Constrained Plug-and-Play Priors for Image Restoration

Area of Science:

• Computational Imaging
• Image Processing
• Optimization Theory

Background:

• The Plug-and-Play (PnP) framework leverages denoisers as implicit image priors for model-based inverse problem solutions.
• Traditional PnP methods offer flexibility but lack physical interpretation for regularization strength, requiring extensive parameter tuning.

Purpose of the Study:

• To introduce the Constrained Plug-and-Play (CPnP) method for image restoration.
• To reformulate PnP as a constrained optimization problem with physically interpretable regularization parameters.

Main Methods:

• Developed the Constrained Plug-and-Play (CPnP) method, reformulating traditional PnP as a constrained optimization problem.
• Designed an efficient Alternating Direction Method of Multipliers (ADMM) algorithm to solve the constrained optimization problem.
• Validated the method on image restoration tasks.

Main Results:

• The regularization parameter in CPnP directly corresponds to the noise level in measurements.
• CPnP demonstrates superior stability and robustness compared to existing methods.
• Achieved competitive image quality performance.

Conclusions:

• CPnP provides a physically meaningful interpretation for regularization in PnP frameworks.
• The proposed ADMM-based approach efficiently solves the constrained optimization problem.
• CPnP offers a more stable, robust, and effective solution for image restoration tasks.