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This paper proposes a nonlinear version of an anomaly detector with a robust regression detection strategy for hyperspectral imagery. In the traditional Mahalanobis distance-based hyperspectral anomaly detectors, the background statistics are easily contaminated by anomaly targets, resulting in a poor detection performance. The traditional detectors also often fail to detect anomaly targets when the samples in the image do not conform to a Gaussian normal distribution. In order to solve these problems, this paper proposes a robust nonlinear anomaly detection (RNAD) method by utilizing robust regression analysis in the kernel feature space. Using the robust regression detection strategy, this method can suppress the contamination of the detection statistics by anomaly targets. Moreover, in this anomaly detection method, the input data are implicitly mapped into an appropriate high-dimensional kernel feature space by nonlinear mapping, which is associated with the selected kernel function. Experiments were conducted on synthetic data and an airborne AVIRIS hyperspectral image, and the experimental results indicate that the proposed hyperspectral anomaly detection approach in this paper outperforms three state-of-art commonly used anomaly detection algorithms.