{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T11:42:51Z","timestamp":1781005371169,"version":"3.54.1"},"reference-count":58,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2019,7,18]],"date-time":"2019-07-18T00:00:00Z","timestamp":1563408000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guohua Geng","award":["61731015"],"award-info":[{"award-number":["61731015"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61731015"],"award-info":[{"award-number":["61731015"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Multiplicative speckle noise removal is a challenging task in image processing. Motivated by the performance of anisotropic diffusion in additive noise removal and the structure of the standard deviation of a compressed speckle noisy image, we address this problem with anisotropic diffusion theories. Firstly, an anisotropic diffusion model based on image statistics, including information on the gradient of the image, gray levels, and noise standard deviation of the image, is proposed. Although the proposed model can effectively remove multiplicative speckle noise, it does not consider the noise at the edge during the denoising process. Hence, we decompose the divergence term in order to make the diffusion at the edge occur along the boundaries rather than perpendicular to the boundaries, and improve the model to meet our requirements. Secondly, the iteration stopping criteria based on kurtosis and correlation in view of the lack of ground truth in real image experiments, is proposed. The optimal values of the parameters in the model are obtained by learning. To improve the denoising effect, post-processing is performed. Finally, the simulation results show that the proposed model can effectively remove the speckle noise and retain minute details of the images for the real ultrasound and RGB color images.<\/jats:p>","DOI":"10.3390\/s19143164","type":"journal-article","created":{"date-parts":[[2019,7,19]],"date-time":"2019-07-19T03:14:41Z","timestamp":1563506081000},"page":"3164","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Anisotropic Diffusion Based Multiplicative Speckle Noise Removal"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4003-899X","authenticated-orcid":false,"given":"Mei","family":"Gao","sequence":"first","affiliation":[{"name":"School of Information Science and Technology, Northwest University, Xi\u2019an 710127, China"},{"name":"School of Science, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Baosheng","family":"Kang","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Northwest University, Xi\u2019an 710127, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiangchu","family":"Feng","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Xidian University, Xi\u2019an 710071, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Northwest University, Xi\u2019an 710127, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenjuan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Science, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"035007","DOI":"10.1088\/0266-5611\/29\/3\/035007","article-title":"Minimization and parameter estimation for seminorm regularization models with I-divergence constraints","volume":"29","author":"Teuber","year":"2013","journal-title":"Inverse Probl."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ulu, A., and Dizdaroglu, B. 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