Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Filter Based Methods For Statistical Linear Inverse Problems   Ill-posed inverse problems are ubiquitous in applications. Under- standing of
algorithms for their solution has been greatly enhanced by a deep understanding
of the linear inverse problem. In the applied communities ensemble-based
filtering methods have recently been used to solve inverse problems by
introducing an artificial dynamical sys- tem. This opens up the possibility of
using a range of other filtering methods, such as 3DVAR and Kalman based
methods, to solve inverse problems, again by introducing an artificial
dynamical system. The aim of this paper is to analyze such methods in the
context of the ill-posed linear inverse problem. Statistical linear inverse
problems are studied in the sense that the observational noise is assumed to be
derived via realization of a Gaussian random variable. We investigate the
asymptotic behavior of filter based methods for these inverse problems.
Rigorous convergence rates are established for 3DVAR and for the Kalman
filters, including minimax rates in some instances. Blowup of 3DVAR and a
variant of its basic form is also presented, and optimality of the Kalman
filter is discussed. These analyses reveal a close connection between
(iterative) regularization schemes in deterministic inverse problems and filter
based methods in data assimilation. Numerical experiments are presented to
illustrate the theory.

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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin