Simultaneous Patch-Group Sparse Coding with Dual-Weighted ℓ_p Minimization for Image Restoration.

Area of Science:

• Computer Vision
• Image Processing
• Signal Processing

Background:

• Sparse coding (SC) models like patch sparse coding (PSC) and group sparse coding (GSC) are effective for image restoration.
• PSC can cause blocking artifacts, while GSC may lead to over-smoothing.
• Conventional ℓ1 minimization for sparse signal estimation has limitations in realistic scenarios.

Purpose of the Study:

• To propose a novel simultaneous patch-group sparse coding (SPG-SC) approach for improved image restoration.
• To address the drawbacks of existing SC models by combining local and nonlocal sparse representations.
• To enhance sparse representation capability using dual-weighted ℓp minimization.

Main Methods:

• Developed a simultaneous patch-group sparse coding (SPG-SC) model.
• Introduced a dual-weighted ℓp minimization for non-convex regularization.
• Utilized an alternating direction method of multipliers (ADMM) framework for a generalized iteration shrinkage algorithm.

Main Results:

• The proposed SPG-SC model simultaneously exploits local sparsity and nonlocal sparse representation.
• Dual-weighted ℓp minimization improved the sparse representation accuracy.
• Experimental results on image inpainting and deblurring showed superior performance compared to state-of-the-art methods.

Conclusions:

• The novel SPG-SC approach with dual-weighted ℓp minimization effectively enhances image restoration.
• The method achieves better objective and perceptual quality than existing algorithms.
• The developed ADMM-based optimization is tractable and efficient for the proposed model.