## Abstract and Applied Analysis

### Fractional-Order Total Variation Image Restoration Based on Primal-Dual Algorithm

#### Abstract

This paper proposes a fractional-order total variation image denoising algorithm based on the primal-dual method, which provides a much more elegant and effective way of treating problems of the algorithm implementation, ill-posed inverse, convergence rate, and blocky effect. The fractional-order total variation model is introduced by generalizing the first-order model, and the corresponding saddle-point and dual formulation are constructed in theory. In order to guarantee $O(1/{N}^{2})$ convergence rate, the primal-dual algorithm was used to solve the constructed saddle-point problem, and the final numerical procedure is given for image denoising. Finally, the experimental results demonstrate that the proposed methodology avoids the blocky effect, achieves state-of-the-art performance, and guarantees $O(1/{N}^{2})$ convergence rate.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 585310, 10 pages.

Dates
First available in Project Euclid: 26 February 2014