Simultaneous Reconstruction and Anomaly Detection of Subsampled Hyperspectral Images Using $l_{({1}/{2})}$ Regularized Joint Sparse and Low-Rank Recovery

This paper focuses on an unsupervised anomaly detection approach from a subsampled hyperspectral image (HSI) data. Unlike the state-of-the-art methods, the proposed method does not require the construction of a large matrix by the vectorization of spectral bands or unfolding of entire HSI data into a huge matrix. Image reconstruction and anomaly detection are performed at the same time on the subsampled HSI data to reduce the storage/transmission requirements and processing time. In the proposed framework, the HSI data are decomposed into background and anomaly by l
_(1/2)
regularized joint sparse and low-rank decomposition. Since the spectral bands of HSI data are highly correlated, it can be effectively utilized for background modeling. Inspired by this fact, the low-dimensional structure of the background is characterized by modeling it as a combination of common low-rank and spectral-specific low-rank components. To further improve the separation between background and anomaly, the recently proposed l
_(1/2)
regularization for the sparse component is employed. The experimental results reveal that the proposed method outperforms the existing methods on both reconstruction quality and detection performance.