Property Analysis of Noise Suppressing L-Filters for Speckle Image Processing

The images formed by coherent imaging systems are characterized by presence of multiplicative noise with nonsymmetrical p.d.f.s. The examples are the Rayleigh and one-side (negative) exponential distributions. For these cases the optimal L-filters are derived for different coefficient censoring by minimizing MSE of residual fluctuations. Some suboptimal L-filters are considered as well. They are the Lpq-filters that use only two order statistics and the trimmed filters with symmetrical and nonsymmetrical coefficient censoring. Those filters are parametrically optimized according to the same criterion. The robust features of the considered filters are analyzed both theoretically using empirical influence functions and numerically with application of contamination noise model. As contaminating factor we exploited the saltand-pepper noise with different probabilities and amplitudes of positive and negative spikes. Output estimate bias and variance were calculated and examined. It is shown that the use of sub-optimal filters is well motivated from different points of view.