About cookies on this site Our websites require some cookies to function properly (required). In addition, other cookies may be used with your consent to analyze site usage, improve the user experience and for advertising. For more information, please review your options. By visiting our website, you agree to our processing of information as described in IBM’sprivacy statement. To provide a smooth navigation, your cookie preferences will be shared across the IBM web domains listed here.
Publication
IEEE TIP
Paper
Exact distribution of edge-preserving MAP estimators for linear signal models with Gaussian measurement noise
Abstract
We derive the exact statistical distribution of maximum a posteriori (MAP) estimators having edge-preserving non-Gaussian priors. Such estimators have been widely advocated for image restoration and reconstruction problems. Previous investigations of these image recovery methods have been primarily empirical; the distribution we derive enables theoretical analysis. The signal model is linear with Gaussian measurement noise. We assume that the energy function of the prior distribution is chosen to ensure a unimodal posterior distribution (for which convexity of the energy function is sufficient), and that the energy function satisfies a uniform Lipschitz regularity condition. The regularity conditions are sufficiently general to encompass popular priors such as the generalized Gaussian Markov random field prior and the Huber prior, even though those priors are not everywhere twice continuously differentiable.