# A Fast Nonlinear Sparse Model for Blind Image Deblurring

## TL;DR

This paper introduces a new nonlinear sparse model for blind image deblurring that improves performance and efficiency.

## Contribution

The novel LN regularization and AGST algorithm offer stronger sparsity and better deblurring results.

## Key findings

- LN regularization provides stronger sparsity than traditional L2, L1, and Lp regularizations.
- The proposed model achieves superior deblurring performance on synthetic and real-world images.
- AGST combined with HQS ensures efficient optimization and computational efficiency.

## Abstract

Blind image deblurring, which requires simultaneous estimation of the latent image and blur kernel, constitutes a classic ill-posed problem. To address this, priors based on L2, L1, and Lp regularizations have been widely adopted. Based on this foundation and combining successful experiences of previous work, this paper introduces LN regularization, a novel nonlinear sparse regularization combining the Lp and L∞ norms via nonlinear coupling. Statistical probability analysis demonstrates that LN regularization achieves stronger sparsity than traditional regularizations like L2, L1, and Lp regularizations. Furthermore, building upon the LN regularization, we propose a novel nonlinear sparse model for blind image deblurring. To optimize the proposed LN regularization, we introduce an Adaptive Generalized Soft-Thresholding (AGST) algorithm and further develop an efficient optimization strategy by integrating AGST with the Half-Quadratic Splitting (HQS) strategy. Extensive experiments conducted on synthetic datasets and real-world images demonstrate that the proposed nonlinear sparse model achieves superior deblurring performance while maintaining completive computational efficiency.