Single image restoration through l2-relaxed truncated l0 analysis-based sparse optimization in tight frames

Image restoration problems, i.e., recovery of an original high-quality image from the degraded observation, arise in various science and engineer areas. Over the past decades, the framelet-based methods are particularly investigated and adopted, owing to the excellent ability of sparse approximating the piecewise-smooth functions such as natural images. In this paper, we propose a novel tight frame-based l(2)-relaxed truncated l(0) analysis-sparsity model that simultaneously exploiting the sparsity and support priors. The resulting nonconvex nonsmooth optimization problem is addressed by using the proposed proximal alternating adaptive hard thresholding (PAAHT) method. We also proved that the sequence generated by the proposed algorithm sublinearly converges. Numerical experiments on several typical image restoration problems demonstrate that the proposed method is more effective than the standard sparsity-inducing algorithms and outperforms several state-of-the-art methods in both objective and perceptual quality. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper proposes a novel tight frame-based algorithm that simultaneously exploits sparsity and support priors for image restoration. Experimental results show that the proposed method is more effective than standard algorithms and outperforms other methods in both objective and perceptual quality.