Optimal Estimation of Wavelet Decomposition Level for a Matching Pursuit Algorithm

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.