An Efficient Tailored Finite Point Method for Rician Denoising and Deblurring

In this paper, we propose using the tailored-finite-point method (TFPM) to solve the resulting parabolic or elliptic equations when minimizing the Rician denoising model developed by Getreuer et al. in [10] using augmented Lagrangian methods (ALM). Different from traditional finite difference schemes, TFPM employs the method of weighted residuals with collocation technique, which helps get more accurate approximate solutions to the equations and thus reserve more details in restored images. Numerical experiments demonstrate that with the new schemes the quality of restored images has been improved. Besides these, the existence of the minimizer of the Rician denoising model have also been established in this paper.