# Convex Denoising using Non-Convex Tight Frame Regularization

arXiv: https://arxiv.org/abs/1504.00976 · HTML: https://mlsanity.com/paper/1504.00976/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2015.

## Built on by (most cited first, 2 of 2)

- [Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms](https://mlsanity.com/paper/2308.10542/) (2023)
- [Local monotone operator learning using non-monotone operators: MnM-MOL](https://mlsanity.com/paper/2312.00386/) (2023)

## Abstract (arXiv)

This paper considers the problem of signal denoising using a sparse tight-frame analysis prior. The L1 norm has been extensively used as a regularizer to promote sparsity; however, it tends to under-estimate non-zero values of the underlying signal. To more accurately estimate non-zero values, we propose the use of a non-convex regularizer, chosen so as to ensure convexity of the objective function. The convexity of the objective function is ensured by constraining the parameter of the non-convex penalty. We use ADMM to obtain a solution and show how to guarantee that ADMM converges to the global optimum of the objective function. We illustrate the proposed method for 1D and 2D signal denoising.