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1998

Inversion of large-support ill-posed linear operators using a piecewise Gaussian MRF

13 years 3 months ago
Inversion of large-support ill-posed linear operators using a piecewise Gaussian MRF
Abstract—We propose a method for the reconstruction of signals and images observed partially through a linear operator with a large support (e.g., a Fourier transform on a sparse set). This inverse problem is ill-posed and we resolve it by incorporating the prior information that the reconstructed objects are composed of smooth regions separated by sharp transitions. This feature is modeled by a piecewise Gaussian (PG) Markov random field (MRF), known also as the weak-string in one dimension and the weak-membrane in two dimensions. The reconstruction is defined as the maximum a posteriori estimate. The prerequisite for the use of such a prior is the success of the optimization stage. The posterior energy corresponding to a PG MRF is generally multimodal and its minimization is particularly problematic. In this context, general forms of simulated annealing rapidly become intractable when the observation operator extends over a large support. In this paper, global optimization is dea...
Mila Nikolova, Jérôme Idier, Ali Moha
Added 23 Dec 2010
Updated 23 Dec 2010
Type Journal
Year 1998
Where TIP
Authors Mila Nikolova, Jérôme Idier, Ali Mohammad-Djafari
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