The key to hyperspectral anomaly detection is to effectively distinguish anomalies from the background, especially in the case that background is complex and anomalies are weak. Hyperspectral imagery (HSI) as an image-spectrum merging cube data can be intrinsically represented as a third-order tensor that integrates spectral information and spatial information. In this article, a prior-based tensor approximation (PTA) is proposed for hyperspectral anomaly detection, in which HSI is decomposed into a background tensor and an anomaly tensor. In the background tensor, a low-rank prior is incorporated into spectral dimension by truncated nuclear norm regularization, and a piecewise-smooth prior on spatial dimension can be embedded by a linear total variation-norm regularization. For anomaly tensor, it is unfolded along spectral dimension coupled with spatial group sparse prior that can be represented by the l2,1-norm regularization. In the designed method, all the priors are integrated into a unified convex framework, and the anomalies can be finally determined by the anomaly tensor. Experimental results validated on several real hyperspectral data sets demonstrate that the proposed algorithm outperforms some state-of-the-art anomaly detection methods.

Recently, the low-rank and sparse decomposition model (LSDM) has been used for anomaly detection in hyperspectral imagery. The traditional LSDM assumes that the sparse component where anomalies and noise reside can be modeled by a single distribution which often potentially confuses weak anomalies and noise. Actually, a single distribution cannot accurately describe different noise characteristics. In this article, a combination of a mixture noise model with low-rank background may more accurately characterize complex distribution. A modified LSDM, by modeling the sparse component as a mixture of Gaussian (MoG), is employed for hyperspectral anomaly detection. In the proposed framework, the variational Bayes (VB) algorithm is applied to infer a posterior MoG model. Once the noise model is determined, anomalies can be easily separated from the noise components. Furthermore, a simple but effective detector based on the Manhattan distance is incorporated for anomaly detection under complex distribution. The experimental results demonstrate that the proposed algorithm outperforms the classic Reed-Xiaoli (RX), and the state-of-the-art detectors, such as robust principal component analysis (RPCA) with RX.

With the increasing availability of multitemporal hyperspectral imagery, hyperspectral change detection under heterogeneous backgrounds is a challenging task. Due to the complexity of background features, traditional change detection algorithms in the spectral domain cannot effectively detect changed features. A novel method using multiple morphological profiles (MMPs) is proposed for hyperspectral change detection to make full use of spatial information. In the designed framework, first, the max-tree/min-tree strategy is applied to extract different attributes of multitemporal hyperspectral images (HSIs), i.e., area attribute and height attribute. Second, a spectral angle weighted-based local absolute distance (SALA) method is designed to reconstruct the discriminative spectral domain. Then, the absolute distance (AD) is adopted to extract changes in constructed feature domain. Finally, a change map is obtained by guided filtering. Experiments conducted on four real hyperspectral datasets demonstrate that the proposed detector achieves better detection performance.

Infrared small-target detection under heterogeneous background, as a challenging task, plays an important role in many applications. In practice, there are not only bright targets but also dim targets, e.g., rescue aircraft and vehicles in the forest fire scene. Considering that most existing infrared small-target detection methods are merely aimed at bright targets, a novel method using multiple morphological profiles (MMP) is proposed, which can detect various types of targets whose brightness varies greatly. In the designed morphological feature extraction, different attributes, i.e., area attribute and height attribute, are applied to extract spatial size and contrast information of small-target in the max-tree and min-tree, respectively. Furthermore, discontinuous pruning values are further utilized for different attributes, and a designed fusion strategy of different pruning values results in more robust detection performance. Experimental results validated on two synthetic data and six real data sets demonstrate that the proposed MMP can not only detect a variety of brightness of targets and different types of targets and kinds of spatial sizes of targets but also further improve the contrast between targets and background, and the background clutter is significantly suppressed.

Tensor-based fusion that couples the high spatial resolution of a multispectral image (MSI) to the high spectral resolution of a hyperspectral image (HSI) is considered. The fusion problem is first formulated mathematically as a convex optimization of a tensor trace norm imposing low-rank spatially as well as spectrally, with an alternating-directions optimization featuring linearization providing the solution. Although prior tensor-based fusion approaches typically resort to tensor decomposition, the proposed algorithm exploits ideas from the field of tensor completion to directly impose a low-rank property spatially and spectrally while avoiding the computationally complex patch clustering and dictionary learning common to competing fusion techniques. Additionally, small modifications to the basic optimization permit a fusion process robust to missing hyperspectral values such as those that can result from dead stripes in real hyperspectral sensors. The experimental evaluations on both synthetic imagery as well as real imagery demonstrate that the resulting low-rank tensor-approximation (LRTA) fusion algorithm preserves both spatial details and texture, yielding significantly improved image quality when compared to other state-of-the-art fusion methods as well as effective restoration under conditions of missing stripes within the HSI.