Kernel-Based Decomposition Model With Total Variation and Sparsity Regularizations via Union Dictionary for Nonlinear Hyperspectral Anomaly Detection

Abstract

Many linear approaches have been extensivelyproposed for the anomaly detection problem in hyperspectral images (HSIs), while nonlinear approaches have been rarely studied although most practical cases are nonlinear. Moreover, these existing nonlinear methods simply nonlinearly map each pixel into a high-dimensional space, which does not describe complex light scattering effects between endmembers. To address the above issues, this paper proposes an endmember-kernel-based decomposition model with total variation and sparsity regularizations via union dictionary for the nonlinear anomaly detection in HSIs. The proposed decomposition model utilizes endmember-kernel theory to handle nonlinear interactions between atoms in the dictionary, allowing for effective characterization of complex light scattering effects. By using this endmember-kernel-based decomposition model, a hyperspectral imagery can be decomposed into three components: anomaly, background, and noise. To separate these components effectively, the total variation (TV) and sparsity regularizations are incorporated into the decomposition model to characterize the spatial properties of the background and the anomaly, respectively. Besides, we present a novel construction framework of union dictionary that combines superpixel segmentation and clustering methods sequentially to achieve more accurate dictionary representation capabilities. Finally, the anomalous level of a tested pixel is calculated by the abundances associated with the anomaly dictionary. The experimental results on both synthetic and real hyperspectral data sets demonstrate that the proposed method outperforms several linear and nonlinear state-of-the-art anomaly detectors.

Spatial Validation of Spectral Unmixing Results: A Systematic Review

“…It is important to emphasize that 97% of these reference maps are available online together with hyperspectral images and/or reference spectral libraries (e.g., [532-535] Figure 8). Therefore, these images were well known: Cuprite (Nevada, USA, e.g., [70,458]), Indian Pines (Indiana, USA, e.g., [78,458]), Jasper Ridge (California, USA, e.g., [68,97]), Salinas Valley (California, USA, e.g., [75,78]) datasets that were acquired with AVIRIS sensors; Pavia (Italy, e.g., [81,85]) datasets that were acquired with the ROSIS sensor; Samson (Florida, USA, e.g., [59,89]) dataset that was acquired with the Samson sensor; University of Houston (Texas, USA, e.g., [59,78],) dataset that was acquired with the CASI-1500 sensor ; Urban (Texas, USA, e.g., [59,68]) and Washington DC Mall (Washington DC, USA, e.g., [81,90]) datasets that were acquired with the HYDICE sensor. As regards the papers that analyzed the multispectral data, most of the authors chose to create the reference maps from the other images, whereas most of the authors that analyzed the hyperspectral data chose to employ the previous reference maps.…”

Hyperspectral Anomaly Detection with Auto-Encoder and Independent Target

“…Chen et al [20] proposed a component decomposition analysis (CDA) to decompose the original data space into three separate spaces intricately by integrating the principal component analysis (PCA) and the independent component analysis (ICA). Some other LRaSR-based HAD algorithms have focused on the dictionary construction [21][22][23][24][25][26]. Huyan et al [21] proposed a BKG and potential anomaly dictionaries construction method, which attempts to guide the separation of BKG, noise, and anomaly, according to the BKG and the potential anomaly dictionary separately.…”

“…Cheng et al [23] designed a joint dictionary construction method based on density peak clustering and combined total variation (TV) and sparse regularization to propose an algorithm for HAD. Wu et al [24] combined superpixel segmentation and clustering methods to design a new joint dictionary construction method and devised an algorithm for nonlinear HAD. Lin et al [25] further developed a HAD algorithm based on robust dictionary construction and regularization of low-rank sparse representation with double collaborative constraints.…”