Pseudo-gradient algorithms for forecasting and filtering cylindrical and circular images

Currently, 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 cylinder. For example, images of a section of a pipeline, a blood vessel, parts during turning, etc. The peculiarity of the domain for specifying such images requires its consideration in their models and processing algorithms. In the present work, autoregressive models of cylindrical images are considered, expressions of the correlation function depending on the autoregression parameters are given. To represent heterogeneous images with random heterogeneities, «doubly stochastic» models in which one or more images control the parameters of the resulting image are used. Note that the spiral scan of a cylindrical image can be considered as a quasiperiodic process due to the correlation of image lines, for example, voiced speech sounds and musical tones. The scans of two or more correlated cylindrical images can serve as a model of a system of correlated quasiperiodic processes. Pseudo-gradient algorithms for filtering and predicting images and processes and for identifying their models are proposed. The conducted statistical modeling showed that these algorithms are close in efficiency to the optimal algorithms constructed with known values of the parameters of the processed data.