Image Denoising Based on Fractional Gradient Vector Flow and Overlapping Group Sparsity as Priors

Area of Science:

• Image Processing
• Computational Mathematics
• Applied Physics

Background:

• Image noise significantly degrades visual quality and hinders subsequent analysis.
• Traditional denoising methods often struggle to balance noise removal with the preservation of image details, such as edges and textures.
• Fractional calculus offers novel mathematical tools for modeling complex phenomena, including image degradation processes.

Purpose of the Study:

• To introduce a novel regularization term, L1-norm based fractional gradient vector flow (LF-GGVF), for advanced image denoising.
• To develop and validate a fractional order variational method for estimating the LF-GGVF.
• To integrate LF-GGVF with overlapping group sparsity as priors within an optimization framework for superior image denoising.

Main Methods:

• Formulation of a fractional order variational method for LF-GGVF estimation.
• Implementation of overlapping group sparsity and LF-GGVF as priors in the denoising optimization framework.
• Approximation of fractional order derivatives using the Riemann-Liouville derivative.
• Numerical optimization via alternating direction method of multipliers (ADMM) and split Bregman techniques.
• Solution of linear equations using an efficient numerical scheme.

Main Results:

• Experimental validation using simulated data, including test images with additive white Gaussian noise.
• Demonstrated superior performance in noise suppression compared to existing methods.
• Exhibited enhanced edge preservation capabilities, maintaining image structure fidelity.
• Quantitative and qualitative assessments confirmed the effectiveness of the proposed LF-GGVF approach.

Conclusions:

• The proposed LF-GGVF regularization term significantly improves image denoising performance.
• The fractional order variational approach effectively estimates LF-GGVF, leading to better noise reduction.
• The combined use of LF-GGVF and overlapping group sparsity offers a robust framework for high-quality image denoising, outperforming conventional techniques.