Markov Random Fields using complex line process: An application to Bayesian image restoration

The problem of image restoration is considered, where the goal is to recover the original image starting from its blurred and noisy degraded version. A Bayesian restoration procedure is introduced based on modeling the image given the measurements as a Markov Random Fields characterized by spatially variant local priors. A suitable complex valued line process is introduced, generalizing previous literature works, to account for both the intensity and the orientation of image edges. The presence and the orientation of image edges are locally estimated by a computationally efficient filtering stage especially tuned to visually relevant image features, namely a first-order Circular Harmonic Function filter. Simulation results shows the effectiveness of the complex line process in describing local image discontinuities.