Restoration of images degraded by signal-dependent noise based on energy minimization: an empirical study

Abstract

Abstract. Most energy minimization-based restoration methods are developed for signal-independent Gaussian noise. The assumption of Gaussian noise distribution leads to a quadratic data fidelity term, which is appealing in optimization. When an image is acquired with a photon counting device, it contains signal-dependent Poisson or mixed Poisson-Gaussian noise. We quantify the loss in performance that occurs when a restoration method suited for Gaussian noise is utilized for mixed noise. Signal-dependent noise can be treated by methods based on either classical maximum a posteriori (MAP) probability approach or on a variance stabilization approach (VST). We compare performances of these approaches on a large image material and observe that VST-based methods outperform those based on MAP in both quality of restoration and in computational efficiency. We quantify improvement achieved by utilizing Huber regularization instead of classical total variation regularization. The conclusion from our study is a recommendation to utilize a VST-based approach combined with regularization by Huber potential for restoration of images degraded by blur and signal-dependent noise. This combination provides a robust and flexible method with good performance and high speed.