Restoring Poissonian Images by a Combined First-Order and Second-Order Variation Approach

The restoration of blurred images corrupted by Poisson noise is an important topic in imaging science. The problem has recently received considerable attention in recent years. In this paper, we propose a combined first-order and second-order variation model to restore blurred images corrupted by Poisson noise. Our model can substantially reduce the staircase effect, while preserving edges in the restored images, since it combines advantages of the first-order and second-order total variation. We study the issues of existence and uniqueness of a minimizer for this variational model. Moreover, we employ a gradient descent method to solve the associated Euler-Lagrange equation. Numerical results demonstrate the validity and efficiency of the proposed method for Poisson noise removal problem.