Choice of the Parameters in A Primal-Dual Algorithm for Bregman Iterated Variational Regularization

Erdem Altuntac

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arXiv · 1807.05793

Choice of the Parameters in A Primal-Dual Algorithm for Bregman Iterated Variational Regularization

Erdem Altuntac

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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 analyse 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.

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Erdem Altuntac. 2020-02-24. Choice of the Parameters in A Primal-Dual Algorithm for Bregman Iterated Variational Regularization. https://arxiv.org/abs/1807.05793

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