Nonlinear reconstruction of images described by Gibbs models

The work is devoted to the problem of nonlinear reconstruction of distorted images. The distortion is assumed to be linear image blur, nonlinear non-delay transformation and Gaussian noise addition applied in series. This distortion collection is characteristic for any image registration procedure. The original non-distorted image is described by a two-dimensional causal autoregression model. Reformulation of the original image two-dimensional causal autoregression model in terms of the equivalent Gibbs model permits one to construct a nonlinear iterative reconstruction algorithm. The reconstruction algorithm is based on the Metropolis-Hastings stochastic relaxation method. The presented results of real distorted image reconstruction by the proposed algorithm illustrate the effectiveness of restoration