Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence rates in expectation for Tikhonov-type regularization of
  Inverse Problems with Poisson data   In this paper we study a Tikhonov-type method for ill-posed nonlinear
operator equations $\gdag = F(\udag)$ where $\gdag$ is an integrable,
non-negative function. We assume that data are drawn from a Poisson process
with density $t\gdag$ where $t>0$ may be interpreted as an exposure time. Such
problems occur in many photonic imaging applications including positron
emission tomography, confocal fluorescence microscopy, astronomic observations,
and phase retrieval problems in optics. Our approach uses a
Kullback-Leibler-type data fidelity functional and allows for general convex
penalty terms. We prove convergence rates of the expectation of the
reconstruction error under a variational source condition as $t\to\infty$ both
for an a priori and for a Lepski{\u\i}-type parameter choice rule.

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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph