A nested primal–dual FISTA-like scheme for composite convex optimization problems

We propose a nested primal–dual algorithm with extrapolation on the primal variable suited for minimizing the sum of two convex functions, one of which is continuously differentiable. The proposed algorithm can be interpreted as an inexact inertial forward–backward algorithm equipped with a prefixed number of inner primal–dual iterations for the proximal evaluation and a “warm–start” … Read more

Implementing Algorithms for Signal and Image Reconstruction on Graphical Processing Units

Several highly effective algorithms that have been proposed recently for compressed sensing and image processing applications can be implemented efficiently on commodity graphical processing units (GPUs). The properties of algorithms and application that make for efficient GPU implementation are discussed, and computational results for several algorithms are presented that show large speedups over CPU implementations. … Read more

An efficient TVL1 algorithm for deblurring multichannel images corrupted by impulsive noise

We extend a recently proposed alternating minimization algorithm to the case of recovering blurry multichannel (color) images corrupted by impulsive rather than Gaussian noise. The algorithm minimizes the sum of a multichannel extension of total variation (TV), either isotropic or anisotropic, and a data fidelity term measured in the L1-norm. We derive the algorithm by … Read more

A Fast Algorithm For Image Deblurring with Total Variation Regularization

We propose and test a simple algorithmic framework for recovering images from blurry and noisy observations based on total variation (TV) regularization when a blurring point-spread function is given. Using a splitting technique, we construct an iterative procedure of alternately solving a pair of easy subproblems associated with an increasing sequence of penalty parameter values. … Read more