Convex regularization of discrete-valued inverse problems

Autor: Clason, Christian, Do, Thi Bich Tram
Rok vydání: 2017
Předmět:
Zdroj: New Trends in Parameter Identification for Mathematical Models, B. Hofmann, A. Leit\~ao, and J. Zubelli (eds.), Birkh\"auser, 2018
Druh dokumentu: Working Paper
DOI: 10.1007/978-3-319-70824-9_2
Popis: This work is concerned with linear inverse problems where a distributed parameter is known a priori to only take on values from a given discrete set. This property can be promoted in Tikhonov regularization with the aid of a suitable convex but nondifferentiable regularization term. This allows applying standard approaches to show well-posedness and convergence rates in Bregman distance. Using the specific properties of the regularization term, it can be shown that convergence (albeit without rates) actually holds pointwise. Furthermore, the resulting Tikhonov functional can be minimized efficiently using a semi-smooth Newton method. Numerical examples illustrate the properties of the regularization term and the numerical solution.
Databáze: arXiv