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.

中文翻译：

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存在异常值的 SAR 图像处理的鲁棒瑞利回归方法

合成孔径雷达 (SAR) 数据中存在异常值（异常值）以及统计图像模型中的错误指定可能会导致推断不准确。为了避免此类问题，提出了基于稳健估计过程的瑞利回归模型作为对此类数据进行建模的更现实的方法。本文旨在获得对异常值的存在具有鲁棒性的瑞利回归模型参数估计量。所提出的方法考虑了加权最大似然法，并使用模拟和测量的 SAR 图像进行了数值实验。蒙特卡罗模拟被用于数值评估所提出的有限信号长度的稳健估计器性能、它们对异常值的敏感性和故障点。例如，非稳健估计器显示的相对偏差值比稳健方法在损坏信号中提供的结果大 65 倍。在敏感性分析和分解点方面，稳健方案导致两种测量的平均绝对值分别减少了约 96 美元和 10 美元，以同情非稳健估计者。此外，使用两个 SAR 数据集将所提出的稳健方案的地面类型和异常检测结果与文献中的竞争方法进行比较。