Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reconciling Bayesian and perimeter regularization for binary inversion   A central theme in classical algorithms for the reconstruction of
discontinuous functions from observational data is perimeter regularization via
the use of the total variation. On the other hand, sparse or noisy data often
demands a probabilistic approach to the reconstruction of images, to enable
uncertainty quantification; the Bayesian approach to inversion, which itself
introduces a form of regularization, is a natural framework in which to carry
this out. In this paper the link between Bayesian inversion methods and
perimeter regularization is explored. In this paper two links are studied: (i)
the maximum a posteriori (MAP) objective function of a suitably chosen Bayesian
phase-field approach is shown to be closely related to a least squares plus
perimeter regularization objective; (ii) sample paths of a suitably chosen
Bayesian level set formulation are shown to possess finite perimeter and to
have the ability to learn about the true perimeter.

29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an