An efficient method for nonnegatively constrained Total Variation-based denoising of medical images corrupted by Poisson noise

Medical images obtained with emission processes are corrupted by Poisson noise. Aim of the paper is to show that the denoising problem can be efficiently modelled in a Bayesian statistical setting by a nonnegatively constrained minimization problem. The objective function is constituted by a data fitting term, the Kullback-Leibler divergence, plus a regularization term, the Total Variation function, weighted by a regularization parameter. We propose an efficient numerical method for the solution of the constrained problem. The method is a Newton projection method, where the inner system is solved by the Conjugate Gradient method, preconditioned and implemented in an efficient way for this specific application. The numerical results on simulated and real medical images prove the effectiveness of the method, both for the accuracy and the computational cost.