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Specifically for the image smoothing step, we replace the least-squares fidelity for Gaussian noise in the Mumford-Shah model with a maximum posterior (MAP) term to deal with Poisson noise and we incorporate the weighted difference of anisotropic and isotropic total variation (AITV) as a regularization to promote the sparsity of image gradients. For such a nonconvex model, we develop a specific splitting scheme and utilize a proximal operator to apply the alternating direction method of multipliers (ADMM). Convergence analysis is provided to validate the efficacy of the ADMM scheme. Numerical experiments on various segmentation scenarios (grayscale\/color and multiphase) showcase that our proposed method outperforms a number of segmentation methods, including the original SaT.<\/jats:p>","DOI":"10.3389\/fcomp.2023.1131317","type":"journal-article","created":{"date-parts":[[2023,6,28]],"date-time":"2023-06-28T09:26:42Z","timestamp":1687944402000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Difference of anisotropic and isotropic TV for segmentation under blur and Poisson noise"],"prefix":"10.3389","volume":"5","author":[{"given":"Kevin","family":"Bui","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yifei","family":"Lou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fredrick","family":"Park","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jack","family":"Xin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1965","published-online":{"date-parts":[[2023,6,28]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"999","DOI":"10.1002\/cpa.3160430805","article-title":"Approximation of functional depending on jumps by elliptic functional via t-convergence","volume":"43","author":"Ambrosio","year":"1990","journal-title":"Commun. 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