Matching Pursuit Decomposition Research Articles

Explicit parameterization of sleep EEG transients

Adaptive time-frequency approximations, implemented via the matching pursuit algorithm, offer description of local signals structures in terms of their time occurrence and width, frequency and amplitude. This allows to construct explicit filters for finding EEG waveforms, known from the visual analysis, in the matching pursuit decomposition of signals. In such a way detectors of relevant structures of both transient and oscillatory nature can be constructed in the space of physically meaningful parameters. This study presents evaluation of changes of power and frequency of sleep spindles and delta waves, related to the depth of the sleep, which were previously assessed in a qualitative way. We confirm quantitatively the decrease of frequencies of sleep spindles and delta waves with the depth of the sleep.

Time-varying techniques for multisensor signal detection

In source detection and localization, the presence of a common but unknown signal can be detected from several noisy sensor measurements using the generalized coherence (GC) estimate. We propose to improve the performance of the GC estimate for multisensor detection using noise-suppressed signal estimates obtained from time-varying techniques. If one of the sensors has a significantly higher signal-to-noise ratio (SNR) than the other sensors, then it could be preprocessed prior to the GC estimate to improve detection performance for the remaining, lower SNR sensors. We perform this processing by estimating time-varying signals of interest with nonlinear phase functions using two methods: a) a modified matching pursuit decomposition (MMPD) algorithm whose dictionary is similar, in time-frequency structure, to the signal and b) an instantaneous frequency (IF) estimation method using highly localized time-frequency representations. The MMPD can yield signal estimates with lower mean square errors than the IF estimation technique but at the expense of higher computational cost and memory requirements. Using simulations, we compare the performance of the GC estimate with the significantly improved performance of the GC estimate that employs the signal estimate from the high SNR sensor. For the two-sensor detection, the estimated signal is also used with a generalized likelihood ratio test statistic to further improve performance

Diversity and channel estimation using time-varying signals and time-frequency techniques

We propose the use of time-varying (TV) signaling in modulation schemes to provide multiuser detection and multipath diversity in TV wireless channels. Specifically, we design an orthogonal linear chirp modulation scheme that is based on assigning different users with optimally designed parameters in order to reduce multiple-access interference. We also derive conditions on the parameters of the modulation signals to achieve multipath diversity. Furthermore, we propose the use of TV pilot signals with nonlinear instantaneous frequency and matched time-frequency (TF) techniques to estimate fast-fading channels with unknown state information. The proposed algorithm simplifies to the estimation of the parameters of multiple linear chirps, which we perform using the modified matching pursuit decomposition. We compare our estimation method with the use of pilot signals with linear instantaneous frequency, which we implement using the reassigned spectrogram. The proposed modulation scheme is applied to a frequency-hopped code-division multiple-access system for which we demonstrate improved performance when compared with frequency-shift-keying (FSK) modulation due to the designed multipath diversity and low multiple-access interference. Our simulations also demonstrate the increased estimation performance when pilot signals with nonlinear structures are used instead of linear structured ones to estimate TV channel parameters.

On conditional spectral moments of Gaussian and damped sinusoidal atoms in adaptive signal decomposition

It is well known that the convergence (with different speeds) of the matching pursuit (MP) signal decomposition algorithm for any dense dictionary is guaranteed. In this paper, we have analysed (in theory and through simulations) the performance and properties of both Gaussian and damped sinusoidal atoms for the MP signal decomposition. We have examined the decomposed signal in ambiguity space (to look for auto-terms concentrated around the origin), and investigated the requirement to have a positive time–frequency representation. We are thus able to propose what kind of dictionary might be more suitable for MP signal decomposition. We have also derived general formulae for the first and second conditional spectral moments, which are useful generalizations of the concept of instantaneous frequency and instantaneous bandwidth, respectively. While the second conditional moment is not positive for many bilinear time–frequency distributions, thus making useless its interpretation as instantaneous bandwidth, we have proved that for MP decomposition based on Gaussian or damped sinusoidal atoms, it is always guaranteed positive.

Characterization of epileptic seizure dynamics using Gabor atom density.

The study of epileptic electroencephalograph (EEG) dynamics can potentially provide insights into seizure onset, evolution and termination. We propose a new synthetic measure based on time-frequency decomposition to provide detailed characterization of these dynamic changes. The matching pursuit (MP) method allows for continuous time-frequency decomposition. We have developed a derivative of the MP method, the Gabor atom density method (GAD) that facilitates interpretation during the dynamic ictal period. The GAD analysis was applied to intracranial recordings of complex partial seizures (n = 43) of mesial temporal origin in 7 patients. Complex partial seizure occurrence is systematically associated with a GAD increase of 400 +/- 150%. The GAD increase coincides with the electrographical evidence of seizure onset. The similarity between seizures in a given patient is very high with uniform onset slope, maximum level and termination pattern. Global GAD responses over all channels can reveal detailed seizure propagation patterns including secondary independent foci and secondary generalization. The GAD measure based on the MP decomposition is a reliable tool to detect seizure occurrence in long-term recordings, to differentiate seizures from artifacts on a multi-channel basis and to examine patterns of seizure propagation. The reproducible GAD pattern suggests consistent changes in signal inner structure and may provide new clues about seizure dynamics and evolution. The GAD method can provide information about seizure dynamics that can contribute to methods of seizure detection. These analyses may lead to better understanding of seizure termination and help facilitate application of responsive seizure control devices in humans.

Matching pursuits with time-frequency dictionaries

The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions. These waveforms are chosen in order to best match the signal structures. Matching pursuits are general procedures to compute adaptive signal representations. With a dictionary of Gabor functions a matching pursuit defines an adaptive time-frequency transform. They derive a signal energy distribution in the time-frequency plane, which does not include interference terms, unlike Wigner and Cohen class distributions. A matching pursuit isolates the signal structures that are coherent with respect to a given dictionary. An application to pattern extraction from noisy signals is described. They compare a matching pursuit decomposition with a signal expansion over an optimized wavepacket orthonormal basis, selected with the algorithm of Coifman and Wickerhauser see (IEEE Trans. Informat. Theory, vol. 38, Mar. 1992).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Comparison of spectral decomposition methods

Comparison of spectral decomposition methods