Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New Advances in Bayesian Calculation for Linear and Nonlinear Inverse
  Problems   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.

13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con