Tensor Approximation With Low-Rank Representation and Kurtosis Correlation Constraint for Hyperspectral Anomaly Detection

Anomaly detection is an active topic in hyperspectral image processing. Recently, low-rank representation (LRR)-based approaches have shown satisfactory results in wide anomaly detection applications. However, the existing LRR methods still have the following two problems: 1) setting a fixed value as a termination condition of the iterative constraint often results in the loss of target information, leading to a low detection rate with some missing targets, and 2) noise after LRR still remains in the sparse part, which increases false alarms. This article proposes the tensor approximation with LRR and the kurtosis correlation constraint (TAKCC) method for anomaly detection. The hyperspectral image is regarded as a third-order tensor for the LRR process. In the optimization process, the background suppression degree is obtained through the background dictionary to determine the iteration termination condition. After the iterative optimization is completed, the low-rank tensor that can fully represent the background is obtained. Also, the difference between the original hyperspectral image tensor and the low-rank tensor is used as the input of the kurtosis correlation constraint. The kurtosis correlation constraint compares the similarity between the current pixel and its surrounding pixels to detect the anomaly, where the kurtosis in the high-order statistical feature is introduced to avoid the interference of noise. The experimental results illustrate that the proposed method can retain the complete target information to highlight targets while suppressing background.