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Constrained Plug-and-Play Priors for Image Restoration.

Alessandro Benfenati1,2, Pasquale Cascarano3

  • 1Environmental and Science Policy Department, University of Milan, Via Celoria 2, 20133 Milano, Italy.

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Constrained Plug-and-Play (CPnP) reformulates image restoration by linking denoiser regularization to noise levels. This method offers improved stability and robustness for inverse problems, enhancing image quality.

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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.