Total variation with overlapping group sparsity for image deblurring under impulse noise.

Area of Science:

• Image processing
• Computational imaging
• Applied mathematics

Background:

• Total variation (TV) regularization is effective for image deblurring and edge preservation.
• TV-based methods often suffer from staircase artifacts, degrading image quality.
• Impulse noise and blurring are common challenges in image restoration.

Purpose of the Study:

• To propose a new model for restoring blurred images corrupted by impulse noise.
• To alleviate staircase effects commonly observed in TV-based deblurring methods.
• To improve the accuracy and quality of restored images.

Main Methods:

• Developed a novel image restoration model incorporating an L1-fidelity term and TV regularization with overlapping group sparsity (OGS).
• Imposed a box constraint to enhance solution accuracy.
• Employed the alternating direction method of multipliers (ADMM) framework for solving the model.
• Utilized an inner majorization minimization (MM) iteration for subproblem optimization.

Main Results:

• The proposed method demonstrated superior performance compared to existing TV-based techniques.
• Numerical results showed significant improvements in restoration quality.
• Evaluations using peak signal-to-noise ratio (PSNR) and relative error (ReE) confirmed enhanced image fidelity.

Conclusions:

• The novel L1-fidelity and OGS-TV regularization model effectively restores blurred images with impulse noise.
• The proposed approach successfully mitigates staircase artifacts, outperforming traditional TV methods.
• The method offers a robust solution for improving image deblurring quality and accuracy.