Optimal Estimation of Wavelet Decomposition Level for a Matching Pursuit Algorithm

In this paper, we consider the application of the matching pursuit algorithm (MPA) for spectral analysis of non-stationary signals. First, we estimate the approximation error and the performance time for various MPA modifications and parameters using central processor unit and graphics processing un...

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Published inEntropy (Basel, Switzerland) Vol. 21; no. 9; p. 843
Main Authors Kaplun, Dmitry, Voznesenskiy, Alexander, Romanov, Sergei, Nepomuceno, Erivelton, Butusov, Denis
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 29.08.2019
MDPI
Subjects
Algorithms
Approximation
Basis functions
Clustering
Cost analysis
Decomposition
decomposition level
Dictionaries
digital signal processing
Discrete Wavelet Transform
Entropy
Fault diagnosis
Graphics processing units
Matched pursuit
Matching
matching pursuit algorithm
Mathematical analysis
Methods
Microprocessors
Noise
Numerical analysis
Optimization
Parameter estimation
Parameter identification
Parameter modification
Signal processing
Sparsity
Spectra
spectral analysis
Spectrum analysis
wavelet transform
Wavelet transforms
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Summary:In this paper, we consider the application of the matching pursuit algorithm (MPA) for spectral analysis of non-stationary signals. First, we estimate the approximation error and the performance time for various MPA modifications and parameters using central processor unit and graphics processing unit (GPU) to identify possible ways to improve the algorithm. Next, we propose the modifications of discrete wavelet transform (DWT) and package wavelet decomposition (PWD) for further use in MPA. We explicitly show that the optimal decomposition level, defined as a level with minimum entropy, in DWT and PWD provides the minimum approximation error and the smallest execution time when applied in MPA as a rough estimate in the case of using wavelets as basis functions (atoms). We provide an example of entropy-based estimation for optimal decomposition level in spectral analysis of seismic signals. The proposed modification of the algorithm significantly reduces its computational costs. Results of spectral analysis obtained with MPA can be used for various signal processing applications, including denoising, clustering, classification, and parameter estimation.
ISSN:1099-4300
1099-4300
DOI:10.3390/e21090843