Algorithms for total variation-based deblurring and denoising:
In this lecture, algorithms for the discretized system of total variation-based deblurring and denoising are presented. We consider efficient iterative methods. Convergence of outer iteration is improved by adding a linear term on both sides of the system of nonlinear equations. In inner iteration, an algebraic multigrid (AMG) method is applied to solve the linearized systems of equations. We also adopt the Krylov subspace method to accelerate the outer nonlinear iteration. Numerical experiments demonstrate that our algorithm is efficient and robust for image restoration over a wide range of noise, not only for images with large noise-to-signal ratios (SNR) and strong blurring operator but also for pure blurring problems without noise. Finally, we show that for some weak blurring operators, the AMG method can deblur the image directly.

References:

• QS Chang, L Chern, W. Wang, J Xu, Methods for total variation-based image denoising, In Proc. PDE-Based Image Processing and Related Inverse Problems, CMA, Oslo, Norway,
• Q. Chang and I. Chern, Acceleration methods for total variation-based image denoising, SIAM J. Sci. Comput. 25 (2003) pp. 983-994.
• L. Alvarez, P. -L. Lions, and J. -M. Morel, Image selective smoothing and edge detection by nonlinear diffusion II, SIAM J. Numer. Anal., 29 (1992), pp. 845-866.