2010
DOI: 10.1007/s10851-010-0243-1
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Proximal Algorithms for Multicomponent Image Recovery Problems

Abstract: In recent years, proximal splitting algorithms have been applied to various monocomponent signal and image recovery problems. In this paper, we address the case of multicomponent problems. We first provide closed form expressions for several important multicomponent proximity operators and then derive extensions of existing proximal algorithms to the multicomponent setting. These results are applied to stereoscopic image recovery, multispectral image denoising, and image decomposition into texture and geometry… Show more

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Cited by 56 publications
(63 citation statements)
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“…Examples of applications of these methods can be found in f-MRI reconstruction [1,2], satellite image restoration [3,4], microscopy image deconvolution [5,6], computed tomography [7], Positron Emission Tomography [8,9], texture-geometry decomposition [10,11,12], machine learning [13,14], stereo vision [15], and audio processing [16,17]. Proximal algorithms have gained much popularity in solving large-size optimization problems involving non-differentiable (or even non finite) functions.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…Examples of applications of these methods can be found in f-MRI reconstruction [1,2], satellite image restoration [3,4], microscopy image deconvolution [5,6], computed tomography [7], Positron Emission Tomography [8,9], texture-geometry decomposition [10,11,12], machine learning [13,14], stereo vision [15], and audio processing [16,17]. Proximal algorithms have gained much popularity in solving large-size optimization problems involving non-differentiable (or even non finite) functions.…”
Section: Introductionmentioning
confidence: 99%
“…By using now the fact that prox 12]) and by invoking Proposition 2.8, the expression of the optimal solution in (35) follows.…”
mentioning
confidence: 99%
“…Note that, if A is the identity matrix, one recovers the usual proximity operator prox f : R N → R N , which is at the core of numerous convex optimization algorithms (see [33,34,35] for tutorials and use for multicomponent image processing). 1 We are now ready to provide Algorithm 1 for the minimization of function F :…”
Section: Minimization Strategymentioning
confidence: 99%
“…16) where the components of s(z) ∈ R N are given by (35). Therefore, for every 17) where, for every z ∈ R N , matrix A log (z) is expressed by (34) where Ω = Ω H +Ω V and the elements of Ω H and Ω V are given by (36).…”
Section: Appendix A2 Log-tvmentioning
confidence: 99%
“…Several methods [19][20][21][22] have been introduced for decomposing a given image into a component with bounded variation, which holds the geometrical information, and an oscillating component, which corresponds to the textural information. A recent work [23] generalized the previous approaches providing a method for decomposing an image in more than two components, while being also able to handle data corrupted with a linear operator and a non-necessarily Gaussian noise.…”
Section: Introductionmentioning
confidence: 99%