Analysis of Minute Features in Speckled Imagery with Maximum Likelihood Estimation

This paper deals with numerical problems arising when performing maximum likelihood parameter estimation in speckled imagery using small samples. The noise that appears in images obtained with coherent illumination, as is the case of sonar, laser, ultrasound-B and synthetic aperture radar, is called speckle, and it can neither be assumed Gaussian nor additive. The properties of speckle noise are well described by the Multiplicative Model, a statistical framework from which stem several important distributions. Amongst these distributions, one is regarded as the Universal Model for speckled data, namely the G0 law. This paper deals with amplitude data, so the G0 A distribution will be used. The literature reports that techniques for obtaining estimates (maximum likelihood, based on moments and on order statistics) of the parameters of the G0 A distribution require samples of hundreeds, even thousands, of observations in order to obtain sensible values. This is verified for maximum likelihood estimation, and a proposal based on alternated optimization is made to alleviate this situation. The proposal is assessed with real and simulated data. A Monte Carlo experiment is devised to estimate the quality of maximum likelihood estimators in small samples, and real data is succesfully analyzed with the proposed alternated procedure. Stylized empirical influence functions are computed and used to choose a maximum likelihood estimator that is resistant to outliers.