Anomaly detecting in hyperspectral imageries based on tensor decomposition with spectral and spatial partitioning

Due to the multidimensional nature of the hyperspectral image (HSI), multi-way arrays (called tensor) are one of the possible solutions for analyzing such data. In tensor algebra, CANDECOMP/PARAFAC decomposition (CPD) is a popular tool which has been successfully applied for the HSI data processing. However, on the one hand, CPD requires large memory for temporal variables. As a result, the memory usually overflows during the process for a real HSI whose size is large. On the other hand, so far no finite algorithm can well-determine the rank of the tensor to be decomposed. An inappropriate number of the rank may over-fit/under-fit the information provided by the tensor. To deal with these problems, this paper proposes an improved CPD with spectral and spatial partitioning for the HSI anomaly detection. First, the original HSI is divided into a set of smaller-sized sub-tensors. Second, CPD is applied onto each sub-tensor. Then, an anomaly detection algorithm is implemented and the detection results are fused along the spectral direction. Experiments with a real HSI data set reveals that the proposed method outperforms the CPD with no partition and the traditional RX anomaly detector with better detection performance.