Open Access

Analysis of Minute Features in Speckled Imagery with Maximum Likelihood Estimation

  • Alejandro C. Frery1Email author,
  • Francisco Cribari-Neto2 and
  • Marcelo O. de Souza2
EURASIP Journal on Advances in Signal Processing20042004:375370

Received: 21 August 2003

Published: 2 December 2004


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 law. This paper deals with amplitude data, so the 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 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.

Keywords and phrases

image analysisinferencelikelihoodcomputationoptimization

Authors’ Affiliations

Departamento de Tecnologia da Informação, Universidade Federal de Alagoas
Departamento de Estatística, CCEN, Universidade Federal de Pernambuco, Cidade Universitária


© Frery et al. 2004