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Choice of the parameters in a primal-dual algorithm for Bregman iterated variational regularization

 
: Altuntac, E.

:

Numerical Algorithms 86 (2021), Nr.2, S.729-759
ISSN: 1017-1398
ISSN: 1572-9265
Englisch
Zeitschriftenaufsatz
Fraunhofer FHR ()

Abstract
Focus of this work is solving a non-smooth constraint minimization problem by a primal-dual splitting algorithm involving proximity operators. The problem is penalized by the Bregman divergence associated with the non-smooth total variation (TV) functional. We analyze two aspects: Firstly, the convergence of the regularized solution of the minimization problem to the minimum norm solution. Second, the convergence of the iteratively regularized minimizer to the minimum norm solution by a primal-dual algorithm. For both aspects, we use the assumption of a variational source condition (VSC). This work emphasizes the impact of the choice of the parameters in stabilization of a primal-dual algorithm. Rates of convergence are obtained in terms of some concave, positive definite index function. The algorithm is applied to a simple two-dimensional image processing problem. Sufficient error analysis profiles are provided based on the size of the forward operator and the noise level in the measurement.

: http://publica.fraunhofer.de/dokumente/N-596702.html