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Duality-based algorithms for total-variation-regularized image restoration. (English) Zbl 1208.90165
Summary: Image restoration models based on total variation (TV) have become popular since their introduction by {\it L. I. Rudin, S. Osher} and {\it E. Fatemi} [Physica D 60, No. 1--4, 259--268 (1992; Zbl 0780.49028)]. The dual formulation of this model has a quadratic objective with separable constraints making projections onto the feasible set easy to compute. This paper proposes the application of gradient projection (GP) algorithms to the dual formulation. We test variants of GP with different step length selection and line search strategies including techniques based on the Barzilai-Borwein method. Global convergence can in some cases be proved by appealing to the existing theory. We also propose a sequential quadratic programming (SQP) approach that takes account of the curvature of the boundary of the dual feasible set. Computational experiments show that the proposed approaches perform well in a wide range of applications and that some are significantly faster than previously proposed methods, particularly when only modest accuracy in the solution is required.

90C30Nonlinear programming
90C52Methods of reduced gradient type
90C55Methods of successive quadratic programming type
Full Text: DOI
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