On the convegence of a sequential penalty function method for constrained minimization
SIAM Journal on Numerical Analysis
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Edge-preserving wavelet thresholding for image denoising
Journal of Computational and Applied Mathematics
Iterated Hard Shrinkage for Minimization Problems with Sparsity Constraints
SIAM Journal on Scientific Computing
Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
Foundations of Computational Mathematics
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
SIAM Journal on Imaging Sciences
Robust kernel methods for sparse MR image reconstruction
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
The digital TV filter and nonlinear denoising
IEEE Transactions on Image Processing
Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering
IEEE Transactions on Image Processing
A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration
IEEE Transactions on Image Processing
A fast algorithm for nonconvex approaches to sparse recovery problems
Signal Processing
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The problem of recovering sparse signals and sparse gradient signals from a small collection of linear measurements is one that arises naturally in many scientific fields. The recently developed Compressed Sensing Framework states that such problems can be solved by searching for the signal of minimum L1-norm, or minimum Total Variation, that satisfies the given acquisition constraints. While L1 optimization algorithms, based on Linear Programming techniques, are highly effective at generating excellent signal reconstructions, their complexity is still too high and renders them impractical for many real applications. In this paper, we propose a novel approach to solve the L1 optimization problems, based on the use of suitable nonlinear filters widely applied for signal and image denoising. The corresponding algorithm has two main advantages: low computational cost and reconstruction capabilities similar to those of Linear Programming optimization methods. We illustrate the effectiveness of the proposed approach with many numerical examples and comparisons.