An Efficient Tailored Finite Point Method for Rician Denoising and Deblurring (Communications in Computational Physics, 2020)
In this paper, we propose using the tailored-finite-point method (TFPM) tosolve the resulting parabolic or elliptic equations when minimizing the Rician denoisingmodel developed by Getreuer et al. in [10] using augmented Lagrangian methods(ALM). Different from traditional finite difference schemes, TFPM employs the methodof weighted residuals with collocation technique, which helps get more accurate approximatesolutions to the equations and thus reserve more details in restored images.Numerical experiments demonstrate that with the new schemes the quality of restoredimages has been improved. Besides these, the existence of the minimizer of the Riciandenoising model have also been established in this paper.
Keywords: Rician denoising; deblurring; variational model; augmented Lagrangian methods; tailored finite point method.