Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bayesian inverse problems with $l_1$ priors: a Randomize-then-Optimize
  approach   Prior distributions for Bayesian inference that rely on the $l_1$-norm of the
parameters are of considerable interest, in part because they promote parameter
fields with less regularity than Gaussian priors (e.g., discontinuities and
blockiness). These $l_1$-type priors include the total variation (TV) prior and
the Besov $B^s_{1,1}$ space prior, and in general yield non-Gaussian posterior
distributions. Sampling from these posteriors is challenging, particularly in
the inverse problem setting where the parameter space is high-dimensional and
the forward problem may be nonlinear. This paper extends the
randomize-then-optimize (RTO) method, an optimization-based sampling algorithm
developed for Bayesian inverse problems with Gaussian priors, to inverse
problems with $l_1$-type priors. We use a variable transformation to convert an
$l_1$-type prior to a standard Gaussian prior, such that the posterior
distribution of the transformed parameters is amenable to Metropolized sampling
via RTO. We demonstrate this approach on several deconvolution problems and an
elliptic PDE inverse problem, using TV or Besov $B^s_{1,1}$ space priors. Our
results show that the transformed RTO algorithm characterizes the correct
posterior distribution and can be more efficient than other sampling
algorithms. The variable transformation can also be extended to other
non-Gaussian priors.

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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
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The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
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The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con