Matching Pursuit Decomposition Research Articles

Time-frequency Techniques in Biomedical Signal Analysis

This review outlines the methodological fundamentals of the most frequently used non-parametric time-frequency analysis techniques in biomedicine and their main properties, as well as providing decision aids concerning their applications. The short-term Fourier transform (STFT), the Gabor transform (GT), the S-transform (ST), the continuous Morlet wavelet transform (CMWT), and the Hilbert transform (HT) are introduced as linear transforms by using a unified concept of the time-frequency representation which is based on a standardized analytic signal. The Wigner-Ville distribution (WVD) serves as an example of the 'quadratic transforms' class. The combination of WVD and GT with the matching pursuit (MP) decomposition and that of the HT with the empirical mode decomposition (EMD) are explained; these belong to the class of signal-adaptive approaches. Similarities between linear transforms are demonstrated and differences with regard to the time-frequency resolution and interference (cross) terms are presented in detail. By means of simulated signals the effects of different time-frequency resolutions of the GT, CMWT, and WVD as well as the resolution-related properties of the interference (cross) terms are shown. The method-inherent drawbacks and their consequences for the application of the time-frequency techniques are demonstrated by instantaneous amplitude, frequency and phase measures and related time-frequency representations (spectrogram, scalogram, time-frequency distribution, phase-locking maps) of measured magnetoencephalographic (MEG) signals. The appropriate selection of a method and its parameter settings will ensure readability of the time-frequency representations and reliability of results. When the time-frequency characteristics of a signal strongly correspond with the time-frequency resolution of the analysis then a method may be considered 'optimal'. The MP-based signal-adaptive approaches are preferred as these provide an appropriate time-frequency resolution for all frequencies while simultaneously reducing interference (cross) terms.

Damage assessment of CFRP composites using a time–frequency approach

A damage assessment methodology using a time–frequency signal processing technique is presented in this article. Delaminations are detected in composite structures with multiple stiffeners. Because Lamb waves are complex in nature, due to wave dispersion and scattering, a robust signal processing technique is required to extract features from Lamb wave signals. In this article, the matching pursuit decomposition algorithm is used for extracting wavelets from the Lamb wave signals in the time–frequency domain. A small time–frequency atom dictionary is defined to avoid the exhaustive search over the time–frequency domain and to reduce the computation costs. The propagation characteristics of Lamb waves in stiffened composite panels are investigated. The delaminations are detected by identifying the converted Lamb wave modes introduced by the structural imperfection. A two-step damage detection approach, which uses both pulse-echo and pitch-catch active sensing schemes, is developed for the identification of delaminations. The delamination is quantified using a signal energy-based damage index. The matching pursuit decomposition algorithm is further used to localize the delamination position by solving a set of nonlinear equations. The results show that the matching pursuit decomposition algorithm can be used to identify and localize the seeded delaminations in composite structures with complex geometries and material properties.

Waveform Mapping and Time-Frequency Processing of DNA and Protein Sequences

Current state-of-the-art approaches for biological sequence querying and alignment require preprocessing and lack robustness to repetitions in the sequence. In addition, these approaches do not provide much support for efficiently querying subsequences, a process that is essential for tracking localized database matches. We propose a query-based alignment method for biological sequences that first maps sequences to time-domain waveforms before processing the waveforms for alignment in the time-frequency plane. The mapping uses waveforms, such as Gaussian functions, with unique sequence representations in the time-frequency plane. The proposed alignment method employs a robust querying algorithm that utilizes a time-frequency signal expansion whose basis function is matched to the basic waveform in the mapped sequences. The resulting WAVEQuery approach was demonstrated for both deoxyribonucleic acid (DNA) and protein sequences using the matching pursuit decomposition as the signal basis expansion. We specifically evaluated the alignment localization of WAVEQuery over repetitive database segments, and we demonstrated its operation in real-time without preprocessing. We also demonstrated that WAVEQuery significantly outperformed the biological sequence alignment method BLAST for queries with repetitive segments for DNA sequences. A generalized version of the WAVEQuery approach with the metaplectic transform is also described for protein sequence structure prediction.

Prognosis of Gear Failures in DC Starter Motors Using Hidden Markov Models

Diagnosis classifies the present state of operation of the equipment, and prognosis predicts the next state of operation and its remaining useful life. In this paper, a prognosis method for the gear faults in dc machines is presented. The proposed method uses the time–frequency features extracted from the motor current as machine health indicators and predicts the future state of fault severity using hidden Markov models (HMMs). Parameter training of HMMs generally needs huge historical data, which are often not available in the case of electrical machines. Methods for computing the parameters from limited data are presented. The proposed prognosis method uses matching pursuit decomposition for estimating state-transition probabilities and experimental observations for computing state-dependent observation probability distributions. The proposed method is illustrated by examples using data collected from the experimental setup.

Nonstationary System Analysis Methods for Underwater Acoustic Communications

The underwater environment can be considered a system with time-varying impulse response, causing time-dependent spectral changes to a transmitted acoustic signal. This is the result of the interaction of the signal with the water column and ocean boundaries or the presence of fast moving object scatterers in the ocean. In underwater acoustic communications using medium-to-high frequencies (0.3–20 kHz), the nonstationary transformation on the transmitted signals can be modeled as multiple time-delay and Doppler-scaling paths. When estimating the channel, a higher processing performance is thus expected if the techniques used employ a matched channel model compared to those that only compensate for wideband effects. Following a matched linear time-varying wideband system representation, we propose two different methods for estimating the underwater acoustic communication environment. The first method follows a canonical time-scale channel model and is based on estimating the coefficients of the discrete wideband spreading function. The second method follows a ray system model and is based on extracting time-scale features for different ray paths using the matching pursuit decomposition algorithm. Both methods are validated and compared using communication data from actual underwater acoustic communication experiments.

On the statistics of matching pursuit angles

Matching pursuit decompositions have been employed for signal coding. For this purpose, matching pursuit coefficients need to be quantized. However, their behavior has been shown to be chaotic in some cases; posing difficulties to their modeling and quantizer design. In this work, a different approach is presented. Instead of trying to model the statistics of matching pursuit coefficients, the statistics of the angle between the residue signal and the element selected in each iteration of the matching pursuit are studied, what allows to model matching pursuits coefficients indirectly. This approach results in a simple statistical model. This is so because one observes that the statistics of such angles do not vary substantially after the first matching pursuit iteration, and can be approximately modeled as independent and identically distributed. Moreover, it is also observed that the probability density functions of matching pursuit angles are reasonably modeled by a single probability density function. This function depends only on the dictionary employed and not on the signal source. The derived statistical model is validated by employing it to design Lloyd–Max quantizers for matching pursuit coefficients. The Lloyd–Max quantizers obtained show good rate×distortion performance when compared to the state-of-the-art methods.

Identification of Detailed Time-Frequency Components in Somatosensory Evoked Potentials

Somatosensory evoked potential (SEP) usually contains a set of detailed temporal components measured and identified in time domain, providing meaningful information on physiological mechanisms of the nervous system. The purpose of this study is to reveal complex and fine time-frequency features of SEP in time-frequency domain using advanced time-frequency analysis (TFA) and pattern classification methods. A high-resolution TFA algorithm, matching pursuit (MP), was proposed to decompose a SEP signal into a string of elementary waves and to provide a time-frequency feature description of the waves. After a dimension reduction by principle component analysis (PCA), a density-guided K-means clustering was followed to identify typical waves existed in SEP. Experimental results on posterior tibial nerve SEP signals of 50 normal adults showed that a series of typical waves were discovered in SEP using the proposed MP decomposition and clustering methods. The statistical properties of these SEP waves were examined and their representative waveforms were synthesized. The identified SEP waves provided a comprehensive and detailed description of time-frequency features of SEP.

IMPROVED 3-D GPR DETECTION BY NUFFT COMBINED WITH MPD METHOD

A combined method of the non-uniform fast fourier transform (NUFFT) migration and the least-square based matching pursuit decomposition (MPD) algorithms is proposed to obtain better discrimination and interpretation for subsurface from ground penetrating radar (GPR) signals. By using the modifled NUFFT migration algorithm, a fast and high resolution GPR reconstruction can be obtained with an additional reduction in storage and computation requirements. By incorporating the MPD algorithm into a migration method, denoised reconstructions are obtained to enhance objects detection, including the identiflcation of objects' geometries and the estimation of their sizes and locations. Several examples from synthetic data and fleld data are demonstrated to establish the efiectiveness of the synergic efiect by comparing it with the conventional migration methods.

A hierarchical classification scheme for computationally efficient damage classification

This article presents a methodology for data mining of sensor signals in a structural health monitoring (SHM) framework for damage classification using a machine-learning-based approach called support vector machines (SVMs). A hierarchical decision tree structure is constructed for damage classification and experiments were conducted on metallic and composite test specimens with surface mounted piezoelectric transducers. Damage was induced in the specimens by fatigue, impact, and tensile loading; in addition, specimens with seeded delaminations were also considered. Data were collected from the surface mounted sensors at different severities of induced damage. A matching pursuit decomposition (MPD) algorithm was used as a feature extraction technique to preprocess the sensor data and extract the input vectors used in classification. Using this binary tree framework, the computational intensity of each successive classifier is reduced and the efficiency of the algorithm as a whole is increased. The results obtained using this classification show that this type of architecture works well for large data sets because a reduced number of comparisons are required. Due to the hierarchical set-up of the classifiers, performance of the classifier as a whole is heavily dependent on the performance of the classifier at higher levels in the classification tree.

Damage Classification Structural Health Monitoring in Bolted Structures Using Time-frequency Techniques

The analysis, detection, and classification of damage in complex bolted structures is an important component of structural health monitoring. In this article, an advanced signal processing and classification method is introduced based on time-frequency techniques. The time-varying signals collected from sensors are decomposed into linear combinations of highly localized Gaussian functions using the matching pursuit decomposition algorithm. These functions are chosen from a dictionary of time-frequency shifted and scaled versions of an elementary Gaussian basis function. The dictionary is also modified to use real measured data as the basis elements in order to obtain a more parsimonious signal representation. Classification is then achieved by matching the extracted damage features in the time-frequency plane. To further improve classification performance, the information collected from multiple sensors is integrated using a Bayesian sensor fusion approach. Results are presented demonstrating the algorithm performance for classifying signals obtained from various types of fastener failure damage in an aluminum plate.

Time-frequency component analysis of somatosensory evoked potentials in rats

BackgroundSomatosensory evoked potential (SEP) signal usually contains a set of detailed temporal components measured and identified in a time domain, giving meaningful information on physiological mechanisms of the nervous system. The purpose of this study is to measure and identify detailed time-frequency components in normal SEP using time-frequency analysis (TFA) methods and to obtain their distribution pattern in the time-frequency domain.MethodsThis paper proposes to apply a high-resolution time-frequency analysis algorithm, the matching pursuit (MP), to extract detailed time-frequency components of SEP signals. The MP algorithm decomposes a SEP signal into a number of elementary time-frequency components and provides a time-frequency parameter description of the components. A clustering by estimation of the probability density function in parameter space is followed to identify stable SEP time-frequency components.ResultsExperimental results on cortical SEP signals of 28 mature rats show that a series of stable SEP time-frequency components can be identified using the MP decomposition algorithm. Based on the statistical properties of the component parameters, an approximated distribution of these components in time-frequency domain is suggested to describe the complex SEP response.ConclusionThis study shows that there is a set of stable and minute time-frequency components in SEP signals, which are revealed by the MP decomposition and clustering. These stable SEP components have specific localizations in the time-frequency domain.

On the Use of Hidden Markov Modeling and Time-frequency Features for Damage Classification in Composite Structures

A novel approach based on hidden Markov models (HMMs) is proposed for damage classification in composite structures. Time-frequency damage features are first extracted from the measured signals using the matching pursuit decomposition algorithm. The features are then incorporated as observation sequences to be modeled statistically by the HMMs. Once built, the HMMs are integrated very efficiently into a Bayesian framework for the classification of structural damage. Both discrete and continuous observation density HMMs are considered; continuous HMMs are shown to yield better accuracy, but at the cost of added computational complexity. A decision fusion procedure is employed to combine the local classification results at each sensor, significantly enhancing the overall classification performance. The utility of the proposed technique is demonstrated by its application to the classification of delamination damage, impact damage, and progressive tensile damage in laminated composites.

Monte Carlo Matching Pursuit Decomposition Method for Damage Quantification in Composite Structures

In wave-based approach, the presence of damage is visualized in terms of the changes in the signature of the resultant wave that propagates through the structure. In structural health monitoring, the fundamental goal is to detect, localize, and quantify these damage signatures. The current approach uses matching pursuit decomposition (MPD) to compare signals from healthy and damaged structures. However, the major drawback of the MPD is that, in the decomposition process, it performs an exhaustive search over a large dictionary of elementary functions. Therefore, this method of decomposition is associated with a large computational expense. In this research, the Monte Carlo matching pursuit decomposition (MCMPD) is proposed, that adapts a smaller dictionary to the signal structure, thus avoiding the exhaustive search over the time-frequency plane. The proposed algorithm, sequentially estimates a dictionary that contains only those components that match the waveform structure, uses the matching pursuits for the decomposition of the signal and if necessary, adapts the dictionary to the structure of the residues for further decomposition. Finally, we demonstrate using real life data that the MCMPD retains the ability of the matching pursuit to decompose waveforms and quantify them accurately while reducing computational expense.

Spectral decomposition using Wigner-Ville distribution with applications to carbonate reservoir characterization

Spectral decomposition of seismic data transforms seismic amplitudes as a function of space and time into spectral amplitudes as a function of frequency, space, and time. It has been used for a variety of applications including determination of layer thickness, stratigraphic visualization, reservoir characterization, and direct hydrocarbon detection. The commonly used spectral decomposition methods—such as STFT (short-time Fourier transform), CWT (continuous wavelet transform), and MPD (matching pursuit decomposition)—are linear in that they compute correlations between the signal and a family of time-frequency functions. Thus, they cannot achieve arbitrarily fine resolution in the time and frequency domain simultaneously due to the limitations imposed by the uncertainty principle (Qian, 2005).

Matching pursuit based on nonparametric waveform estimation

Matching pursuit (MP) extracts signal feature components by decomposing the observed signal into a linear expansion of waveforms that are selected from a redundant dictionary of basis functions. It is difficult to predefine a parametric basis function that contains all prior information about the observed signal in practice, which restricted the application of MP. Focusing on this defect of MP, we present a modified algorithm of MP which decomposes the observed signal into a series combinations of waveforms, these waveforms are calculated by the nonparametric waveform estimation (NWE) method and used to best match the signal local structures. As a result, it is not needed to predefine the parametric basis function. With the NWE method, the adaptive adjustment of template signals makes it unnecessary for the method to require priori information, so that in practical applications it has better flexibility and adaptability. The extraction results of simulation signals are compared with the traditional MP decomposition, thus verifying the function of the proposed method. The extraction of testing signals on the rotor rig has again verified the feasibility and effectiveness of the method.

Matching pursuit decomposition of MEG auditory evoked fields

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Conditional spectral moments in matching pursuit based on the chirplet elementary function

In this paper, we derive closed form formulae for the first- and the second-order conditional spectral moments, which are generalizations of the concept of instantaneous frequency (IF) and instantaneous bandwidth (IB). We prove that for the matching pursuit (MP) distribution, based on the chirplet elementary function, the first-order conditional spectral moment or the IF is guaranteed to be real valued and the IB is always positive. In addition, not only is the second-order conditional spectral moment positive but so also are all even higher-order conditional spectral moments. These new properties are shown to be additional reasons for using the MP decomposition. We also compare the chirplet and Gaussian atoms, because both always give positive values for the Wigner-Ville distribution (WVD), and therefore the MP distribution is also always positive. We show that when the chirplet atom is used, the MP distribution has superior resolution and the convergence is faster when compared with the Gaussian atom. Finally, as the MP algorithm is computationally demanding, we study how to overcome this limitation when using the chirplet atom.

The gas reservoir response in PP- and PS-wave frequency sections

Spectral decomposition using the method of Matching Pursuit Decomposition (MPD) for PP-and PS-wave data has higher resolution and higher consistency over the entire time-frequency plane. The MPD algorithm avoids the problems of inaccurate analytic time point and the time window size choice that may occur during a Fourier transform. The PP-wave attenuation is greater than the PS-wave attenuation while propagating through gas reservoirs. There are some stronger amplitude low-frequency shadows on the PP-wave single frequency sections beneath gas reservoirs which are not seen on corresponding PS-wave single frequency sections. Therefore, hydrocarbons are predicted from comparing the behavior on both frequency sections. The time-frequency analysis for multi-component data is decomposed by MPD for data from northeast China containing rich gas reservoirs. The gas response character is analyzed on different wave mode single frequency sections. We describe the MPD algorithm, compare it to other spectral decomposition methods, and show some examples of detecting low-frequency shadows beneath gas reservoirs.

A matching pursuit-based signal complexity measure for the analysis of newborn EEG

This paper presents a new relative measure of signal complexity, referred to here as relative structural complexity (RSC), which is based on the matching pursuit (MP) decomposition. By relative, we refer to the fact that this new measure is highly dependent on the decomposition dictionary used by MP. The structural part of the definition points to the fact that this new measure is related to the structure, or composition, of the signal under analysis. After a formal definition, the proposed RSC measure is used in the analysis of newborn electroencephalogram (EEG). To do this, firstly, a time-frequency decomposition dictionary is specifically designed to compactly represent the newborn EEG seizure state using MP. We then show, through the analysis of synthetic and real newborn EEG data, that the relative structural complexity measure can indicate changes in EEG structure as it transitions between the two EEG states; namely seizure and background (non-seizure).

Seismic time-frequency spectral decomposition by matching pursuit

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 spectrum. This time-frequency spectrum may be used in turn for lithological analysis—for instance, detection of a gas reservoir. Investigation shows that the low-frequency shadow associated with a carbonate gas reservoir still exists, even high-frequency amplitudes are compensated by inverse-[Formula: see text] filtering.