Two-stage filtration algorithm with interframe non-causal processing for multichannel image with presence of uncorrelated noise

Abstract

In many modern information and technical systems multichannel images have several applications. The multichannel image can be presented as a set of images of an object of a research which are received in various areas of a frequency range. Such images can be exposed to the distorting influence of the noise. One of the most widespread types of the noise is the additive uncorrelated noise. Optimal filtration algorithms are characterized by huge computing complexity that often limits their practical realization. Therefore development of algorithms of a filtration of multichannel images which provide the acceptable precision characteristics at moderate computing expenses is an important task. With use of property of conditional independence an expression for calculation of a posteriori density of probability of pixels of the multichannel image at a two-stage filtration with non causal frame and causal interframe processing in the presence of an additive uncorrelated noise is created. Expressions for the image pixel estimate calculation and dispersion of estimate error at a two-stage noncausal frame and causal interframe filtration for a Gaussian images filtration are created. Developed algorithm allows to lower a mean square deviation of estimate error more than twice in comparison with an algorithm of interframe averaging for a model example when processing the sequence of the Gaussian images distorted by additive white Gaussian noise. One-dimensional processing along each of coordinates is carried out at the first stage of an algorithm, and at the second stage union of the obtained data is made. The created algorithm is concretized for a case of processing of the Gaussian images distorted by additive white Gaussian noise. The two-stage approach implemented in the synthesized algorithm allows to reduce significantly computing complexity in comparison with an optimal algorithm, providing at the same time the acceptable precision characteristics and considering dimension of the multichannel image.

Синтезирован двухэтапный алгоритм фильтрации многоканального изображения на фоне белого шума, в котором на первом этапе выполняется совместная одномерная фильтрация каждого изображения по строкам и столбцам, а на втором – объединение полученных оценок изображений в каждой точке. Этот алгоритм позволяет су- щественно увеличить точность фильтрации по сравнению с алгоритмом межкадрового усреднения и обеспечить при этом приемлемую вычислительную сложность по сравнению с оптимальным алгоритмом.