Showing papers on "Wavelet packet decomposition published in 2007"

A New SURE Approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding

Abstract: This paper introduces a new approach to orthonormal wavelet image denoising. Instead of postulating a statistical model for the wavelet coefficients, we directly parametrize the denoising process as a sum of elementary nonlinear processes with unknown weights. We then minimize an estimate of the mean square error between the clean image and the denoised one. The key point is that we have at our disposal a very accurate, statistically unbiased, MSE estimate-Stein's unbiased risk estimate-that depends on the noisy image alone, not on the clean one. Like the MSE, this estimate is quadratic in the unknown weights, and its minimization amounts to solving a linear system of equations. The existence of this a priori estimate makes it unnecessary to devise a specific statistical model for the wavelet coefficients. Instead, and contrary to the custom in the literature, these coefficients are not considered random any more. We describe an interscale orthonormal wavelet thresholding algorithm based on this new approach and show its near-optimal performance-both regarding quality and CPU requirement-by comparing it with the results of three state-of-the-art nonredundant denoising algorithms on a large set of test images. An interesting fallout of this study is the development of a new, group-delay-based, parent-child prediction in a wavelet dyadic tree

The Undecimated Wavelet Decomposition and its Reconstruction

Abstract: This paper describes the undecimated wavelet transform and its reconstruction. In the first part, we show the relation between two well known undecimated wavelet transforms, the standard undecimated wavelet transform and the isotropic undecimated wavelet transform. Then we present new filter banks specially designed for undecimated wavelet decompositions which have some useful properties such as being robust to ringing artifacts which appear generally in wavelet-based denoising methods. A range of examples illustrates the results

Rectification of the Bias in the Wavelet Power Spectrum

Abstract: This paper addresses a bias problem in the estimate of wavelet power spectra for atmospheric and oceanic datasets. For a time series comprised of sine waves with the same amplitude at different frequencies the conventionally adopted wavelet method does not produce a spectrum with identical peaks, in contrast to a Fourier analysis. The wavelet power spectrum in this definition, that is, the transform coefficient squared (to within a constant factor), is equivalent to the integration of energy (in physical space) over the influence period (time scale) the series spans. Thus, a physically consistent definition of energy for the wavelet power spectrum should be the transform coefficient squared divided by the scale it associates. Such adjusted wavelet power spectrum results in a substantial improvement in the spectral estimate, allowing for a comparison of the spectral peaks across scales. The improvement is validated with an artificial time series and a real coastal sea level record. Also examined is the previous example of the wavelet analysis of the Nino-3 SST data.

A Sorted Neighborhood Approach for Detecting Duplicated Regions in Image Forgeries Based on DWT and SVD

Abstract: The presence of duplicated regions in the image can be considered as a tell-tale sign for image forgery, which belongs to the research field of digital image forensics. In this paper, a blind forensics approach based on DWT (discrete wavelet transform) and SVD (singular value decomposition) is proposed to detect the specific artifact. Firstly, DWT is applied to the image, and SVD is used on fixed-size blocks of low-frequency component in wavelet sub-band to yield a reduced dimension representation. Then the SV vectors are then lexicographically sorted and duplicated image blocks will be close in the sorted list, and therefore will be compared during the detection steps. The experimental results demonstrate that the proposed approach can not only decrease computational complexity, but also localize the duplicated regions accurately even when the image was highly compressed or edge processed.

Transform Coding Techniques for Lossy Hyperspectral Data Compression

Abstract: Transform-based lossy compression has a huge potential for hyperspectral data reduction. Hyperspectral data are 3-D, and the nature of their correlation is different in each dimension. This calls for a careful design of the 3-D transform to be used for compression. In this paper, we investigate the transform design and rate allocation stage for lossy compression of hyperspectral data. First, we select a set of 3-D transforms, obtained by combining in various ways wavelets, wavelet packets, the discrete cosine transform, and the Karhunen-Loegraveve transform (KLT), and evaluate the coding efficiency of these combinations. Second, we propose a low-complexity version of the KLT, in which complexity and performance can be balanced in a scalable way, allowing one to design the transform that better matches a specific application. Third, we integrate this, as well as other existing transforms, in the framework of Part 2 of the Joint Photographic Experts Group (JPEG) 2000 standard, taking advantage of the high coding efficiency of JPEG 2000, and exploiting the interoperability of an international standard. We introduce an evaluation framework based on both reconstruction fidelity and impact on image exploitation, and evaluate the proposed algorithm by applying this framework to AVIRIS scenes. It is shown that the scheme based on the proposed low-complexity KLT significantly outperforms previous schemes as to rate-distortion performance. As for impact on exploitation, we consider multiclass hard classification, spectral unmixing, binary classification, and anomaly detection as benchmark applications

Diagnosis of Broken Bar Fault in Induction Machines Using Discrete Wavelet Transform without Slip Estimation

Abstract: The aim of this paper is to present a wavelet-based method for broken-bar detection in squirrel-cage induction machines. The frequency-domain methods, which are commonly used, need speed information or accurate slip estimation for frequency-component localization in any spectrum. Nevertheless, the fault frequency bandwidth can be well defined for any squirrel-cage induction machine due to numerous previous investigations. The proposed approach consists in the energy evaluation of a known bandwidth with time-scale analysis using the discrete wavelet transform. This new technique has been applied to the stator-current space-vector magnitude and the instantaneous magnitude of the stator-current signal for different broken-bar fault severities and load levels.

Short-Term Traffic Volume Forecasting Using Kalman Filter with Discrete Wavelet Decomposition

Abstract: : This article investigates the application of Kalman filter with discrete wavelet analysis in short-term traffic volume forecasting. Short-term traffic volume data are often corrupted by local noises, which may significantly affect the prediction accuracy of short-term traffic volumes. Discrete wavelet decomposition analysis is used to divide the original data into several approximate and detailed data such that the Kalman filter model can then be applied to the denoised data and the prediction accuracy can be improved. Two types of wavelet Kalman filter models based on Daubechies 4 and Haar mother wavelets are investigated. Traffic volume data collected from four different locations are used for comparison in this study. The test results show that both proposed wavelet Kalman filter models outperform the direct Kalman filter model in terms of mean absolute percentage error and root mean square error.

Seismic time-frequency spectral decomposition by matching pursuit

Abstract: A seismic trace may be decomposed into a series of wavelets that match their time-frequency signature by using a matching pursuit algorithm, an iterative procedure of wavelet selection among a large and redundant dictionary. For reflection seismic signals, the Morlet wavelet may be employed, because it can represent quantitatively the energy attenuation and velocity dispersion of acoustic waves propagating through porous media. The efficiency of an adaptive wavelet selection is improved by making first a preliminary estimate and then a localized refining search, whereas complex-trace attributes and derived analytical expressions are also used in various stages. For a constituent wavelet, the scale is an important adaptive parameter that controls the width of wavelet in time and the bandwidth of the frequency spectrum. After matching pursuit decomposition, deleting wavelets with either very small or very large scale values can suppress spikes and sinusoid functions effectively from the time-frequency spect...

A study on compactly supported orthogonal vector-valued wavelets and wavelet packets

Abstract: In this paper, vector-valued multiresolution analysis and orthogonal vector-valued wavelets are introduced. The definition for orthogonal vector-valued wavelet packets is proposed. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is derived by means of paraunitary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. The properties of the vector-valued wavelet packets are investigated by using operator theory and algebra theory. In particular, it is shown how to construct various orthonormal bases of L2(R, Cs) from the orthogonal vector-valued wavelet packets.

Generalized Daubechies Wavelet Families

Abstract: We present a generalization of the orthonormal Daubechies wavelets and of their related biorthogonal flavors (Cohen-Daubechies-Feauveau, 9/7). Our fundamental constraint is that the scaling functions should reproduce a predefined set of exponential polynomials. This allows one to tune the corresponding wavelet transform to a specific class of signals, thereby ensuring good approximation and sparsity properties. The main difference with the classical construction of Daubechies is that the multiresolution spaces are derived from scale-dependent generating functions. However, from an algorithmic standpoint, Mallat's fast wavelet transform algorithm can still be applied; the only adaptation consists in using scale-dependent filter banks. Finite support ensures the same computational efficiency as in the classical case. We characterize the scaling and wavelet filters, construct them and show several examples of the associated functions. We prove that these functions are square-integrable and that they converge to their classical counterparts of the corresponding order.

Nonstationary Gaussian processes in wavelet domain: synthesis, estimation, and significance testing.

Abstract: We propose an equivalence class of nonstationary Gaussian stochastic processes defined in the wavelet domain. These processes are characterized by means of wavelet multipliers and exhibit well-defined time-dependent spectral properties. They allow one to generate realizations of any wavelet spectrum. Based on this framework, we study the estimation of continuous wavelet spectra, i.e., we calculate variance and bias of arbitrary estimated continuous wavelet spectra. Finally, we develop an areawise significance test for continuous wavelet spectra to overcome the difficulties of multiple testing; it uses basic properties of continuous wavelet transform to decide whether a pointwise significant result is a real feature of the process or indistinguishable from typical stochastic fluctuations. This test is compared to the conventional one in terms of sensitivity and specificity. A software package for continuous wavelet spectral analysis and synthesis is presented.

Robust Image Watermarking Based on Multiband Wavelets and Empirical Mode Decomposition

Abstract: In this paper, we propose a blind image watermarking algorithm based on the multiband wavelet transformation and the empirical mode decomposition. Unlike the watermark algorithms based on the traditional two-band wavelet transform, where the watermark bits are embedded directly on the wavelet coefficients, in the proposed scheme, we embed the watermark bits in the mean trend of some middle-frequency subimages in the wavelet domain. We further select appropriate dilation factor and filters in the multiband wavelet transform to achieve better performance in terms of perceptually invisibility and the robustness of the watermark. The experimental results show that the proposed blind watermarking scheme is robust against JPEG compression, Gaussian noise, salt and pepper noise, median filtering, and Con-vFilter attacks. The comparison analysis demonstrate that our scheme has better performance than the watermarking schemes reported recently.

Compression of Biomedical Signals With Mother Wavelet Optimization and Best-Basis Wavelet Packet Selection

Abstract: We propose a novel scheme for signal compression based on the discrete wavelet packet transform (DWPT) decompositon. The mother wavelet and the basis of wavelet packets were optimized and the wavelet coefficients were encoded with a modified version of the embedded zerotree algorithm. This signal dependant compression scheme was designed by a two-step process. The first (internal optimization) was the best basis selection that was performed for a given mother wavelet. For this purpose, three additive cost functions were applied and compared. The second (external optimization) was the selection of the mother wavelet based on the minimal distortion of the decoded signal given a fixed compression ratio. The mother wavelet was parameterized in the multiresolution analysis framework by the scaling filter, which is sufficient to define the entire decomposition in the orthogonal case. The method was tested on two sets of ten electromyographic (EMG) and ten electrocardiographic (ECG) signals that were compressed with compression ratios in the range of 50%-90%. For 90% compression ratio of EMG (ECG) signals, the percent residual difference after compression decreased from (mean ) 48.69.9% (21.58.4%) with discrete wavelet transform (DWT) using the wavelet leading to poorest performance to 28.43.0% (6.71.9%) with DWPT, with optimal basis selection and wavelet optimization. In conclusion, best basis selection and optimization of the mother wavelet through parameterization led to substantial improvement of performance in signal compression with respect to DWT and randon selection of the mother wavelet. The method provides an adaptive approach for optimal signal representation for compression and can thus be applied to any type of biomedical signal.

Wavelet analysis and applications

Abstract: Wavelet Theory.- Local Smoothness Conditions on a Function Which Guarantee Convergence of Double Walsh-Fourier Series of This Function.- Linear Transformations of ?N and Problems of Convergence of Fourier Series of Functions Which Equal Zero on Some Set.- Sidon Type Inequalities for Wavelets.- Almansi Decomposition for Dunkl-Helmholtz Operators.- An Uncertainty Principle for Operators.- Uncertainty Principle for Clifford Geometric Algebras Cl n,0, n = 3 (mod 4) Based on Clifford Fourier Transform.- Orthogonal Wavelet Vectors in a Hilbert Space.- Operator Frames for .- On the Stability of Multi-wavelet Frames.- Biorthogonal Wavelets Associated with Two-Dimensional Interpolatory Function.- Parameterization of Orthogonal Filter Bank with Linear Phase.- On Multivariate Wavelets with Trigonometric Vanishing Moments.- Directional Wavelet Analysis with Fourier-Type Bases for Image Processing.- Unitary Systems and Wavelet Sets.- Clifford Analysis and the Continuous Spherical Wavelet Transform.- Clifford-Jacobi Polynomials and the Associated Continuous Wavelet Transform in Euclidean Space.- Wavelet Leaders in Multifractal Analysis.- Application of Fast Wavelet Transformation in Parametric System Identification.- Image Denoising by a Novel Digital Curvelet Reconstruction Algorithm.- Condition Number for Under-Determined Toeplitz Systems.- Powell-Sabin Spline Prewavelets on the Hexagonal Lattice.- Time-Frequency Aspects of Nonlinear Fourier Atoms.- Mono-components for Signal Decomposition.- Signal-Adaptive Aeroelastic Flight Data Analysis with HHT.- An Adaptive Data Analysis Method for Nonlinear and Nonstationary Time Series: The Empirical Mode Decomposition and Hilbert Spectral Analysis.- Wavelet Applications.- Transfer Colors from CVHD to MRI Based on Wavelets Transform.- Medical Image Fusion by Multi-resolution Analysis of Wavelets Transform.- Salient Building Detection from a Single Nature Image via Wavelet Decomposition.- SAR Images Despeckling via Bayesian Fuzzy Shrinkage Based on Stationary Wavelet Transform.- Super-Resolution Reconstruction Using Haar Wavelet Estimation.- The Design of Hilbert Transform Pairs in Dual-Tree Complex Wavelet Transform.- Supervised Learning Using Characteristic Generalized Gaussian Density and Its Application to Chinese Materia Medica Identification.- A Novel Algorithm of Singular Points Detection for Fingerprint Images.- Wavelet Receiver: A New Receiver Scheme for Doubly-Selective Channels.- Face Retrieval with Relevance Feedback Using Lifting Wavelets Features.- High-Resolution Image Reconstruction Using Wavelet Lifting Scheme.- Mulitiresolution Spatial Data Compression Using Lifting Scheme.- Ridgelet Transform as a Feature Extraction Method in Remote Sensing Image Recognition.- Analysis of Frequency Spectrum for Geometric Modeling in Digital Geometry.- Detection of Spindles in Sleep EEGs Using a Novel Algorithm Based on the Hilbert-Huang Transform.- A Wavelet-Domain Hidden Markov Tree Model with Localized Parameters for Image Denoising.

Feature extraction of hyperspectral images using wavelet and matching pursuit

Abstract: Since hyperspectral images contain rich and fine spectral information, an improvement of land use/cover classification accuracy is highly expected from the utilization of such images. However, the traditional statistics-based classification methods which have been successfully applied to multispectral data in the past are not as effective as to hyperspectral data. One major reason is that the number of spectral bands is too large relative to the number of training samples. This problem is caused by curse of dimensionality, which refers to the fact that the sample size required for training a specific classifier grows exponentially with the number of spectral bands. A simple but sometimes very effective way to overcome this problem is to reduce the dimensionality of hyperspectral images. This can be done by feature extraction that a small number of salient features are extracted from the hyperspectral data when confronted with a limited size of training samples. In this paper, a new feature extraction method based on the matching pursuit (MP) is proposed to extract useful features for the classification of hyperspectral images. The matching pursuit algorithm uses a greedy strategy to find an adaptive and optimal representation of the hyperspectral data iteratively from a highly redundant wavelet packets dictionary. An AVIRIS data set was tested to illustrate the classification performance after matching pursuit method was applied. In addition, some existing feature extraction methods based on the wavelet transform are also compared with the matching pursuit method in terms of the classification accuracies. The experiment results showed that the wavelet and matching pursuit method exactly provide an effective tool for feature extraction. The classification problem caused by curse of dimensionality can be avoided by matching pursuit and wavelet-based dimensionality reduction.

Unit Root Tests with Wavelets

Abstract: This paper develops a wavelet (spectral) approach to test the presence of a unit root in a stochastic process The wavelet approach is appealing, since it is based directly on the different behavior of the spectra of a unit root process and that of a short memory stationary process By decomposing the variance (energy) of the underlying process into the variance of its low frequency components and that of its high frequency components via the discrete wavelet transformation (DWT), we design unit root tests against near unit root alternatives Since DWT is an energy preserving transformation and able to disbalance energy across high and low frequency components of a series, it is possible to isolate the most persistent component of a series in a small number of scaling coefficients We demonstrate the size and power properties of our tests through Monte Carlo simulations

Multiadaptive Bionic Wavelet Transform: Application to ECG Denoising and Baseline Wandering Reduction

Abstract: 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 -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.

Accelerometry Based Classification of Walking Patterns Using Time-frequency Analysis

Abstract: In this work, 33 dimensional time-frequency domain features were developed and evaluated to detect five different human walking patterns from data acquired using a triaxial accelerometer attached at the waist above the iliac spine. 52 subjects were asked to walk on a flat surface along a corridor, walk up and down a flight of a stairway and walk up and down a constant gradient slope, in an unsupervised manner. Time-frequency domain features of acceleration data in anterior-posterior (AP), medio-lateral (ML) and vertical (VT) direction were developed. The acceleration signal in each direction was decomposed to six detailed signals at different wavelet scales by using the wavelet packet transform. The rms values and standard deviations of the decomposed signals at scales 5 to 2 corresponding to the 0.78-18.75 Hz frequency band were calculated. The energies in the 0.39-18.75 Hz frequency band of acceleration signal in AP, ML and VT directions were also computed. The back-end of the system was a multi-layer perceptron (MLP) Neural Networks (NNs) classifier. Overall classification accuracies of 88.54% and 92.05% were achieved by using a round robin (RR) and random frame selecting (RFS) train-test method respectively for the five walking patterns.

Wavelet packet neural networks for texture classification

Abstract: Texture can be defined as a local statistical pattern of texture primitives in observer’s domain of interest Texture classification aims to assign texture labels to unknown textures, according to training samples and classification rules This paper describes the usage of wavelet packet neural networks (WPNN) for texture classification problem The proposed schema composed of a wavelet packet feature extractor and a multi-layer perceptron classifier Entropy and energy features are integrated wavelet feature extractor The performed experimental studies show the effectiveness of the WPNN structure The overall success rate is about 95%

Video Denoising Based on Inter-frame Statistical Modeling of Wavelet Coefficients

Abstract: The paper proposes a joint probability density function to model the video wavelet coefficients of any two neighboring frames and then applies this statistical model for denoising. The parameter of the density function that measures the correlation between the wavelet coefficients of the two frames is used as an index for the motion. The joint density function is employed for spatial filtering of the noisy wavelet coefficients by developing a bivariate maximum a posteriori estimator. A recursive time averaging of the spatially filtered wavelet coefficients is adopted for further noise reduction. Simulation results on test video sequences show an improved performance both in terms of the peak signal-to-noise ratio and the perceptual quality compared to that of the other denoising algorithms

Real-Time Implementation of Wavelet Packet Transform-Based Diagnosis and Protection of Three-Phase Induction Motors

Abstract: This paper presents a real-time implementation of an online protection technique for induction motor fault detection and diagnosis. The protection system utilizes a wavelet packet transform (WPT)-based algorithm for detecting and diagnosing various disturbances occurring in three-phase induction motors. The criterion for the detection is the comparison of the coefficients of the WPT of line currents using a mother wavelet at the second level of resolution with a threshold determined experimentally during the healthy condition of the motor. The algorithm is implemented in real-time using the Texas Instrument TMS320C31 32-b floating-point digital signal processor with the help of object-oriented programming. The proposed technique is tested on two three-phase induction motors. The online test results give a response signal at the instant or within one cycle of disturbance in all cases of investigated faults. In addition, the algorithm is also tested during no load and full load operating conditions of the motor.