Revisiting the Regularizers in Blind Image Deblurring With a New One

Area of Science:

• Computational Imaging
• Computer Vision
• Image Processing
• Optimization

Background:

• Non-blind image deblurring regularization is well-established.
• Current blind deblurring methods often use L0+X regularization, lacking a unified model.
• Existing blind deblurring methods face challenges in numerical efficiency and intuitive modeling.

Purpose of the Study:

• To revisit and differentiate deterministic image regularization in blind deblurring from non-blind deblurring.
• To propose a novel regularization approach for blind deblurring based on redescending potential functions (RDP).
• To establish an intimate relationship between non-blind and blind deblurring regularization.

Main Methods:

• Revisiting representative deterministic image regularization terms in MAP-based blind deblurring.
• Formulating blind deblurring regularization using redescending potential functions (RDP).
• Demonstrating the proposed RDP-induced regularization on benchmark deblurring problems.

Main Results:

• A novel RDP-induced regularization term for blind deblurring is derived.
• This RDP term is shown to be the first-order derivative of a non-convex edge-preserving regularization for non-blind deblurring.
• The proposed method demonstrates competitive performance against state-of-the-art L0+X style methods on benchmark datasets.

Conclusions:

• A unified regularization framework is established between non-blind and blind image deblurring.
• The RDP-induced regularization offers a physically intuitive, practically effective, and efficient alternative for blind deblurring.
• This work opens new avenues for modeling blind deblurring problems.