# A Simple Local Minimal Intensity Prior and An Improved Algorithm for Blind Image Deblurring

## TL;DR

This paper introduces a simplified sparsity prior called patch-wise minimal pixels (PMP) for blind image deblurring, along with an efficient algorithm that outperforms existing methods in stability, quality, and computational speed.

## Contribution

The work proposes a novel sparsity prior (PMP) and an improved algorithm that avoids approximations, enhancing efficiency and effectiveness in blind image deblurring.

## Key findings

- The proposed algorithm achieves better stability than state-of-the-art methods.
- It demonstrates superior deblurring quality and robustness.
- It is more computationally efficient than existing approaches.

## Abstract

Blind image deblurring is a long standing challenging problem in image processing and low-level vision. Recently, sophisticated priors such as dark channel prior, extreme channel prior, and local maximum gradient prior, have shown promising effectiveness. However, these methods are computationally expensive. Meanwhile, since these priors involved subproblems cannot be solved explicitly, approximate solution is commonly used, which limits the best exploitation of their capability. To address these problems, this work firstly proposes a simplified sparsity prior of local minimal pixels, namely patch-wise minimal pixels (PMP). The PMP of clear images is much more sparse than that of blurred ones, and hence is very effective in discriminating between clear and blurred images. Then, a novel algorithm is designed to efficiently exploit the sparsity of PMP in deblurring. The new algorithm flexibly imposes sparsity inducing on the PMP under the MAP framework rather than directly uses the half quadratic splitting algorithm. By this, it avoids non-rigorous approximation solution in existing algorithms, while being much more computationally efficient. Extensive experiments demonstrate that the proposed algorithm can achieve better practical stability compared with state-of-the-arts. In terms of deblurring quality, robustness and computational efficiency, the new algorithm is superior to state-of-the-arts. Code for reproducing the results of the new method is available at https://github.com/FWen/deblur-pmp.git.