Union of one-dimensional filtering results f homogenous image and correlated noise using non-causal processing

Abstract

Introduction. The noise signals are spatially correlated in a number of image filtration tasks. Such noises occur in the case of analogue transmission of television signals using the PAL standard, in images demosaicing in digital cameras and in the images obtained using magnetic resonance imaging. The task of filtering speckle in coherent imaging systems such as synthetic aperture radar and an ultrasonic imaging system with certain limitations can be assigned to this class of noise.
The theoretical results. The expression for the joint posterior probability density of pixels at each point with non-causal processing was obtained using the properties of the Markov and conditional independence of image and correlated noise pixels on the row and column. It describes the union procedure of a posteriori distributions at processing pixel calculated at the first stage using an optimal algorithm for nonlinear recursive filtering of dimensional Markov sequences of the row and column from their beginning and end. Algorithm for expectation and the correlation matrix calculation of the joint posterior probability density of pixels is obtained in the case of Gaussian images and correlated noise. Non-causal processing which merges the estimates obtained in the first step of filtering in rows and columns is made for each pixel. Algorithms combined results of one-dimensional image and correleated noise filtering with half-causal and causal processing are the part of the resulting non-causal algorithm.
Experimental results. For the above example the use of developed two-stage non-causal algorithm allows to increase the SNR by 6.1 dB. The information union for the second stage provides a 2.5 dB gain in addition to the gain obtained in the first step in filtration only by rows. Compared to the two-phase half-causal and causal algorithm the non-causal filtering algorithm provided a gain in SNR of 0.59 dB and 1.49 dB, respectively.
Conclusions.The synthesized non-causal algorithm combined results of one-dimensional image and correlated noise filtering allows to take into account all the estimates in the row and column. Estimates intersect at processing point which improves the effectiveness of the processing compared with the algorithms of causal and half-causal two-stage filtration.