## Inversion Of Large-Support Ill-Posed Linear . . . (1998)

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Venue: | IEEE TRANSACTIONS ON IMAGE PROCESSING |

Citations: | 20 - 12 self |

### BibTeX

@ARTICLE{Nikolova98inversionof,

author = {Mila Nikolova and Jérôme Idier and Ali Mohammad-Djafari},

title = { Inversion Of Large-Support Ill-Posed Linear . . . },

journal = {IEEE TRANSACTIONS ON IMAGE PROCESSING},

year = {1998},

volume = {7},

number = {4},

pages = {571--585}

}

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### 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

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