From Group Sparse Coding to Rank Minimization: A Novel Denoising Model for Low-level Image Restoration
This work addresses image restoration problems for applications like denoising and deblurring, but it is incremental as it builds on existing low-rank and group sparse coding theories with a new relaxation method.
The paper tackles low-level image restoration by proposing a novel denoising model that connects group sparse coding with rank minimization, using a weighted nonconvex relaxation to overcome bias in nuclear norm minimization, and it achieves significantly higher PSNR/FSIM values than state-of-the-art methods in experiments on tasks like compressive sensing and inpainting.
Recently, low-rank matrix recovery theory has been emerging as a significant progress for various image processing problems. Meanwhile, the group sparse coding (GSC) theory has led to great successes in image restoration (IR) problem with each group contains low-rank property. In this paper, we propose a novel low-rank minimization based denoising model for IR tasks under the perspective of GSC, an important connection between our denoising model and rank minimization problem has been put forward. To overcome the bias problem caused by convex nuclear norm minimization (NNM) for rank approximation, a more generalized and flexible rank relaxation function is employed, namely weighted nonconvex relaxation. Accordingly, an efficient iteratively-reweighted algorithm is proposed to handle the resulting minimization problem combing with the popular L_(1/2) and L_(2/3) thresholding operators. Finally, our proposed denoising model is applied to IR problems via an alternating direction method of multipliers (ADMM) strategy. Typical IR experiments on image compressive sensing (CS), inpainting, deblurring and impulsive noise removal demonstrate that our proposed method can achieve significantly higher PSNR/FSIM values than many relevant state-of-the-art methods.