{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,12]],"date-time":"2025-12-12T13:35:18Z","timestamp":1765546518604,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,8,29]],"date-time":"2019-08-29T00:00:00Z","timestamp":1567036800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["17-71-20077"],"award-info":[{"award-number":["17-71-20077"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/e21090843","type":"journal-article","created":{"date-parts":[[2019,8,29]],"date-time":"2019-08-29T11:26:22Z","timestamp":1567077982000},"page":"843","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Optimal Estimation of Wavelet Decomposition Level for a Matching Pursuit Algorithm"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2765-4509","authenticated-orcid":false,"given":"Dmitry","family":"Kaplun","sequence":"first","affiliation":[{"name":"Department of Automation and Control Processes, St. Petersburg Electrotechnical University \u201cLETI\u201d, Saint Petersburg 197376, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0667-7851","authenticated-orcid":false,"given":"Alexander","family":"Voznesenskiy","sequence":"additional","affiliation":[{"name":"Department of Automation and Control Processes, St. Petersburg Electrotechnical University \u201cLETI\u201d, Saint Petersburg 197376, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8647-9096","authenticated-orcid":false,"given":"Sergei","family":"Romanov","sequence":"additional","affiliation":[{"name":"Department of Automation and Control Processes, St. Petersburg Electrotechnical University \u201cLETI\u201d, Saint Petersburg 197376, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5841-2193","authenticated-orcid":false,"given":"Erivelton","family":"Nepomuceno","sequence":"additional","affiliation":[{"name":"Control and Modelling Group (GCOM), Department of Electrical Engineering, Federal University of S\u00e3o Jo\u00e3o del-Rei, S\u00e3o Jo\u00e3o del-Rei, Minas Gerais 36307-352, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8941-4220","authenticated-orcid":false,"given":"Denis","family":"Butusov","sequence":"additional","affiliation":[{"name":"Youth Research Institute, Saint Petersburg Electrotechnical University \u201cLETI\u201d, Saint Petersburg 197376, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,29]]},"reference":[{"key":"ref_1","unstructured":"Ifeachor, E.C., and Jervis, B.W. 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