In this paper, we propose a fast proximity point algorithm and apply it to total
variation (TV) based image restoration. The novel method is derived from the idea
of establishing a general proximity point operator framework based on which new
first-order schemes for total variation (TV) based image restoration have been proposed.
Many current algorithms for TV-based image restoration, such as Chambolle's projection
algorithm, the split Bregman algorithm, the Bermudez-Moreno algorithm, the Jia-Zhao
denoising algorithm, and the fixed point algorithm, can be viewed as special cases of the
new first-order schemes. Moreover, the convergence of the new algorithm has been analyzed
at length. Finally, we make comparisons with the split Bregman algorithm which is one of
the best algorithms for solving TV-based image restoration at present. Numerical
experiments illustrate the efficiency of the proposed algorithms.