Optimal filtering of multidimensional random fields generated by autoregressions with multiple roots of characteristic equations

The use of mathematical models allows to compare the theoretical expressions and simulation results. Autoregressive random fields can be used for description of the images, however, such models have pronounced anisotropy, and the simulated images are too sharp. The elimination of this drawback is possible through the use of models with multiple roots of characteristic equations. The analysis shows that using models with multiple roots in filtering images with smoothly varying brightness provides smaller errors than the use of autoregressive random fields. However, studies of the dependences of filtering efficiency on various model parameters and signal-to-noise ratios for multidimensional autoregressive random fields were almost not carried out. The article discusses the solution of the problem of optimal filtering of images based on models with multiple roots of characteristic equations. Theoretical dependences of the relative variance of the filtering error on the dimension of random fields are obtained. Furthermore, it was presented some results of filtering real images by such model in comparison with autoregressive model.