An alternating iterative minimisation algorithm for the double-regularised total least square functional

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http://hdl.handle.net/10138/232767

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Bleyer , I R & Ramlau , R 2015 , ' An alternating iterative minimisation algorithm for the double-regularised total least square functional ' , Inverse Problems , vol. 31 , no. 7 , 075004 . https://doi.org/10.1088/0266-5611/31/7/075004

Title: An alternating iterative minimisation algorithm for the double-regularised total least square functional
Author: Bleyer, Ismael Rodrigo; Ramlau, Ronny
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2015-07
Language: eng
Number of pages: 21
Belongs to series: Inverse Problems
ISSN: 0266-5611
URI: http://hdl.handle.net/10138/232767
Abstract: The total least squares (TLS) method is a successful approach for linear problems if both the right-hand side and the operator are contaminated by some noise. For ill-posed problems, a regularisation strategy has to be considered to stabilise the computed solution. Recently a double regularised TLS method was proposed within an infinite dimensional setup and it reconstructs both function and operator, reflected on the bilinear forms Our main focuses are on the design and the implementation of an algorithm with particular emphasis on alternating minimisation strategy, for solving not only the double regularised TLS problem, but a vast class of optimisation problems: on the minimisation of a bilinear functional of two variables.
Subject: ill-posed problems
noisy operator
noisy right-hand side
regularised total least squares
alternating minimisation
wavelets
subderivatives
CONVEX-FUNCTIONS
111 Mathematics
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