{"id":1869,"date":"2015-06-01T09:00:00","date_gmt":"2015-06-01T09:00:00","guid":{"rendered":"https:\/\/wp.lancs.ac.uk\/icvl\/?p=1869"},"modified":"2023-03-26T08:01:41","modified_gmt":"2023-03-26T08:01:41","slug":"a-new-constrained-total-variational-deblurring-model-and-its-fast-algorithm","status":"publish","type":"post","link":"http:\/\/wp.lancs.ac.uk\/icvl\/2015\/06\/01\/a-new-constrained-total-variational-deblurring-model-and-its-fast-algorithm\/","title":{"rendered":"A new constrained total variational deblurring model and its fast algorithm"},"content":{"rendered":"\n<p>Williams BM, Chen K, Harding SP. A new constrained total variational deblurring model and its fast algorithm. Numerical Algorithms. 2015 Jun;69:415-41.<\/p>\n\n\n\n<p><a href=\"https:\/\/link.springer.com\/article\/10.1007\/s11075-014-9904-2\">https:\/\/link.springer.com\/article\/10.1007\/s11075-014-9904-2<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Abstract<\/h2>\n\n\n\n<p>Although image intensities are non-negative quantities, imposing positivity is not always considered in restoration models due to a lack of simple and robust methods of imposing the constraint. This paper proposes a suitable exponential type transform and applies it to the commonly-used total variation model to achieve implicitly constrained solution (positivity at its lower bound and a prescribed intensity value at the upper bound). Further to establish convergence, a convex model is proposed through a relaxation of the transformed functional. Numerical algorithms are presented to solve the resulting non-linear partial differential equations. Test results show that the proposed method is competitive when compared with existing methods in simple cases and more superior in other cases.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Williams BM, Chen K, Harding SP. Numerical Algorithms. 2015 Jun;69:415-41.<\/p>\n","protected":false},"author":1442,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[12],"tags":[122,23],"class_list":["post-1869","post","type-post","status-publish","format-standard","hentry","category-journal-paper","tag-122","tag-bryan-m-williams"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"http:\/\/wp.lancs.ac.uk\/icvl\/wp-json\/wp\/v2\/posts\/1869","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/wp.lancs.ac.uk\/icvl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/wp.lancs.ac.uk\/icvl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/wp.lancs.ac.uk\/icvl\/wp-json\/wp\/v2\/users\/1442"}],"replies":[{"embeddable":true,"href":"http:\/\/wp.lancs.ac.uk\/icvl\/wp-json\/wp\/v2\/comments?post=1869"}],"version-history":[{"count":1,"href":"http:\/\/wp.lancs.ac.uk\/icvl\/wp-json\/wp\/v2\/posts\/1869\/revisions"}],"predecessor-version":[{"id":1870,"href":"http:\/\/wp.lancs.ac.uk\/icvl\/wp-json\/wp\/v2\/posts\/1869\/revisions\/1870"}],"wp:attachment":[{"href":"http:\/\/wp.lancs.ac.uk\/icvl\/wp-json\/wp\/v2\/media?parent=1869"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/wp.lancs.ac.uk\/icvl\/wp-json\/wp\/v2\/categories?post=1869"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/wp.lancs.ac.uk\/icvl\/wp-json\/wp\/v2\/tags?post=1869"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}