# Total Variation Denoising via the Moreau Envelope

arXiv: https://arxiv.org/abs/1701.00439 · HTML: https://mlsanity.com/paper/1701.00439/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jan 2017.

## Built on by (most cited first, 3 of 3)

- [Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithms](https://mlsanity.com/paper/2305.15988/) (2023)
- [Self-Verification in Image Denoising](https://mlsanity.com/paper/2111.00666/) (2021)
- [Framelet-Based Blind Image Restoration with Minimax Concave Regularization](https://mlsanity.com/paper/2604.19314/) (2026)

## Abstract (arXiv)

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.