On regularization for image restoration problems from the viewpoint of a Bayesian information criterion

The image restoration problems that arise in early vision are formulated as ill-posed inverse problems. Through regularization, they should be well-posedly solved. This is an approach to exact modeling for constraints on visual systems. The problem of modeling for constraints can be regarded as that of estimating the mean of the marginal conditional distribution of a random function based on prior information. First, the basic models with non-symmetric half plane causality for noisy and blurred image are introduced. Secondly, the parameters of the image model can be estimated from distorted images using the adaptive identification technique based on multiple edge models. Thirdly, after reformulating the image restoration problem as a class of Bayesian estimation problems, this can be well-posedly solved using a 2-D Kalman filter-type algorithm with edge-adaptation. The algorithm makes it possible to optimize a stochastic image model from the standpoint of a Bayesian information criterion. Lastly, a restoration example is given to demonstrate the feasibility and validity of the authors´ approach