Total Variation Denoising via the Moreau Envelope

Abstract

Total variation denoising is a nonlinear filtering method well suited for the estimation of piecewise-constant signals observed in additive white Gaussian noise. The method is defined by the minimization of a particular non-differentiable convex cost function. This paper describes a generalization of this cost function that can yield more accurate estimation of piecewise constant signals. The new cost function involves a non-convex penalty (regularizer) designed to maintain the convexity of the cost function. The new penalty is based on the Moreau envelope. The proposed total variation denoising method can be implemented using forward-backward splitting.

arXiv comment7 pages; IEEE Signal Processing Letters (preprint)

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Cited by in corpus (6)

• Sparse Regularization via Convex Analysis
• On Solving SAR Imaging Inverse Problems Using Non-Convex Regularization with a Cauchy-based Penalty
• Convergence Guarantees for Non-Convex Optimisation with Cauchy-Based Penalties
• Improved Sparse Low-Rank Matrix Estimation
• Automatic Tuning of Denoising Algorithms Parameters Without Ground Truth
• A Convex-Nonconvex Strategy for Grouped Variable Selection