Nested Iterative Algorithms for Convex Constrained Image Recovery Problems

The objective of this paper is to develop methods for solving image recovery problems subject to constraints on the solution. More precisely, we will be interested in problems which can be formulated as the minimization over a closed convex constraint set of the sum of two convex functions $f$ and $...

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Vydáno v:SIAM journal on imaging sciences Ročník 2; číslo 2; s. 730 - 762
Hlavní autoři: Chaux, Caroline, Pesquet, Jean-Christophe, Pustelnik, Nelly
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Society for Industrial and Applied Mathematics 01.01.2009
Témata:
Algorithms
Computation and Language
Computer Science
Convergence
Gaussian
Minimization
Noise
Optimization
Recovery
ISSN:1936-4954, 1936-4954
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Popis
Shrnutí:The objective of this paper is to develop methods for solving image recovery problems subject to constraints on the solution. More precisely, we will be interested in problems which can be formulated as the minimization over a closed convex constraint set of the sum of two convex functions $f$ and $g$, where $f$ may be nonsmooth and $g$ is differentiable with a Lipschitz-continuous gradient. To reach this goal, we derive two types of algorithms that combine forward-backward and Douglas-Rachford iterations. The weak convergence of the proposed algorithms is proved. In the case when the Lipschitz-continuity property of the gradient of $g$ is not satisfied, we also show that, under some assumptions, it remains possible to apply these methods to the considered optimization problem by making use of a quadratic extension technique. The effectiveness of the algorithms is demonstrated for two wavelet-based image restoration problems involving a signal-dependent Gaussian noise and a Poisson noise, respectively.
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ISSN:1936-4954
1936-4954
DOI:10.1137/080727749