Abstract
This paper is concerned with a classical denoising and deblurring problem in image recovery. Our approach is based on a variational method. By using the Legendre--Fenchel transform, we show how the nonquadratic criterion to be minimized can be split into a sequence of half-quadratic problems easier to solve numerically. First we prove an existence and uniqueness result, and then we describe the algorithm for computing the solution and we give a proof of convergence. Finally, we present some experimental results for synthetic and real images.
Keywords
DeblurringMathematicsUniquenessConvergence (economics)Image restorationLegendre polynomialsApplied mathematicsImage denoisingSequence (biology)Image (mathematics)Quadratic equationAlgorithmMathematical optimizationImage processingMathematical analysisComputer visionComputer scienceGeometry
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Publication Info
- Year
- 1997
- Type
- article
- Volume
- 34
- Issue
- 5
- Pages
- 1948-1979
- Citations
- 307
- Access
- Closed
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Cite This
Gilles Aubert,
Luminita A. Vese
(1997).
A Variational Method in Image Recovery.
SIAM Journal on Numerical Analysis
, 34
(5)
, 1948-1979.
https://doi.org/10.1137/s003614299529230x
Identifiers
- DOI
- 10.1137/s003614299529230x