TY - JOUR
T1 - Image Super-Resolution Reconstruction by Huber Regularization and Tailored Finite Point Method
AU - Yang , Wenli
AU - Huang , Zhongyi
AU - Zhu , Wei
JO - Journal of Computational Mathematics
VL - 2
SP - 313
EP - 336
PY - 2024
DA - 2024/01
SN - 42
DO - http://doi.org/10.4208/jcm.2201-m2021-0287
UR - https://global-sci.org/intro/article_detail/jcm/22882.html
KW - Image super-resolution, Variational model, Augmented Lagrangian methods,
Tailored finite point method.
AB - <p style="text-align: justify;">In this paper, we propose using the tailored finite point method (TFPM) to solve the
resulting parabolic or elliptic equations when minimizing the Huber regularization based
image super-resolution model using the augmented Lagrangian method (ALM). The Huber regularization based image super-resolution model can ameliorate the staircase for
restored images. TFPM employs the method of weighted residuals with collocation technique, which helps get more accurate approximate solutions to the equations and reserve
more details in restored images. We compare the new schemes with the Marquina-Osher
model, the image super-resolution convolutional neural network (SRCNN) and the classical
interpolation methods: bilinear interpolation, nearest-neighbor interpolation and bicubic
interpolation. Numerical experiments are presented to demonstrate that with the new
schemes the quality of the super-resolution images has been improved. Besides these, the
existence of the minimizer of the Huber regularization based image super-resolution model
and the convergence of the proposed algorithm are also established in this paper.</p>