{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:30:32Z","timestamp":1760239832597,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2020,12,18]],"date-time":"2020-12-18T00:00:00Z","timestamp":1608249600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11874096"],"award-info":[{"award-number":["11874096"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The acoustic imaging (AI) technique could map the position and the strength of the sound source via the signal processing of the microphone array. Conventional methods, including far-field beamforming (BF) and near-field acoustic holography (NAH), are limited to the frequency range of measured objects. A method called Bregman iteration based acoustic imaging (BI-AI) is proposed to enhance the performance of the two-dimensional acoustic imaging in the far-field and near-field measurements. For the large-scale \u21131 norm problem, Bregman iteration (BI) acquires the sparse solution; the fast iterative shrinkage-thresholding algorithm (FISTA) solves each sub-problem. The interpolating wavelet method extracts the information about sources and refines the computational grid to underpin BI-AI in the low-frequency range. The capabilities of the proposed method were validated by the comparison between some tried-and-tested methods processing simulated and experimental data. The results showed that BI-AI separates the coherent sources well in the low-frequency range compared with wideband acoustical holography (WBH); BI-AI estimates better strength and reduces the width of main lobe compared with \u21131 generalized inverse beamforming (\u21131-GIB).<\/jats:p>","DOI":"10.3390\/s20247298","type":"journal-article","created":{"date-parts":[[2020,12,21]],"date-time":"2020-12-21T01:01:08Z","timestamp":1608512468000},"page":"7298","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Robust Acoustic Imaging Based on Bregman Iteration and Fast Iterative Shrinkage-Thresholding Algorithm"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2149-8755","authenticated-orcid":false,"given":"Linsen","family":"Huang","sequence":"first","affiliation":[{"name":"School of Automotive Engineering, Chongqing University, 174 Shazhengjie, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaoyu","family":"Song","sequence":"additional","affiliation":[{"name":"School of Automotive Engineering, Chongqing University, 174 Shazhengjie, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6930-457X","authenticated-orcid":false,"given":"Zhongming","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Automotive Engineering, Chongqing University, 174 Shazhengjie, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhifei","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Automotive Engineering, Chongqing University, 174 Shazhengjie, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yansong","family":"He","sequence":"additional","affiliation":[{"name":"School of Automotive Engineering, Chongqing University, 174 Shazhengjie, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,18]]},"reference":[{"key":"ref_1","first-page":"199","article-title":"Sound sources reconstruction techniques: A review of their evolution and new trends","volume":"90","author":"Tenenbaum","year":"2004","journal-title":"Acta Acust. 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