Two-stage causal unifrom image filtration with presence of correlated noise

Abstract

Introduction. Quality of raw single SAR images is low due to the presence of a specific type of noise in the form of speckle noise. Therefore it is necessary to use filtering for SAR images preprocessing. However, the developed filters often ignore spatial correlation of speckle which occurs in practice. This reduces the efficiency of noise suppression. Optimal two-dimensional noise filtering algorithms require large computational costs. In this paper we propose a two-step algorithm for filtering the correlated noise which can significantly reduce the computational costs compared to the two-dimensional filtering algorithms. Proposed algorithm also have computational efficiency of one-dimensional recurrence algorithms.

Theoretical results. For the description of an image and the correlated noise (CN) by rows and columns Gaussian Markov models in the form of discrete dynamical systems are used. The joint one-dimensional algorithm for image and noise filtration by rows and columns is used in the first step. It was created on the basis of Kalman filtering apparatus by combining models’ state vectors of the images and CN. Prediction and filtering errors in image and CN are correlated at each point. The algorithm obtained with the use of conditional independence of properties for images and CN pixels by row and column is executed in the second phase. An expression for the a posteriori probability density of the image and CN samples, as well as an algorithm for computing its expectation and the correlation matrix are given. The two-stage filtering algorithm belongs to a class of causal because the second stage of the filtration uses results from first stage for combining. First stage is executed by the rows and columns on the received observations up to current sample with inclusion.

Experimental results. In the example image and CN have separable exponential and gaussian correlation functions respectively. The application of the developed algorithm has allowed to increase the SNR by 4.7 dB. The data fusion algorithm in the second stage provides a gain of 1 dB in addition to the gain obtained in the first stage by filtering only by rows. The developed algorithm provided gain of 1.6 dB SNR compared to the two-step filtering algorithm for discrete white noise with the same noise variance.

Conclusions.The two-step algorithm for filtering CN on the uniform image was obtained. Developed algorithm has the first stage where joint one-dimensional filtering of the image and CN is performed by the rows and columns. The second stage is the union of the estimates derived from image and CP at each point. This algorithm significantly reduces computation cost compared to an optimal two-dimensional algorithm and thus ensure acceptable accuracy characteristics that are higher than that of one-dimensional filtering algorithms.