A second-order extension of TV regularization for image deblurring

In this paper, we propose a novel second-order regularizer based on the maximum response of the second-order directional derivative, assuming that the image under consideration belongs to the class of piecewise-linear signals. Compared to total-variation regularization that preserves edges but transforms piecewise-smooth regions into piecewise-constant regions, the proposed model is able to restore piecewise-linear regions and finer details. Deconvolution experiments demonstrate the performance of our approach in terms of the quality of reconstruction.