M-Estimators of Roughness and Scale for -Modelled SAR Imagery
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-Estimators of Roughness and Scale for GA0 -Modelled SAR Imagery Oscar H. Bustos Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina Email: [email protected]
María Magdalena Lucini Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina Email: [email protected]
Alejandro C. Frery Centro de Informática, Universidade Federal de Pernambuco, CP 7851, 50732-970 Recife - PE, Brasil Email: [email protected] Received 31 July 2001 and in revised form 10 October 2001 The GA0 distribution is assumed as the universal model for multilook amplitude SAR imagery data under the multiplicative model. This distribution has two unknown parameters related to the roughness and the scale of the signal, that can be used in image analysis and processing. It can be seen that maximum likelihood and moment estimators for its parameters can be influenced by small percentages of “outliers”; hence, it is of outmost importance to find robust estimators for these parameters. One of the best-known classes of robust techniques is that of M-estimators, which are an extension of the maximum likelihood estimation method. In this work we derive the M-estimators for the parameters of the GA0 distribution, and compare them with maximum likelihood estimators with a Monte-Carlo experience. It is checked that this robust technique is superior to the classical approach under the presence of corner reflectors, a common source of contamination in SAR images. Numerical issues are addressed, and a practical example is provided. Keywords and phrases: inference, likelihood, M-estimators, Monte-Carlo method, multiplicative model, speckle, synthetic aperture radar, robustness.
1. INTRODUCTION The statistical modeling of synthetic aperture radar (SAR) imagery has provided some of the best tools for the processing and understanding of this kind of data. Among the statistical approaches the most successful is the multiplicative model. This model offers a set of distributions that, with a few parameters, are able to characterize most of SAR data. This model is presented, for instance, in [1], and extended in [2]. This extension is a general and tractable set of distributions within the multiplicative model, used to describe every kind of SAR return. It was then called a universal model, and its properties are studied in [3, 4, 5]. In this paper, the problem of estimating the parameters of this extension, namely of the GA0 distribution, is studied for the single look (the noisiest) situation. Two typical estimation situations arise in image processing and analysis, namely large and small samples, being the latter considered in this work. The small samples problem arises in, for instance, im-
age filtering where with a few observations within a window a new value is computed. Statistical inference with small samples is subjected to many problems, mainly bias, large variance, and sensitivity to deviations from the hypothesized mod
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