Iglesias-Hernandez, Marco, A., Lin, Kui, Lu, Shuai and Stuart, A. M. (2017) Filter based methods for statistical linear inverse problems. Communications in Mathematical Sciences, 15 (7). pp. 1867-1896. doi:10.4310/CMS.2017.v15.n7.a4 ISSN 1539-6746.

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Abstract

Ill-posed inverse problems are ubiquitous in applications. Understanding 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 system. 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 linear inverse problem.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Algorithms, Random noise theory, Kalman filtering
Journal or Publication Title:	Communications in Mathematical Sciences
Publisher:	International Press
ISSN:	1539-6746
Official Date:	16 October 2017
Dates:	Date Event 16 October 2017 Published 6 May 2017 Accepted
Volume:	15
Number:	7
Page Range:	pp. 1867-1896
DOI:	10.4310/CMS.2017.v15.n7.a4
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	8 December 2017
Date of first compliant Open Access:	8 December 2017
Funder:	China. Guo jia ke xue ji shu bu [Ministry of Science and Technology] (CMST)
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID Programme Grant EQUIP Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266 UNSPECIFIED Office of Naval Research http://dx.doi.org/10.13039/100000006 91130004 National Natural Science Foundation of China http://dx.doi.org/10.13039/501100001809 11522108 National Natural Science Foundation of China http://dx.doi.org/10.13039/501100001809 14QA1400400 Science and Technology Commission of Shanghai Municipality http://dx.doi.org/10.13039/501100003399 Grant number B08018 Program for New Century Excellent Talents in University http://dx.doi.org/10.13039/501100004602 2015CB856003 Ministry of Science and Technology of the People's Republic of China http://dx.doi.org/10.13039/501100002855

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