Minimizing Isotropic Total Variation without Subiterations

Abstract

Total variation (TV) is one of the most popular regularizers in the context of ill-posed image reconstruction problems. Due to its particular structure, minimization of a TV-regularized function with a fast iterative shrinkage/thresholding algorithm (FISTA) requires additional sub-iterations, which may lead to a prohibitively slow reconstruction when dealing with very large scale imaging problems. In this work, we introduce a novel variant of FISTA for isotropic TV that circumvents the need for subiterations. Specifically, our algorithm replaces the exact TV proximal with a componentwise thresholding of the image gradient in a way that ensures the convergence of the algorithm to the true TV solution with arbitrarily high precision. International Traveling Workshop on Interactions Between Sparse Models and Technology (iTWIST) This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Copyright c © Mitsubishi Electric Research Laboratories, Inc., 2016 201 Broadway, Cambridge, Massachusetts 02139 Minimizing Isotropic Total Variation without Subiterations

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