A new development of non-local image denoising using fixed-point iteration for non-convex ℓp sparse optimization

Area of Science:

• Computer Vision
• Image Processing
• Signal Processing

Background:

• Sparse representation is crucial for image denoising.
• Existing methods for Schatten-p norm minimization have limitations in accuracy and rigor.
• Measuring structural similarity is key to preserving image details.

Purpose of the Study:

• To propose an efficient image denoising scheme using group-based sparse representation and Schatten-p norm minimization.
• To develop a more rigorous and accurate proximal operator for sparse optimization in ℓp space.
• To analyze the optimal power 'p' for different noise levels and enhance denoising performance.

Main Methods:

• Establishing equivalence between group-based sparse representation and Schatten-p norm minimization.
• Constructing a proximal operator for sparse optimization in ℓp space (p ∈ (0, 1]) via fixed-point iteration.
• Analyzing the relationship between noise level and optimal power 'p', incorporating dictionary learning.

Main Results:

• The proposed Spatially Adaptive Fixed Point Iteration (SAFPI) algorithm achieves superior denoising performance.
• SAFPI demonstrates significant improvements in Peak Signal-to-Noise Ratio (PSNR) and Structure Similarity (SSIM).
• The method effectively retains image structure information, outperforming BM3D, WNNM, and WSNM.

Conclusions:

• The SAFPI algorithm offers a state-of-the-art solution for image denoising.
• The study provides a more accurate and rigorous approach to Schatten-p norm minimization.
• Optimal power 'p' selection is noise-level dependent, enhancing denoising efficacy.