Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Iterative methods for total variation denoising
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Convex analysis and variational problems
Convex analysis and variational problems
SIAM Journal on Scientific Computing
Nonmonotone Spectral Projected Gradient Methods on Convex Sets
SIAM Journal on Optimization
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming
Numerische Mathematik
Second-order Cone Programming Methods for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Journal of Mathematical Imaging and Vision
A unifying approach to isotropic and anisotropic total variation denoising models
Journal of Computational and Applied Mathematics
SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
Some projection methods with the BB step sizes for variational inequalities
Journal of Computational and Applied Mathematics
Fast Algorithms for Image Reconstruction with Application to Partially Parallel MR Imaging
SIAM Journal on Imaging Sciences
Bregman operator splitting with variable stepsize for total variation image reconstruction
Computational Optimization and Applications
Journal of Computational Physics
Nonlinear multigrid method for solving the anisotropic image denoising models
Numerical Algorithms
International Journal of Bioinformatics Research and Applications
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Image restoration models based on total variation (TV) have become popular since their introduction by Rudin, Osher, and Fatemi (ROF) in 1992. 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 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 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.