Image Super-Resolution Reconstruction by Huber Regularization and Tailored Finite Point Method (Journal of Computational Mathematics, 2024)
In this paper, we propose using the tailored finite point method (TFPM) to solve theresulting parabolic or elliptic equations when minimizing the Huber regularization basedimage super-resolution model using the augmented Lagrangian method (ALM). The Huber regularization based image super-resolution model can ameliorate the staircase forrestored images. TFPM employs the method of weighted residuals with collocation technique, which helps get more accurate approximate solutions to the equations and reservemore details in restored images. We compare the new schemes with the Marquina-Oshermodel, the image super-resolution convolutional neural network (SRCNN) and the classicalinterpolation methods: bilinear interpolation, nearest-neighbor interpolation and bicubicinterpolation. Numerical experiments are presented to demonstrate that with the newschemes the quality of the super-resolution images has been improved. Besides these, theexistence of the minimizer of the Huber regularization based image super-resolution modeland the convergence of the proposed algorithm are also established in this paper.