Abstract
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.
Highlights
Most of the real signals are non-stationary
The last of the paper is organized as follows: In Section 2 we introduce the basic matching pursuit algorithm, in Section 3 we estimate the computational complexity and approximation quality of MP, and in Section 4 we provide optimization of MPA through the estimation of the optimal level of wavelet decomposition based on the entropy value
The resulting estimation of the optimal decomposition level can be used as an approximate value in the MPA in the case of using wavelets as basis functions
Summary
Most of the real signals (seismic, biological, hydroacoustic, etc.) are non-stationary. Processing of such signals includes denoising, randomness degree estimation, short-term local features extraction, filtering, etc. Despite the fact that the processing of non-stationary signals has been studied for a long time (wavelets were described in the late 1980s), there are several unsolved problems, as follows: Working in conditions of a priori uncertainty of signal parameters, processing complex non-stationary signals with multiple local features, and multi-component signal analysis [1,2,3]. Current advances in applied mathematics and digital signal processing, along with the development of high-performance hardware, allow the effective application of numerous mathematical techniques, including continuous and discrete wavelet transforms. Using wavelets for non-stationary signal analysis provides the following possibilities [4]: Entropy 2019, 21, 843; doi:10.3390/e21090843 www.mdpi.com/journal/entropy
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