It has been demonstrated that nuclear-norm-based low-rank representation is capable of modeling cluttered backgrounds in hyperspectral images (HSIs) for robust anomaly detection. However, minimizing the nuclear norm regularizes each singular value equally during rank reduction, which restricts the capacity and flexibility of modeling the major structures of the background. To address this problem, we propose detection of anomaly pixels in HSIs using the weighted nuclear norm, which can preserve the major singular values during rank reduction. We present a down-up sampling scheme to remove plausible anomaly pixels from the image as much as possible and learn a robust principal component analysis (PCA) background dictionary. From a dictionary, we develop a weighted nuclear-norm minimization model to represent the background with a low-rank coefficients matrix that can be effectively optimized using the standard alternating direction method of multipliers (ADMM). Due to the flexible modeling capacity using the weighted nuclear norm, anomaly pixels can be distinguished from the background with the reconstruction error. The experimental results on two real HSIs datasets demonstrate the effectiveness of the proposed method for anomaly detection.

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