{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:58:42Z","timestamp":1760241522024,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,4,12]],"date-time":"2018-04-12T00:00:00Z","timestamp":1523491200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Blurred image restoration poses a great challenge under the non-Gaussian noise environments in various communication systems. In order to restore images from blur and alpha-stable noise while also preserving their edges, this paper proposes a variational method to restore the blurred images with alpha-stable noises based on the property of the meridian distribution and the total variation (TV). Since the variational model is non-convex, it cannot guarantee a global optimal solution. To overcome this drawback, we also incorporate an additional penalty term into the deblurring and denoising model and propose a strictly convex variational method. Due to the convexity of our model, the primal-dual algorithm is adopted to solve this convex variational problem. Our simulation results validate the proposed method.<\/jats:p>","DOI":"10.3390\/s18041175","type":"journal-article","created":{"date-parts":[[2018,4,12]],"date-time":"2018-04-12T12:19:27Z","timestamp":1523535567000},"page":"1175","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A Convex Constraint Variational Method for Restoring Blurred Images in the Presence of Alpha-Stable Noises"],"prefix":"10.3390","volume":"18","author":[{"given":"Zhenzhen","family":"Yang","sequence":"first","affiliation":[{"name":"National Engineering Research Center of Communication and Network Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"},{"name":"Key Lab of Broadband Wireless Communication and Sensor Network Technology, Nanjing University of Posts and Telecommunications, Ministry of Education, Nanjing 210003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhen","family":"Yang","sequence":"additional","affiliation":[{"name":"National Engineering Research Center of Communication and Network Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"},{"name":"Key Lab of Broadband Wireless Communication and Sensor Network Technology, Nanjing University of Posts and Telecommunications, Ministry of Education, Nanjing 210003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3888-2881","authenticated-orcid":false,"given":"Guan","family":"Gui","sequence":"additional","affiliation":[{"name":"National Engineering Research Center of Communication and Network Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"},{"name":"Key Lab of Broadband Wireless Communication and Sensor Network Technology, Nanjing University of Posts and Telecommunications, Ministry of Education, Nanjing 210003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/dac.3104","article-title":"Stable adaptive channel estimation method under impulsive noise environments","volume":"30","author":"Gui","year":"2017","journal-title":"Int. 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