Abstract
The total variation (TV) model with a fidelity term of the generalized Kullback–Leibler (KL) divergence is a classical method for Poissonian image deblurring. In this paper, we propose a new TV-KL model with a spatially dependent regularization parameter. This model is able to preserve small details of images while homogeneous regions still remain sufficiently smooth. The automated selection of the regularization parameter is based on the local discrepancy function. The corresponding minimization problem with a spatially adapted regularization parameter can be solved efficiently by the split Bregman method. Numerical experiments demonstrate that the proposed algorithm has the potential to enhance regions of images containing detail and remove Poisson noise simultaneously, which leads to an improvement in the signal-to-noise ratio and the mean absolute error for deblurring results.
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