume grew progressively. Several accelerometers were installed at various locations along the testing cable to collect vibration signals.
Chen, Hui; Lin, Zan; Mo, Lin; Wu, Hegang; Wu, Tong; Tan, Chao
2015-12-01
Spectrum is inherently local in nature since it can be thought of as a signal being composed of various frequency components. Wavelet transform (WT) is a powerful tool that partitions a signal into components with different frequency. The property of multi-resolution enables WT a very effective and natural tool for analyzing spectrum-like signal. In this study, a continuous wavelet transform (CWT)-based variable selection procedure was proposed to search for a set of informative wavelet coefficients for constructing a near-infrared (NIR) spectral diagnosis model of cancer. The CWT provided a fine multi-resolution feature space for selecting best predictors. A measure of discriminating power (DP) was defined to evaluate the coefficients. Partial least squares-discriminant analysis (PLS-DA) was used as the classification algorithm. A NIR spectral dataset associated to cancer diagnosis was used for experiment. The optimal results obtained correspond to the wavelet of db2. It revealed that on condition of having better performance on the training set, the optimal PLS-DA model using only 40 wavelet coefficients in 10 scales achieved the same performance as the one using all the variables in the original space on the test set: an overall accuracy of 93.8%, sensitivity of 92.5% and specificity of 96.3%. It confirms that the CWT-based feature selection coupled with PLS-DA is feasible and effective for constructing models of diagnostic cancer by NIR spectroscopy. PMID:26143320
Fundamental Study on Vibration Diagnosis for High Speed Rotational Machine using Wavelet Transform
NASA Astrophysics Data System (ADS)
Kawada, Masatake; Yamada, Koji; Yamashita, Katsuya
In this paper we presented results of fundamental study to introduce the wavelet transform to vibration diagnosis for high-speed rotational machine such as steam turbine, gas turbine, and generator and so on. It is required to detect and distinguish typical vibration of high-speed rotational machine accurately in order to diagnose the machine. The wavelet transform is used in many fields because it is able to visualize phenomenon in time-frequency domain and to detect the beginning time and the duration of it. We made a model rotor supported with two journal bearings to simulate contact vibration, clearance vibration, and oil whip. The vibration phenomena were measured with vertical and horizontal displacement meters at the rotor and vertical and horizontal accelerometers at the rotor bearing and visualized in the time-frequency domain by the wavelet transform. It is found that the dynamic spectra obtained by the wavelet transform of the vertical and horizontal components of displacement and acceleration signals are different for each vibration phenomenon, therefore, this method is able to distinguish each kind of vibration phenomenon. Each vibration phenomenon can be detected and distinguished at the early stage.
An iterative algorithm for background removal in spectroscopy by wavelet transforms.
Galloway, C M; Le Ru, E C; Etchegoin, P G
2009-12-01
Wavelet transforms are an extremely powerful tool when it comes to processing signals that have very "low frequency" components or non-periodic events. Our particular interest here is in the ability of wavelet transforms to remove backgrounds of spectroscopic signals. We will discuss the case of surface-enhanced Raman spectroscopy (SERS) for illustration, but the situation it depicts is widespread throughout a myriad of different types of spectroscopies (IR, NMR, etc.). We outline a purpose-built algorithm that we have developed to perform an iterative wavelet transform. In this algorithm, the effect of the signal peaks above the background is reduced after each iteration until the fit converges close to the real background. Experimental examples of two different SERS applications are given: one involving broad backgrounds (that do not vary much among spectra), and another that involves single molecule SERS (SM-SERS) measurements with narrower (and varying) backgrounds. In both cases, we will show that wavelet transforms can be used to fit the background with a great deal of accuracy, thus providing the framework for automatic background removal of large sets of data (typically obtained in time-series or spatial mappings). A MATLAB((R)) based application that utilizes the iterative algorithm developed here is freely available to download from http://www.victoria.ac.nz/raman/publis/codes/cobra.aspx. PMID:20030982
Vector and parallel wavelet transforms for the analysis of time-varying signals
Uhl, A.
1995-12-01
An algorithm for computing the continous wavelet transform is implemented on a Convex C3440 Vectorcomputer and on a workstation cluster using PVM. On the cluster a master-slave programming scheme using an asynchronous pool of tasks method is applied. Timings, speedups and load balancing considerations are presented.
NASA Astrophysics Data System (ADS)
Singh, Hukum
2016-05-01
An optical color image encryption in the Fractional Wavelet Transform (FWT) domain is carried out. The original images are segregated into three colors components: R (red), G (green) and B (blue). After that the components are encrypted separately using double random phase encoding (DRPE) in the FWT domain. Random phase masks (RPMs) are used in the input as well as in Fourier plane. The images to be encrypted are transformed with the discrete wavelet transform (DWT), the resulting coefficients from the DWT are multiplied each one by masks different form RPM. Masks are independent each other and the results are applied an inverse discrete Wavelet Transform (IDWT), obtaining the encrypted images. The input images are recovered from their corresponding encrypted images by using the correct parameters of the FWT, and its digital implementation has been performed using MATLAB 7.6.0 (R2008a). The mother wavelet family and fractional orders associated with the FWT are extra keys that access difficulty an attacker; thereby the scheme is more secure as compared to conventional techniques. The sensitivity of proposed scheme is verified with encryption parameters, occlusions, and noise attacks.
Multi-focus image fusion algorithm based on adaptive PCNN and wavelet transform
NASA Astrophysics Data System (ADS)
Wu, Zhi-guo; Wang, Ming-jia; Han, Guang-liang
2011-08-01
Being an efficient method of information fusion, image fusion has been used in many fields such as machine vision, medical diagnosis, military applications and remote sensing. In this paper, Pulse Coupled Neural Network (PCNN) is introduced in this research field for its interesting properties in image processing, including segmentation, target recognition et al. and a novel algorithm based on PCNN and Wavelet Transform for Multi-focus image fusion is proposed. First, the two original images are decomposed by wavelet transform. Then, based on the PCNN, a fusion rule in the Wavelet domain is given. This algorithm uses the wavelet coefficient in each frequency domain as the linking strength, so that its value can be chosen adaptively. Wavelet coefficients map to the range of image gray-scale. The output threshold function attenuates to minimum gray over time. Then all pixels of image get the ignition. So, the output of PCNN in each iteration time is ignition wavelet coefficients of threshold strength in different time. At this moment, the sequences of ignition of wavelet coefficients represent ignition timing of each neuron. The ignition timing of PCNN in each neuron is mapped to corresponding image gray-scale range, which is a picture of ignition timing mapping. Then it can judge the targets in the neuron are obvious features or not obvious. The fusion coefficients are decided by the compare-selection operator with the firing time gradient maps and the fusion image is reconstructed by wavelet inverse transform. Furthermore, by this algorithm, the threshold adjusting constant is estimated by appointed iteration number. Furthermore, In order to sufficient reflect order of the firing time, the threshold adjusting constant αΘ is estimated by appointed iteration number. So after the iteration achieved, each of the wavelet coefficient is activated. In order to verify the effectiveness of proposed rules, the experiments upon Multi-focus image are done. Moreover
Blind watermark algorithm on 3D motion model based on wavelet transform
NASA Astrophysics Data System (ADS)
Qi, Hu; Zhai, Lang
2013-12-01
With the continuous development of 3D vision technology, digital watermark technology, as the best choice for copyright protection, has fused with it gradually. This paper proposed a blind watermark plan of 3D motion model based on wavelet transform, and made it loaded into the Vega real-time visual simulation system. Firstly, put 3D model into affine transform, and take the distance from the center of gravity to the vertex of 3D object in order to generate a one-dimensional discrete signal; then make this signal into wavelet transform to change its frequency coefficients and embed watermark, finally generate 3D motion model with watermarking. In fixed affine space, achieve the robustness in translation, revolving and proportion transforms. The results show that this approach has better performances not only in robustness, but also in watermark- invisibility.
NASA Astrophysics Data System (ADS)
Isah, Abdulnasir; Chang, Phang
2016-06-01
In this article we propose the wavelet operational method based on shifted Legendre polynomial to obtain the numerical solutions of non-linear systems of fractional order differential equations (NSFDEs). The operational matrix of fractional derivative derived through wavelet-polynomial transformation are used together with the collocation method to turn the NSFDEs to a system of non-linear algebraic equations. Illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques.
Etchepareborda, Pablo; Vadnjal, Ana Laura; Federico, Alejandro; Kaufmann, Guillermo H
2012-09-15
We evaluate the extension of the exact nonlinear reconstruction technique developed for digital holography to the phase-recovery problems presented by other optical interferometric methods, which use carrier modulation. It is shown that the introduction of an analytic wavelet analysis in the ridge of the cepstrum transformation corresponding to the analyzed interferogram can be closely related to the well-known wavelet analysis of the interferometric intensity. Subsequently, the phase-recovery process is improved. The advantages and limitations of this framework are analyzed and discussed using numerical simulations in singular scalar light fields and in temporal speckle pattern interferometry. PMID:23041878
Application Of Continuous Wavelet Transform On Aeromagnetic Data To Identify Volcanic Rocks
NASA Astrophysics Data System (ADS)
Yang, Y.; Li, Y.; Liu, T.
2008-12-01
This paper focuses on the application of continuous wavelet transform on aeromagnetic data, to locate and characterize volcanic rocks. The studied structure is sited in the north centre of the Huanghua depression in the Bohaiwan basin of east China. As channels of magmatism activities, the faults have caused multi-stage magma outpouring and intrusion, forming igneous rocks of different series of strata. As a traditional frequency decomposition method, the discrete wavelet transform is unable to localize frequency variations over time. To handle this problem, the short time Fourier transform method is widely used for the decomposition of non-stationary signals. One problem with this approach is that the fixed width `window function' results in limited resolution. Therefore, the continuous wavelet transform decomposition was used as an alternative approach to overcome this resolution problem. In the continuous wavelet transform, the signal is multiplied with a function similar to a `window function' but the width of the window is not fixed. The time window width is allowed to vary depending upon the frequency that is being considered. As for the magnetic anomalies of igneous rocks, they have different frequencies due to their depths; by analyzing the complex wavelet-based time-frequency characteristics of certain frequencies, we can identify the residual anomalies caused by volcanic rocks in different depths. The theoretical results show that local high frequency spectrum anomalies are the reflection of magnetic sources, and different scales (or different center frequencies) reflect different source depths, with larger scales for deeper sources. Therefore, by analyzing the complex wavelet-based frequency spectrum under different centre frequencies, we can analyze the distribution of magnetic field sources. Then the continuous wavelet transform was applied on the RTP aeromagnetic data of our study area. The data processing results present a detailed description of the
Dual tree complex wavelet transform based denoising of optical microscopy images.
Bal, Ufuk
2012-12-01
Photon shot noise is the main noise source of optical microscopy images and can be modeled by a Poisson process. Several discrete wavelet transform based methods have been proposed in the literature for denoising images corrupted by Poisson noise. However, the discrete wavelet transform (DWT) has disadvantages such as shift variance, aliasing, and lack of directional selectivity. To overcome these problems, a dual tree complex wavelet transform is used in our proposed denoising algorithm. Our denoising algorithm is based on the assumption that for the Poisson noise case threshold values for wavelet coefficients can be estimated from the approximation coefficients. Our proposed method was compared with one of the state of the art denoising algorithms. Better results were obtained by using the proposed algorithm in terms of image quality metrics. Furthermore, the contrast enhancement effect of the proposed method on collagen fıber images is examined. Our method allows fast and efficient enhancement of images obtained under low light intensity conditions. PMID:23243573
Wavelet transformation to determine impedance spectra of lithium-ion rechargeable battery
NASA Astrophysics Data System (ADS)
Hoshi, Yoshinao; Yakabe, Natsuki; Isobe, Koichiro; Saito, Toshiki; Shitanda, Isao; Itagaki, Masayuki
2016-05-01
A new analytical method is proposed to determine the electrochemical impedance of lithium-ion rechargeable batteries (LIRB) from time domain data by wavelet transformation (WT). The WT is a waveform analysis method that can transform data in the time domain to the frequency domain while retaining time information. In this transformation, the frequency domain data are obtained by the convolution integral of a mother wavelet and original time domain data. A complex Morlet mother wavelet (CMMW) is used to obtain the complex number data in the frequency domain. The CMMW is expressed by combining a Gaussian function and sinusoidal term. The theory to select a set of suitable conditions for variables and constants related to the CMMW, i.e., band, scale, and time parameters, is established by determining impedance spectra from wavelet coefficients using input voltage to the equivalent circuit and the output current. The impedance spectrum of LIRB determined by WT agrees well with that measured using a frequency response analyzer.
Continuous wavelet transform analysis of one-dimensional quantum bound states from first principles
Handy, C.R.; Murenzi, R.
1996-11-01
Over the last decade, Handy and Bessis have developed a moment-problem-based, multiscale quantization theory, the eigenvalue moment method (EMM), which has proven effective in solving singular, strongly coupled, multidimensional Schr{umlt o}dinger Hamiltonians. We extend the scope of EMM by demonstrating its essential role in the generation of wavelet transforms for one-dimensional quantum systems. Combining this with the function-wavelet reconstruction formulas currently available, we are able to recover the wave function systematically, from first principles, through a multiscale process proceeding from large spatial scales to smaller ones. This accomplishment also addresses another outstanding problem, that of reconstructing a function from its moments. For the class of problems considered, the combined EMM-wavelet analysis yields a definitive solution. {copyright} {ital 1996 The American Physical Society.}
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.
[Ultrasound image de-noising based on nonlinear diffusion of complex wavelet transform].
Hou, Wen; Wu, Yiquan
2012-04-01
Ultrasound images are easily corrupted by speckle noise, which limits its further application in medical diagnoses. An image de-noising method combining dual-tree complex wavelet transform (DT-CWT) with nonlinear diffusion is proposed in this paper. Firstly, an image is decomposed by DT-CWT. Then adaptive-contrast-factor diffusion and total variation diffusion are applied to high-frequency component and low-frequency component, respectively. Finally the image is synthesized. The experimental results are given. The comparisons of the image de-noising results are made with those of the image de-noising methods based on the combination of wavelet shrinkage with total variation diffusion, the combination of wavelet/multiwavelet with nonlinear diffusion. It is shown that the proposed image de-noising method based on DT-CWT and nonlinear diffusion can obtain superior results. It can both remove speckle noise and preserve the original edges and textural features more efficiently. PMID:22616185
De-Noising Ultrasound Images of Colon Tumors Using Daubechies Wavelet Transform
NASA Astrophysics Data System (ADS)
Moraru, Luminita; Moldovanu, Simona; Nicolae, Mariana Carmen
2011-10-01
In this paper, we present a new approach to analysis of the cancer of the colon in ultrasonography. A speckle suppression method was presented. Daubechies wavelet transform is used due to its approximate shift invariance property and extra information in imaginary plane of complex wavelet domain when compared to real wavelet domain. The methods that we propose have provided quite satisfactory results and show the usefulness of image processing techniques in the diagnosis by means of medical imaging. Local echogenicity variance of ROI is utilized so as to compare with local echogenicity distribution within entire acquired image. Also the image was analyzed using the histogram which interprets the gray-level of images. Such information is valuable for the discrimination of tumors. The aim of this work is not the substitution of the specialist, but the generation of a series of parameters which reduce the need of carrying out the biopsy.
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).
Hoang, Vu Dang; Ly, Dong Thi Ha; Tho, Nguyen Huu; Minh Thi Nguyen, Hue
2014-01-01
The application of first-order derivative and wavelet transforms to UV spectra and ratio spectra was proposed for the simultaneous determination of ibuprofen and paracetamol in their combined tablets. A new hybrid approach on the combined use of first-order derivative and wavelet transforms to spectra was also discussed. In this application, DWT (sym6 and haar), CWT (mexh), and FWT were optimized to give the highest spectral recoveries. Calibration graphs in the linear concentration ranges of ibuprofen (12–32 mg/L) and paracetamol (20–40 mg/L) were obtained by measuring the amplitudes of the transformed signals. Our proposed spectrophotometric methods were statistically compared to HPLC in terms of precision and accuracy. PMID:24949492
Hoang, Vu Dang; Ly, Dong Thi Ha; Tho, Nguyen Huu; Nguyen, Hue Minh Thi
2014-01-01
The application of first-order derivative and wavelet transforms to UV spectra and ratio spectra was proposed for the simultaneous determination of ibuprofen and paracetamol in their combined tablets. A new hybrid approach on the combined use of first-order derivative and wavelet transforms to spectra was also discussed. In this application, DWT (sym6 and haar), CWT (mexh), and FWT were optimized to give the highest spectral recoveries. Calibration graphs in the linear concentration ranges of ibuprofen (12-32 mg/L) and paracetamol (20-40 mg/L) were obtained by measuring the amplitudes of the transformed signals. Our proposed spectrophotometric methods were statistically compared to HPLC in terms of precision and accuracy. PMID:24949492
NASA Astrophysics Data System (ADS)
Singer, H. M.; Singer, I.
2006-09-01
The phase-field-crystal model [K. R. Elder and M. Grant, Phys. Rev. E 70, 051605 (2004)] produces multigrain structures on atomistic length scale but on diffusive time scales. Since individual atoms are resolved but are treated identically it is difficult to distinguish the exact position of grain boundaries and defects within grains. In order to analyze and visualize the whole grains a two-dimensional wavelet transform has been developed, which is capable of extracting grain boundaries and the lattice orientation of a grain relative to a laboratory frame of reference. This transformation makes it possible not only to easily visualize the multigrain structure, but also to perform exact measurements on low- and high-angle boundaries, grain size distributions and boundary-angle distributions, which can then be compared to experimental data. The presented wavelet transform can also be applied to results of other atomistic simulations, e.g., molecular dynamics or granular materials.
NASA Astrophysics Data System (ADS)
Fernandez, Sergio; Gdeisat, Munther A.; Salvi, Joaquim; Burton, David
2011-06-01
Fringe pattern analysis in coded structured light constitutes an active field of research. Techniques based on first projecting a sinusoidal pattern and then recovering the phase deviation permit the computation of the phase map and its corresponding depth map, leading to a dense acquisition of the measuring object. Among these techniques, the ones based on time-frequency analysis permit to extract the depth map from a single image, thus having potential applications measuring moving objects. The main techniques are Fourier Transform (FT), Windowed Fourier Transform (WFT) and Wavelet Transform (WT). This paper first analyzes the pros and cons of these three techniques, then a new algorithm for the automatic selection of the window size in WFT is proposed. This algorithm is compared to the traditional WT using adapted mother wavelet signals both with simulated and real objects, showing the performance results for quantitative and qualitative evaluations of the new method.
Coastal hurricane damage assessment via wavelet transform of remotely sensed imagery
NASA Astrophysics Data System (ADS)
Crowsey, Ricky Carl
This dissertation uses post storm imagery processed using wavelet transforms to investigate the capability of wavelet transform-based methods to classify post storm damage of residential areas. Five level Haar, Meyer, Symlets, and Coiflets wavelet transform decompositions of the post storm imagery are inputs to damage classification models of post hurricane and tornado damage. Hurricanes Ike, Rita, Katrina, and Ivan are examined as are the 2011 Joplin and Tuscaloosa tornadoes. Wavelet transform-based classification methods yielded varying classification accuracies for the four hurricanes examined, ranging from 67 percent to 89 percent classification accuracy for classification models informed by samples from the storms classified. Classification accuracies fall when the samples being classified are from a hurricane not informing the classification model, from 17 percent for Rita classified with an Ike-based model, 41 percent for Rita classified with an Ike-Katrina-based model, to 69 percent for Rita classified with an Ike-Katrina-Ivan-based model. The variability within and poor classification accuracy of these models can be attributed to the large variations in the four hurricane events studied and the significant differences in impacted land cover for each of these storms. Classification accuracies improved when these variations were limited via examination of residential areas impacted by 2011 Joplin and Tuscaloosa tornadoes. Damage classification models required as few as nineteen to as many as fifty nine wavelet coefficients to explain the variability in the hurricane storm data samples, and included all four wavelet functions studied. A similar analysis of the tornado damaged areas resulted in a damage classification model with only six wavelet coefficients, four Meyer-based, one Symlets-based and one Haar-based. Classification accuracies ranged from 96 percent for samples included in the model formation to 85 percent for samples not included in the model
A FPGA system for QRS complex detection based on Integer Wavelet Transform
NASA Astrophysics Data System (ADS)
Stojanović, R.; Karadaglić, D.; Mirković, M.; Milošević, D.
2011-01-01
Due to complexity of their mathematical computation, many QRS detectors are implemented in software and cannot operate in real time. The paper presents a real-time hardware based solution for this task. To filter ECG signal and to extract QRS complex it employs the Integer Wavelet Transform. The system includes several components and is incorporated in a single FPGA chip what makes it suitable for direct embedding in medical instruments or wearable health care devices. It has sufficient accuracy (about 95%), showing remarkable noise immunity and low cost. Additionally, each system component is composed of several identical blocks/cells what makes the design highly generic. The capacity of today existing FPGAs allows even dozens of detectors to be placed in a single chip. After the theoretical introduction of wavelets and the review of their application in QRS detection, it will be shown how some basic wavelets can be optimized for easy hardware implementation. For this purpose the migration to the integer arithmetic and additional simplifications in calculations has to be done. Further, the system architecture will be presented with the demonstrations in both, software simulation and real testing. At the end, the working performances and preliminary results will be outlined and discussed. The same principle can be applied with other signals where the hardware implementation of wavelet transform can be of benefit.
An application of wavelet transform for decomposition of millimeter-wave spectroscopic signals
Gopalan, K.; Gopalsami, N.; Bakhtiari, S.; Raptis, A.C.
1994-08-01
Millimeter-wave technique, based on rotational energy transitions of molecules, holds promise for remote monitoring of environmentally hazardous effluents from processes. Argonne National Laboratory is developing a millimeter-wave sensor based on active swept-frequency radar technique in the frequency range of 220-320 GHz. Because the line widths of millimeter-wave spectra of molecules at atmospheric pressure are broad ({approximately} 4 GHz half-width at half height), the composite spectrum of multicomponent mixtures of chemicals is generally complex and overlapping. This paper presents an application of discrete wavelet transform for efficient representation and decomposition of millimeter-wave spectral data. A two-layer back propagation neural network is trained using multifrequency wavelet coefficients of the signals as input features and the known composition of different chemicals in the mixture as target output vectors. After training, composition of an unknown mixture of the base chemicals is determined using the wavelet representation of its absorption spectra. Simulated and experimental spectral data were used to test the wavelet transform technique. Accurate values of individual chemical compositions resulted for noise-free laboratory data. In addition, the technique showed more robustness than conventional multivariate techniques under noisy conditions.
Feature Extraction using Wavelet Transform for Multi-class Fault Detection of Induction Motor
NASA Astrophysics Data System (ADS)
Chattopadhyay, P.; Konar, P.
2014-01-01
In this paper the theoretical aspects and feature extraction capabilities of continuous wavelet transform (CWT) and discrete wavelet transform (DWT) are experimentally verified from the point of view of fault diagnosis of induction motors. Vertical frame vibration signal is analyzed to develop a wavelet based multi-class fault detection scheme. The redundant and high dimensionality information of CWT makes it computationally in-efficient. Using greedy-search feature selection technique (Greedy-CWT) the redundancy is eliminated to a great extent and found much superior to the widely used DWT technique, even in presence of high level of noise. The results are verified using MLP, SVM, RBF classifiers. The feature selection technique has enabled determination of the most relevant CWT scales and corresponding coefficients. Thus, the inherent limitations of CWT like proper selection of scales and redundant information are eliminated. In the present investigation `db8' is found as the best mother wavelet, due to its long period and higher number of vanishing moments, for detection of motor faults.
1/f Noise decomposition in random telegraph signals using the wavelet transform
NASA Astrophysics Data System (ADS)
Principato, Fabio; Ferrante, Gaetano
2007-07-01
By using the continuous wavelet transform with Haar basis the second-order properties of the wavelet coefficients are derived for the random telegraph signal (RTS) and for the 1/f noise which is obtained by summation of many RTSs. The correlation structure of the Haar wavelet coefficients for these processes is found. For the wavelet spectrum of the 1/f noise some characteristics related to the distribution of the relaxation times of the RTS are derived. A statistical test based on the characterization of the time evolution of the scalogram is developed, which allows to detect non-stationarity in the times τ's which compose the 1/f process and to identify the time scales of the relaxation times where the non-stationarity is localized. The proposed method allows to distinguish noise signals with 1/f power spectral density generated by RTSs, and thus gives informations on the origin of this type of 1/f noise which cannot be obtained using the Fourier transform or other methods based on second-order statistical analysis. The reported treatment is applied to both simulated and experimental signals. The present analysis is based on the McWhorter [ 1/f Noise and germanium surface properties, in: R.H. Kingstone (Ed.), Semiconductor Surface Physics, University of Pennsylvania Press, Philadelphia, PA, 1957, pp. 207-228] model of low frequency electric noise, and the obtained results are expected to prove especially useful for semiconductor devices.
Localization and de-noising seismic signals on SASW measurement by wavelet transform
NASA Astrophysics Data System (ADS)
Golestani, Alireza; S. Kolbadi, S. Mahdi; Heshmati, Ali Akbar
2013-11-01
SASW method is a nondestructive in situ testing method that is used to determine the dynamic properties of soil sites and pavement systems. Phase information and dispersion characteristics of a wave propagating through these systems have a significant role in the processing of recorded data. Inversion of the dispersive phase data provides information on the variation of shear-wave velocity with depth. However, in the case of sanded residual soil, it is not easy to produce the reliable phase spectrum curve. Due to natural noises and other human intervention in surface wave date generation deal with to reliable phase spectrum curve for sanded residual soil turn into the complex issue for geological scientist. In this paper, a time-frequency analysis based on complex Gaussian Derivative wavelet was applied to detect and localize all the events that are not identifiable by conventional signal processing methods. Then, the performance of discrete wavelet transform (DWT) in noise reduction of these recorded seismic signals was evaluated. Furthermore, in particular the influence of the decomposition level choice was investigated on efficiency of this process. This method is developed by various wavelet thresholding techniques which provide many options for controllable de-noising at each level of signal decomposition. Also, it obviates the need for high computation time compare with continuous wavelet transform. According to the results, the proposed method is powerful to visualize the interested spectrum range of seismic signals and to de-noise at low level decomposition.
Amin, Hafeez Ullah; Malik, Aamir Saeed; Ahmad, Rana Fayyaz; Badruddin, Nasreen; Kamel, Nidal; Hussain, Muhammad; Chooi, Weng-Tink
2015-03-01
This paper describes a discrete wavelet transform-based feature extraction scheme for the classification of EEG signals. In this scheme, the discrete wavelet transform is applied on EEG signals and the relative wavelet energy is calculated in terms of detailed coefficients and the approximation coefficients of the last decomposition level. The extracted relative wavelet energy features are passed to classifiers for the classification purpose. The EEG dataset employed for the validation of the proposed method consisted of two classes: (1) the EEG signals recorded during the complex cognitive task--Raven's advance progressive metric test and (2) the EEG signals recorded in rest condition--eyes open. The performance of four different classifiers was evaluated with four performance measures, i.e., accuracy, sensitivity, specificity and precision values. The accuracy was achieved above 98 % by the support vector machine, multi-layer perceptron and the K-nearest neighbor classifiers with approximation (A4) and detailed coefficients (D4), which represent the frequency range of 0.53-3.06 and 3.06-6.12 Hz, respectively. The findings of this study demonstrated that the proposed feature extraction approach has the potential to classify the EEG signals recorded during a complex cognitive task by achieving a high accuracy rate. PMID:25649845
Hoang, Vu Dang; Loan, Nguyen Thi; Tho, Vu Thi; Nguyen, Hue Minh Thi
2014-01-01
Signal processing methods based on the use of derivative, Fourier and wavelet transforms were proposed for the spectrophotometric simultaneous determination of cefoperazone and sulbactam in powders for injection. These transforms were successfully applied to UV spectra and ratio spectra to find suitable working wavelengths. Wavelet signal processing was proved to have distinct advantages (i.e. higher peak intensity obtained, additional smooth function and scaling factor process eliminated) over derivative and Fourier transforms. Especially, a better resolution of spectral overlapping bands was obtained by the use of double signal transform in the sequences such as (i) spectra pre-processed by Fractional Wavelet Transform and subsequently subjected to Continuous Wavelet Transform or Discrete Wavelet Transform, and (ii) derivative - wavelet transforms combined. Calibration graphs for cefoperazone and sulbactam were recorded for the range 10-35 mg/L. Good accuracy and precision were reported for all proposed methods by analyzing synthetic mixtures of cefoperazone and sulbactam. Furthermore, these methods were statistically comparable to RP-HPLC. PMID:24374557