Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems

This paper studies gradient-based schemes for image denoising and deblurring prob-lems based on the discretized total variation (TV) minimization model with con-straints. We derive a fast algorithm for the constrained TV-based image deburring problem. To achieve this task we combine an acceleration of the well known dual approach to the denoising problem with a novel monotone version of a fast iterative shrinkage/thresholding algorithm (FISTA) we have recently introduced. The result-ing gradient-based algorithm shares a remarkable simplicity together with a proven global rate of convergence which is signicantly better than currently known gradient projections-based methods. Our results are applicable to both the anisotropic and isotropic discretized TV functionals. Initial numerical results demonstrate the viabil-ity and eciency of the proposed algorithms on image deblurring problems with box constraints.