Blur identification analysis in blind edge-preserving image restoration

Tonazzini A.

Restoration  Segmentation. Edge and feature detection  Probability and statistics. Probabilistic algorithms (including Monte Carlo) 

This paper proposes exploiting edge-preserving regularization lo improve the quality of both the image and the blur estimates in blind restoration. Indeed, edge-preserving regularization allows for a more reliable detection of the intensity discontinuities. Since the most part of the information which is needed for the estimation of the blur is located across the discontinuity edges, we infer that a better estimate of the blur parameters can be obtained as well. I n a fully Bayesian approach, assuming that the image is modeled through a coupled MRF with an explicit, binary and constrained line process, our method is based on the joint maximization of a distribution of the image field, the data and the blur parameters. This very complex joint maximization can be decomposed into a sequence of MAP and/or ML estimations, to be alternately and iteratively performed, with a significant reduction of complexity and computational load. In a previous paper55, a similar approach was adopted lo simultaneously estimate the image and its MRF model hyperparameters (unsupervised restoration). In that case, the presence of an explicit and binary line field was exploited to decrease the computational cost of the usually very expensive hyperparameter estimation step. Successively, an overall Bayesian estimation procedure was established, where blind restoration is merged with unsupervised restoration far a completely data driven image recovery42, and a specialized neural network architecture was devised for its fast and efficient implementation. In the present paper we recall the theoretical assessment of blind, unsupervised image restoration, summarize the main features of our approach, and experimentally analyze several qualitative and quantitative aspects of joint image estimation and blur identification. In particular, we show how the use of edge-preserving image models can help in obtaining good blur estimates even in presence of a significant amount of noise, without any need for smoothness assumptions on the blur coefficients, which would polarize the solution towards often unrealistic uniform blurs.