Adaptive fractional-order total variation image restoration with split Bregman iteration

Area of Science:

• Image processing and computer vision
• Applied mathematics
• Signal processing

Background:

• Image restoration faces challenges with staircase artifacts and adaptive regularization parameter selection.
• Existing methods struggle to balance detail preservation and artifact reduction.

Purpose of the Study:

• To propose an adaptive fractional-order total variation l1 regularization (AFOTV-l1) model for enhanced image restoration.
• To develop an improved fractional-order differential kernel mask (IFODKM) for better detail preservation and artifact avoidance.
• To introduce a novel adaptive strategy for regularization parameters.

Main Methods:

• An adaptive fractional-order total variation l1 regularization (AFOTV-l1) model was developed.
• The split Bregman iteration algorithm (SBI) was employed for image estimation.
• An improved fractional-order differential kernel mask (IFODKM) with extended degrees of freedom was designed.

Main Results:

• The proposed IFODKM effectively preserves image details and mitigates staircase artifacts.
• The SBI algorithm ensured fast convergence and minimal errors in image estimation.
• Experimental results demonstrated superior approximation, robustness, and convergence compared to existing methods.

Conclusions:

• The AFOTV-l1 model with IFODKM offers significant improvements in image restoration quality.
• The adaptive regularization strategy enhances performance across different image characteristics.
• The method shows strong potential for practical applications in image restoration.