Open AccessArticle
A Fast Nonlinear Sparse Model for Blind Image Deblurring
by
Zirui Zhang, Zheng Guo, Zhenhua Xu, Huasong Chen, Chunyong Wang, Yang Song, Jiancheng Lai, Yunjing Ji and Zhenhua Li
J. Imaging 2025, 11(10), 327; https://doi.org/10.3390/jimaging11100327 (registering DOI) - 23 Sep 2025
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
,
, and
regularizations have been widely adopted. Based on this foundation
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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
,
, and
regularizations have been widely adopted. Based on this foundation and combining successful experiences of previous work, this paper introduces
regularization, a novel nonlinear sparse regularization combining the
and
norms via nonlinear coupling. Statistical probability analysis demonstrates that
regularization achieves stronger sparsity than traditional regularizations like
,
, and
regularizations. Furthermore, building upon the
regularization, we propose a novel nonlinear sparse model for blind image deblurring. To optimize the proposed
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.
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