Box constrained total generalized variation model and primal-dual algorithm for Poisson noise removal

We consider the image denoising problem under Poisson noise. To further enhance the image denoising effect, a box constraint is incorporated into the total generalized variation (TGV) model by simply projecting all pixel values of the denoised image to lie in a certain interval (e.g., [0, 1] for normalized images and [0, 255] for 8-bit images). Thus, a box constrained TGV model is proposed. Computationally, combining with the dual representation of the second-order TGV regularization, our proposed model is transformed into a minimax problem, and the Chambolle-Pock's first-order primal-dual algorithm is used to compute the saddle point of the minimax problem. In addition, the convergence of Algorithm 1 is discussed. Numerical experiments demonstrate that our proposed model not only gets better visual effects but also obtains higher signal-to-noise ratio, peak signal-to-noise ratio and structural similarity index than several existing state-of-the-art methods.