{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T16:36:34Z","timestamp":1783182994378,"version":"3.54.6"},"reference-count":30,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,6,16]],"date-time":"2021-06-16T00:00:00Z","timestamp":1623801600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100017142","name":"Gruppo Nazionale per il Calcolo Scientifico","doi-asserted-by":"publisher","award":["2019"],"award-info":[{"award-number":["2019"]}],"id":[{"id":"10.13039\/100017142","id-type":"DOI","asserted-by":"publisher"}]},{"name":"V:ALERE Program of the University of Campania \u201cL. Vanvitelli\u201d","award":["2019"],"award-info":[{"award-number":["2019"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Imaging"],"abstract":"<jats:p>We are interested in the restoration of noisy and blurry images where the texture mainly follows a single direction (i.e., directional images). Problems of this type arise, for example, in microscopy or computed tomography for carbon or glass fibres. In order to deal with these problems, the Directional Total Generalized Variation (DTGV) was developed by Kongskov et al. in 2017 and 2019, in the case of impulse and Gaussian noise. In this article we focus on images corrupted by Poisson noise, extending the DTGV regularization to image restoration models where the data fitting term is the generalized Kullback\u2013Leibler divergence. We also propose a technique for the identification of the main texture direction, which improves upon the techniques used in the aforementioned work about DTGV. We solve the problem by an ADMM algorithm with proven convergence and subproblems that can be solved exactly at a low computational cost. Numerical results on both phantom and real images demonstrate the effectiveness of our approach.<\/jats:p>","DOI":"10.3390\/jimaging7060099","type":"journal-article","created":{"date-parts":[[2021,6,16]],"date-time":"2021-06-16T21:58:32Z","timestamp":1623880712000},"page":"99","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Directional TGV-Based Image Restoration under Poisson Noise"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8215-0771","authenticated-orcid":false,"given":"Daniela","family":"di Serafino","sequence":"first","affiliation":[{"name":"Department of Mathematics and Applications \u201cR. Caccioppoli\u201d, University of Naples Federico II, 80126 Naples, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1250-8218","authenticated-orcid":false,"given":"Germana","family":"Landi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Bologna, 40126 Bologna, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2140-8094","authenticated-orcid":false,"given":"Marco","family":"Viola","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Physics, University of Campania \u201cL. Vanvitelli\u201d, 81100 Caserta, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"123006","DOI":"10.1088\/0266-5611\/25\/12\/123006","article-title":"Image deblurring with Poisson data: From cells to galaxies","volume":"25","author":"Bertero","year":"2009","journal-title":"Inverse Probl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1109\/TMI.1982.4307558","article-title":"Maximum Likelihood Reconstruction for Emission Tomography","volume":"1","author":"Shepp","year":"1982","journal-title":"IEEE Trans. Med. 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