  The presence of outliers (anomalous values) in synthetic aperture radar (SAR)
data and the misspecification in statistical image models may result in
inaccurate inferences. To avoid such issues, the Rayleigh regression model
based on a robust estimation process is proposed as a more realistic approach
to model this type of data. This paper aims at obtaining Rayleigh regression
model parameter estimators robust to the presence of outliers. The proposed
approach considered the weighted maximum likelihood method and was submitted to
numerical experiments using simulated and measured SAR images. Monte Carlo
simulations were employed for the numerical assessment of the proposed robust
estimator performance in finite signal lengths, their sensitivity to outliers,
and the breakdown point. For instance, the non-robust estimators show a
relative bias value $65$-fold larger than the results provided by the robust
approach in corrupted signals. In terms of sensitivity analysis and break down
point, the robust scheme resulted in a reduction of about $96\%$ and $10\%$,
respectively, in the mean absolute value of both measures, in compassion to the
non-robust estimators. Moreover, two SAR data sets were used to compare the
ground type and anomaly detection results of the proposed robust scheme with
competing methods in the literature.
