The Gaussian mixture is a patch prior that has enjoyed tremendous success in image processing. In this work, by using Gaussian factor modeling, its dedicated Expectation Maximization (EM) inference as well as a statistical filter selection and algorithm stopping rule, we develop SURE (Stein's Unbiased Risk Estimator) guided Piecewise Linear Estimation (S-PLE), a patch-based prior learning algorithm capable of delivering state-of-the-art performance at image denoising. In light of this algorithm's features and its results, we also seek to address the number of components to be included when setting up a Gaussian mixture for image patch modeling. By juxtaposing both options, we show that a simple learned prior can perform as well if not better than a much richer yet fixed prior.
