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By minimizing a single objective function, the approach utilizes simultaneously two quite different sources of information for restoration: spatial context in terms of some smoothness prior and nonspatial statistics in terms of the novel prior utilizing the Wasserstein distance between probability measures. We study the combination of the functional lifting technique with two different relaxations of the histogram prior and derive a jointly convex variational approach. Mathematical equivalence of both relaxations is established, and cases where optimality holds are discussed. Additionally, we present an efficient algorithmic scheme for the numerical treatment of the presented model. Experiments using the basic total variation based denoising approach as a case study demonstrate our novel regularization approach.<\/jats:p>","DOI":"10.1137\/120897535","type":"journal-article","created":{"date-parts":[[2013,9,17]],"date-time":"2013-09-17T11:38:51Z","timestamp":1379417931000},"page":"1719-1735","source":"Crossref","is-referenced-by-count":19,"title":["Convex Variational Image Restoration with Histogram Priors"],"prefix":"10.1137","volume":"6","author":[{"given":"Paul","family":"Swoboda","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christoph","family":"Schn\u00f6rr","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2013,9,17]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s005260100152"},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"L. Ambrosio, N. Fusco, and D. 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