ТЕКУЩИЕ И УСТАНОВИВШИЕСЯ ОШИБКИ ПСЕВДОГРАДИЕНТНОЙ ФИЛЬТРАЦИИ ЦИЛИНДРИЧЕСКИХ ИЗОБРАЖЕНИЙ

Abstract

When solving many practical problems, such as the Earth and Space monitoring, medical diagnostics, navigation, robotics, etc., the challenges of image and other multidimensional data processing arise. To solve these problems successfully, their mathematical formulation is required, including a mathematical description that is an image model. Most studies in image processing methods, consider the images as a system of random variables specified on a rectangular grid with dimensions of two and higher. There are much less studies in images defined on curved surfaces. However, many real images are given on cylindrical surfaces, for example, the surface of a pipeline, a tank, a rotation shaft, and etc. Therefore, for a formal description of such images, their corresponding models are required. The 2D models are unsuitable for that it is not possible to represent the correlation properties of a cylindrical image with a rectangular image. The article describes the autoregressive models defined on a spiral-shaped cylindrical grid, that is on a helical line. This model can also be used to represent quasiperiodic stochastic processes. One of the main tasks of image processing is the problem of filtering them against the background of noise considered in this article. In this case the parameters of real images are usually unknown a priori. In addition the images often have significant and random heterogeneity. In this paper the authors use the adaptive pseudogradient algorithms based on cylindrical models to filter homogeneous and inhomogeneous images. These algorithms do not require setting the values of image parameters. The values of the root-mean-square filtering error are obtained based on the parameters of images and noise.