An alternating iterative minimisation algorithm for the double-regularised total least square functional. (19th May 2015)

• Record Type: Journal Article
• Authors: Bleyer, Ismael Rodrigo; Ramlau, Ronny
• Is Part Of: Inverse problems. Volume 31:Number 7(2015:Jul.)
• Publication Date: 2015-05-19
• Subjects: ill-posed problems -- noisy operator -- noisy right-hand side -- regularised total least squares -- alternating minimisation -- wavelets -- subderivatives; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/31/7/075004
• Languages: English
• ISSNs: 0266-5611

Abstract

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.