The total variation (TV) minimization models are widely used in image processing, mainly due to their remarkable ability in preserving edges. There are many methods for solving the TV model. These methods, however, seldom consider the positivity constraint one should impose on image-processing problems. In this paper we develop and implement a new approach for TV image restoration. Our method is based on the multiplicative iterative algorithm originally developed for tomographic image reconstruction. The advantages of our algorithm are that it is very easy to derive and implement under different image noise models and it respects the positivity constraint. Our method can be applied to various noise models commonly used in image restoration, such as the Gaussian noise model, the Poisson noise model, and the impulsive noise model. In the numerical tests, we apply our algorithm to deblur images corrupted by Gaussian noise. The results show that our method give better restored images than the forward–backward splitting algorithm.
A Splitting Algorithm for Coupled System of Primal–Dual Monotone Inclusions