Homomorphic Two-Stage Image Sequence Filtering Algorithm in the Presence of Correlated Speckle Noise

Abstract

Introduction. An images received from synthetic-aperture radar and ultrasonic medical coherent systems are distorted by speckle noise which can be spatially correlated. Sequence frame processing is applied due to poor quality of source images. The large number of filters for processing the images distorted by a multiplicative speckle noise were developed at the present time. Most of existing filters don’t take into account spatial correlation in the speckle noise which leads to lower efficiency of noise suppression. Image sequence processing leads to processed data volume increase. Thus, a problem of computing complexity and practical implementability of the filtering algorithms used for speckle noise suppression is even more relevant. Theoretical results. The task of filtering the sequence of images in the presence of correlated speckle noise becomes the task of filtering a signal component in the presence of the additive correlated noise as a result of homomorphic transformation. An expression for posteriori probability density of signal component pixel and the correlated noise pixel in each point of the sequence of images was created using property of the conditional independence. It’s used for combining received posterior distributions at the first stage as a result of executing one-dimensional non-linear filtering. The algorithm of computation of mathematical expectation and correlation matrix of joint posteriori probability density of a signal and correlated noise pixels in each point for a case of gaussian posterior distributions for non-causal intraframe and causal interframe processing is synthesized. Experimental results. The developed algorithm allows to receive a gain in signal-to-noise ratio in 5.8-1 dB for a model example by processing from one to five frames compared to interframe averaging algorithm. The number of segmentation errors for the images filtered by Otsu algorithm using three frames is 2 % for the developed algorithm and 18 % for interframe averaging. Conclusion. The homomorphic two-stage filtering algorithm of the sequence of images in the presence of correlated speckle noise was developed. It uses two-stage joint filtering of a signal component and the additive correlated noise with intraframe not causal and interframe causal processing after homomorphic transformation.