New Advances in Bayesian Calculation for Linear and Nonlinear Inverse Problems

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dc.creatorMohammad-Djafari, A.
dc.date2001-11-14
dc.date.accessioned2026-07-07T05:46:39Z
dc.date.available2026-07-07T05:46:39Z
dc.descriptionThe 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.
dc.descriptionPresented at MaxEnt96. Appeared in Proceedings of the Maximum Entropy Conference, Berg-en-Dal, South Africa, M. Sears, V. Nedeljkovic, N.E. Pendock and S. Sibisi (Ed.), pp 92-102
dc.identifierhttps://arxiv.org/abs/physics/0111121
dc.identifierhttp://arxiv.org/abs/physics/0111121
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/84414
dc.subjectData Analysis, Statistics and Probability
dc.titleNew Advances in Bayesian Calculation for Linear and Nonlinear Inverse Problems
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