A Fast and Effective Algorithm for a Poisson Denoising Model With Total Variation

In this letter, we present a fast and effective algorithm for solving the Poisson-modified total variation model proposed in [Le et al., “A variational approach to reconstructing images corrupted by Poisson noise,” J. Math. Imag. Vis., vol. 27, no 3, pp. 257-263, Apr. 2007]. The existence and uniqueness of solution for the model are proved by using a different method. A semi-implicit difference scheme is designed to discretize the derived gradient descent flow with a large time step. Different from the original numerical scheme, our scheme is conditional stable with a less stringent condition and can ensure that the numerical solution is strictly positive in image domain. Experimental results show the efficiency and effectiveness of our algorithm.