Automated Parameter Selection for Total Variation Minimization in Image Restoration
This work addresses the practical challenge of automatic parameter tuning for total variation-based image restoration, which is important for users who need robust and user-friendly methods.
The paper presents automated algorithms for selecting scalar or locally varying regularization parameters for total variation models in image restoration, based on the discrepancy principle. Numerical experiments demonstrate efficiency and competitiveness in image denoising and deblurring.
Algorithms for automatically selecting a scalar or locally varying regularization parameter for total variation models with an $L^τ$-data fidelity term, $τ\in \{1,2\}$, are presented. The automated selection of the regularization parameter is based on the discrepancy principle, whereby in each iteration a total variation model has to be minimized. In the case of a locally varying parameter this amounts to solve a multi-scale total variation minimization problem. For solving the constituted multi-scale total variation model convergent first and second order methods are introduced and analyzed. Numerical experiments for image denoising and image deblurring show the efficiency, the competitiveness, and the performance of the proposed fully automated scalar and locally varying parameter selection algorithms.