Models and filtering of circular images with harmonic components of the covariance function.

Nowadays, image processing problems are becoming increasingly important due to development of the aerospace Earth monitoring systems, medical devices etc. But the most of the image processing works deal with images defined on rectangular two-dimensional grids or grids of higher dimension. In some practical situations, images are set on a circle. The peculiarity of such images requires its consideration in their models. In the early works of the authors, several autoregressive models of such images were proposed. However, these models can generate images with positive covariation functions. Sometimes the impact of the external environment and internal features of the object lead to the presence of harmonic components. For example, facies, eye, virus, sunflower, etc. To represent such images, complex roots are necessary in characteristic equation of autoregressive model. In the present paper, autoregressive models of circular quasiperiodic images are considered. The expressions of their covariance functions are given. The pseudo-gradient algorithms for model identification, and images forecasting and filtering are proposed. [ABSTRACT FROM AUTHOR]