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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
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.
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:
- 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.