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Image restoration subject to a total variation constraint.

Patrick L Combettes1, Jean-Christophe Pesquet

  • 1Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie--Paris 6, 75005 Paris, France. plc@math.jussieu.fr

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|September 29, 2004
PubMed
Summary

This study introduces total variation as a constraint in convex programming for image restoration. This novel approach enables efficient image denoising and deconvolution with added flexibility.

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Area of Science:

  • Image processing and computer vision.
  • Mathematical optimization and convex analysis.

Background:

  • Total variation is crucial for image recovery with piecewise smooth components.
  • Existing methods exclusively use total variation as an objective to minimize.

Purpose of the Study:

  • To propose an alternative formulation using total variation as a constraint.
  • To enable the incorporation of additional constraints in image restoration.
  • To demonstrate efficient solutions for image denoising and deconvolution.

Main Methods:

  • Formulating total variation as a constraint within a convex programming framework.
  • Employing block-iterative methods to solve the resulting optimization problem.

Main Results:

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  • Successfully applied the method to image denoising.
  • Successfully applied the method to image deconvolution.
  • Demonstrated the efficiency and flexibility of the proposed approach.

Conclusions:

  • The proposed method offers a flexible and efficient alternative for image restoration.
  • Using total variation as a constraint expands its applicability in image processing.
  • This framework facilitates the integration of multiple constraints for enhanced image recovery.