EURASIP Journal on Applied Signal Processing 
Volume 2004 (2004), Issue 16, Pages 2476-2491
doi:10.1155/S111086570440907X

Analysis of Minute Features in Speckled Imagery with Maximum Likelihood Estimation

Alejandro C. Frery,1 Francisco Cribari-Neto,2 and Marcelo O. de Souza2

 1Departamento de Tecnologia da Informação, Universidade Federal de Alagoas, Campus A. C. Simões, BR 104 Norte km 14, Bloco 12, Tabuleiro dos Martins, Maceió 57072-970, Brazil
2Departamento de Estatística, CCEN, Universidade Federal de Pernambuco, Cidade Universitária, Recife 50740-540, Brazil
Received 21 August 2003; Revised 18 June 2004

Abstract

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 𝒢A0 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 𝒢A0 distribution require samples of hundreds, even thousands, of observations in order to obtain sensible values. This is verified for maximum likelihood estimation, and a proposal based on alternate optimization is made to alleviate this situation. The proposal is assessed with real and simulated data, showing that the convergence problems are no longer present. A Monte Carlo experiment is devised to estimate the quality of maximum likelihood estimators in small samples, and real data is successfully analyzed with the proposed alternated procedure. Stylized empirical influence functions are computed and used to choose a strategy for computing maximum likelihood estimates that is resistant to outliers.