# Framelet-Based Blind Image Restoration with Minimax Concave Regularization

arXiv: https://arxiv.org/abs/2604.19314 · HTML: https://mlsanity.com/paper/2604.19314/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 32 references that are in the map.
- First posted on arXiv 21 Apr 2026.

## Builds on (most cited first, 4 of 4)

- [Sparse Regularization via Convex Analysis](https://mlsanity.com/paper/1803.06765/) (2018)
- [Total Variation Denoising via the Moreau Envelope](https://mlsanity.com/paper/1701.00439/) (2017)
- [Point spread function estimation for blind image deblurring problems based on framelet transform](https://mlsanity.com/paper/2112.11004/) (2021)
- [A Class of Nonconvex Penalties Preserving Overall Convexity in Optimization-Based Mean Filtering](https://mlsanity.com/paper/1604.06589/) (2016)

## Abstract (arXiv)

Recovering corrupted images is one of the most challenging problems in image processing. Among various restoration tasks, blind image deblurring has been extensively studied due to its practical importance and inherent difficulty. In this problem, both the point spread function (PSF) and the underlying latent sharp image must be estimated simultaneously. This problem cannot be solved directly due to its ill-posed nature. One powerful tool for solving such problems is total variation (TV) regularization. The ℓ0-norm regularization within the TV framework has been widely adopted to promote sparsity in image gradients or transform domains, leading to improved preservation of edges and fine structures. However, the use of the ℓ0-norm results in a highly nonconvex and computationally intractable optimization problem, which limits its practical applicability. To overcome these difficulties, we employ the minimax concave penalty (MCP), which promotes enhanced sparsity and provides a closer approximation to the ℓ0-norm. In addition, a reweighted ℓ1-norm regularization is incorporated to further reduce estimation bias and improve the preservation of fine image details and textures. After introducing the proposed model, a numerical algorithm is developed to solve the resulting optimization problem. The effectiveness of the proposed approach is then demonstrated through experimental evaluations on several test images.