dorsal/arxiv
View SchemaNew Advances in Bayesian Calculation for Linear and Nonlinear Inverse Problems
| Authors | A. Mohammad-Djafari |
|---|---|
| Categories | |
| ArXiv ID | physics/0111121 |
| URL | https://arxiv.org/abs/physics/0111121 |
Abstract
The Bayesian approach has proved to be a coherent approach to handle ill posed Inverse problems. However, the Bayesian calculations need either an optimization or an integral calculation. The maximum a posteriori (MAP) estimation requires the minimization of a compound criterion which, in general, has two parts: a data fitting part and a prior part. In many situations the criterion to be minimized becomes multimodal. The cost of the Simulated Annealing (SA) based techniques is in general huge for inverse problems. Recently a deterministic optimization technique, based on Graduated Non Convexity (GNC), have been proposed to overcome this difficulty. The objective of this paper is to show two specific implementations of this technique for the following situations: -- Linear inverse problems where the solution is modeled as a piecewise continuous function. The non convexity of the criterion is then due to the special choice of the prior; -- A nonlinear inverse problem which arises in inverse scattering where the non convexity of the criterion is due to the likelihood part. Keywords: Inverse problems, Regularization, Bayesian calculation, Global optimization, Graduated Non Convexity.
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"abstract": "The Bayesian approach has proved to be a coherent approach to handle ill\nposed Inverse problems. However, the Bayesian calculations need either an\noptimization or an integral calculation. The maximum a posteriori (MAP)\nestimation requires the minimization of a compound criterion which, in general,\nhas two parts: a data fitting part and a prior part. In many situations the\ncriterion to be minimized becomes multimodal. The cost of the Simulated\nAnnealing (SA) based techniques is in general huge for inverse problems.\nRecently a deterministic optimization technique, based on Graduated Non\nConvexity (GNC), have been proposed to overcome this difficulty. The objective\nof this paper is to show two specific implementations of this technique for the\nfollowing situations: -- Linear inverse problems where the solution is modeled\nas a piecewise continuous function. The non convexity of the criterion is then\ndue to the special choice of the prior; -- A nonlinear inverse problem which\narises in inverse scattering where the non convexity of the criterion is due to\nthe likelihood part. Keywords: Inverse problems, Regularization, Bayesian\ncalculation, Global optimization, Graduated Non Convexity.",
"arxiv_id": "physics/0111121",
"authors": [
"A. Mohammad-Djafari"
],
"categories": [
"physics.data-an"
],
"title": "New Advances in Bayesian Calculation for Linear and Nonlinear Inverse Problems",
"url": "https://arxiv.org/abs/physics/0111121"
},
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