A Novel Cluster Kernel RX Algorithm for Anomaly and Change Detection Using Hyperspectral Images

Abstract: Real-time anomaly detection has received wide attention in remote sensing image processing because many moving targets must be detected on a timely basis. A widely-used anomaly detection algorithm is the Reed-Xiaoli (RX) algorithm that was proposed by Reed and Yu. The kernel RX algorithm proposed by Kwon and Nasrabadi is a nonlinear version of the RX algorithm and outperforms the RX algorithm in terms of detection accuracy. However, the kernel RX algorithm is computationally more expensive. This paper presents a novel real-time anomaly detection framework based on the kernel RX algorithm. In the kernel RX detector, the inverse covariance matrix and the estimated mean of the background data in the kernel space are non-causal and computationally inefficient. In this work, a local causal sliding array window is used to ensure the causality of the detection system. Using the matrix inversion lemma and the Woodbury matrix identity, both the inverse covariance matrix and estimated mean can be recursively derived without extensive repetitive calculations, and, therefore, the real-time kernel RX detector can be implemented and processed pixel-by-pixel in real time. To substantiate its effectiveness and utility in real-time anomaly detection, real hyperspectral data sets are utilized for experiments.

Anomaly detection is useful for environmental surveillance, maritime observation, and various other remote sensing applications. Among various anomaly detectors, the Reed-Xiaoli (RX) detector is one of the most well-established, with global/local and linear/nonlinear variants. The Global RX detector struggles with complex backgrounds and small-scale anomalies due to its reliance on global statistical data, while Local RX is slow, noisy, and challenging to tune. We propose a tile-based RX detection method that maintains global context while effectively capturing localized patterns. To handle background complexity within each tile, we employ Randomized RX (RRX) as an efficient approximation of kernel RX (KRX). As validated by our experiments, our method achieves high accuracy with execution time comparable to Global RX by leveraging the strengths of global and local approaches through RRX.

Whether or not a hyperspectral anomaly detector is effective is determined by two crucial issues, anomaly detectability and background suppressibility (BS), both of which are very closely related to two factors, the datasets used for a selected hyperspectral anomaly detector and detection measures used for its performance evaluation. This paper explores how anomaly detectability and BS play key roles in hyperspectral anomaly detection (HAD). To address these two issues, we investigate three key elements attributed to HAD. One is a selected hyperspectral anomaly detector, and another is the datasets used for experiments. The third one is the detection measures used to evaluate the effectiveness of a hyperspectral anomaly detector. As for hyperspectral anomaly detectors, twelve commonly used anomaly detectors were evaluated and compared. To address the appropriate use of datasets for HAD, seven popular and widely used datasets were studied for HAD. As for the third issue, the traditional area under a receiver operating characteristic (ROC) curve of detection probability—PD versus false alarm probability, PF, (AUC(D,F))—was extended to 3D ROC analysis where a 3D ROC curve was developed to generate three 2D ROC curves from which eight detection measures could be derived to evaluate HAD in all round aspects, including anomaly detectability, BS and joint anomaly detectability and BS. Qualitative analysis showed that many works reported in the literature which claimed that their developed hyperspectral anomaly detectors performed better than other anomaly detectors are actually not true because they overlooked these two issues. Specifically, a comprehensive study via extensive experiments demonstrated that these 3D ROC curve-derived detection measures can be further used to address the various characterizations of different data scenes and also to provide explanations as to why certain data scenes are not suitable for HAD.

Hyperspectral imaging is endowed with outstanding discriminability between different land types by its comprehensive sensing of the spectrum, thus favored applying to anomaly detection. However, blurring effect, as a critical cause for quality deterioration of hyperspectral imaging, has been omitted by previous hyperspectral anomaly detection models. On one hand, given that anomalies are sparsely distributed in nature, such blurring effect entangling neighboring pixels severely weighs those detection models down. On the other hand, abnormal objects jeopardize the low-dimensional structure of the image, thus deblurring those images with anomalies is more challenging than normal ones. Hence, it is of much significance to investigate anomaly detection using blurred hyperspectral images. To this end, this paper proposes a generalized non-convex surrogated tensor framework that is able to perform anomaly detection robustly to blurring effects on hyperspectral images. The proposed framework is featured to be a unified paradigm which guarantees convergence for a broad class of non-convex surrogates. Through treating the spatial and spectral low-rankness adaptively via Block Term Decomposition, the unevenness in the multi-linear low-rankness of hyperspectral image is comprehensively considered, which together with the non-convex surrogates results in a tighter modeling of the low-dimensional prior of hyperspectral images. Extensive experiments demonstrate the superiority of the proposed method compared with the state-of-the-art methods on both hyperspectral image deblurring and anomaly detection.

Anomaly detection is one of the most important applications of hyperspectral imaging technology. It is a challenging task due to the high dimensionality of hyperspectral images (HSIs), redundant information, noisy bands, and the limited capability of utilizing spatial information. In this paper, we address these problems and propose a novel anomaly detection method in HSIs. Our approach, called structure tensor and guided filter (STGF)-based strategy for anomaly detection, is based on the characteristics of HSIs. First, a novel band selection algorithm is proposed to reduce dimension, remove noisy bands, and select bands with effective information. Second, the selected bands are decomposed into two parts according to the characteristics of anomalies that are usually in a small area. Followed by this step, the backgrounds are removed through a simple differential operation for each selected band. Considering that not all of the bands provide the same contributions to anomaly detection, we then fuse the differential maps by a novel adaptive weighting method to obtain an initial detection map. Finally, GF is conducted to rectify the previous map under the condition that the neighboring pixels usually have quite strong correlations with each other. Experiments have been conducted on real-scene remote sensing HSI. Comparative analyses validate that the proposed STGF method presents superior performance in terms of detection accuracy and computational time.

Anomaly detection is one of the most important applications of hyperspectral imagery. In this paper, we propose a hyperspectral image anomaly detection method using collaborative representation detector with PCA remove outlier (PCAroCRD). The algorithm has two versions: global and local. In the collaborative representation detection (CRD) algorithm, if the test pixel is an anomalous pixel and several samples from background are also anomalous and similar to test pixel, then the judge error is likely to happen. In the proposed algorithm, PCA is adopted to extract main pixels information and remove abnormal pixels from background so as to obtain higher detection accuracy before estimating the samples. Experimental results indicate that the proposed algorithm outperforms the original collaborative representation detector (CRD), kernel version of CRD (KCRD), advanced CRD (CRDBORAD), and the traditional detection methods such as Global Reed-Xiaoli (RX) algorithm and the Local RX.

The compressed sensing (CS) theorem is a novel sampling approach that breaks through the conventional Nyquist sampling limit and brings a revolution in the field of signal processing. This article investigates the compression technique for CS hyperspectral images so as to illustrate the superiority provided by this new theorem. First, several comparative experiments are used to reveal that the drawback of prior compression techniques, designed for the data acquired by the conventional hyperspectral imaging system, is either low compression ratio or a waste of sampling resource. After a condensed analysis, we state that the CS theorem provides the probability of avoiding such defects. Then a straightforward scheme, which takes advantage of spectral correlation, is proposed to compress the CS hyperspectral images to reduce the data size further. Moreover, a flexible recovery strategy is designed to speed up the reconstruction of original bands from the corresponding CS images. The experimental results based on the actual hyperspectral images have demonstrated the efficiency of this proposed technique.

The general objective of anomaly detection (AD) in hyperspectral imagery is to detect full-pixel targets. To meet this purpose, the global AD methods can achieve more reliable results than the local methods in terms of time and accuracy. The kernel-based Support Vector Data Description (SVDD) has recently received great attention in the hyperspectral AD applications. This paper presents a global SVDD-based method for autonomous full-pixel AD. The method consists of three steps: clustering, background modeling, and autonomous AD. Experimental results on a hyperspectral dataset show the superiority of the proposed method comparing to the global-based SVDD method.

In Chap. 5, a particular subtarget detection technique in active hyperspectral target detection, called constrained energy minimization (CEM), was developed for its real-time and causal implementation. Rather than CEM, this chapter focuses on passive hyperspectral target detection and investigates a commonly used passive target detection technique, anomaly detection (AD), especially for real-time and causal processing capabilities that are developed for CEM in Chap. 5 and will also be derived in a similar manner for AD. To this end, this chapter can be considered a companion chapter of Chap. 5. Technically speaking, passive target detection must be carried out without any prior knowledge, specifically, a complete lack of availability of target knowledge. Owing to the nature of hyperspectral imaging sensors, which can uncover many unknown material substances, passive hyperspectral target detection is a major task in hyperspectral image analysis and has been studied extensively in the literature. Applications of passive target detection include surveillance and monitoring, where no knowledge is required a priori. Of particular interest in passive target detection is AD, which is generally performed in a completely blind environment. To suppress unknown backgrounds, AD makes use of the global sample correlation/covariance matrix R/K, referred to as R/K-AD, so as to enhance its detectability. In general, anomalies appear unexpectedly and cannot be detected by visual inspection. Most importantly, they vary with time and data sample vectors. Accordingly, developing real-time processing for R/K-AD on a timely basis sample by sample is crucial and critical in many real-world applications, for example, abnormalities in agriculture and forestry, environmental monitoring, combat vehicles on a battlefield, drug trafficking in law enforcement, and food inspection. As noted in Chap. 5, this real-time process requires that causality be included in an algorithm’s design. In analogy with real-time CEM, the concept of a causal sample correlation matrix (CSCRM), introduced in Chap. 5, is also applicable to AD for this purpose. However, in a broader sense, CSCRM is expanded into a causal sample correlation/covariance matrix (CSCRM/CSCVM) to replace R/K with CSCRM/CSCVM specified by R(r n )/K(r n ), respectively, where r n is the current data sample vector being processed. The capability for real-time processing is then derived from such a CSCRM/CSCVM because CSCRM/CSCVM varies with data sample vectors. Thus, a causal processing of K-AD/R-AD requires repeatedly calculating inverses of such sample-varying CSCRM/CSCVM and must be processed in a causal manner sample by sample, referred to as causal K-AD/R-AD (CR-K-AD/CR-AD). To further reduce computational complexity and computer processing time for CK-AD/CR-AD, the notion of innovation in a Kalman filter developed in Chap. 3 is once again used to derive recursive causal update equations to calculate CSCRM/CSCVM, which leads to recursive versions of K-AD/R-AD, to be called recursive CK-AD/CR-AD (R-CK-AD/R-CR-AD). In particular, when R-CK-AD/R-CR-AD is realized by real-time processing, it is referred to as RT CK-AD/RT-CR-AD in this chapter.

Collaborative representation-based detector (CRD), as the most representative anomaly detection method, has been widely applied in the field of hyperspectral anomaly detection (HAD). However, the sliding dual window of the original CRD introduces high computational complexity. Moreover, most HAD models only consider a single spectral or spatial feature of the hyperspectral image (HSI), which is unhelpful for improving detection accuracy. To solve these problems, in terms of speed and accuracy, we propose a novel anomaly detection approach, named Random Collective Representation-based Detector with Multiple Feature (RCRDMF). This method includes the following steps. This method first extract the different features include spectral feature, Gabor feature, extended multiattribute profile (EMAP) feature, and extended morphological profile (EMP) feature matrix from the HSI image, which enables us to improve the accuracy of HAD by combining the multiple spectral and spatial features. The ensemble and random collaborative representation detector (ERCRD) method is then applied, which can improve the anomaly detection speed. Finally, an adaptive weight approach is proposed to calculate the weight for each feature. Experimental results on six hyperspectral datasets demonstrate that the proposed approach has the superiority over accuracy and speed.

Nowadays, due to the ability of extracting deep features, the deep learning-based anomaly detection (AD) methods for hyperspectral images (HSIs) have been widely studied. However, all these AD methods treat the tasks of feature extraction and AD separately. Besides, most of them also do not make use of abundant spatial information of HSIs. Thus, a spectral–spatial hyperspectral AD method via collaborative representation constraint stacked autoencoders (SSCRSAE) is proposed. First, the collaborative representation constraint is imposed on the stacked autoencoders to extract deep nonlinear features that are more suitable for the collaborative representation-based detector (CRD). Then, CRD is used to for obtaining the preliminary detection result, which is more convenient for real HSIs because of no need for assuming the distribution of the background. Finally, aiming at further improving the SSCRSAE detector's performance, a novel spectral–spatial AD procedure is designed for calculating the final detection result by considering the spatial information of an HSI. Experimental results express that the proposed SSCRSAE exceeds eight state-of-the-art anomaly detectors used for comparison.

Anomalies in data may be caused by errors in the data, but sometimes the appearance of anomalous data often also suggests the emergence of a new domain or a new underlying process. Anomaly detection has therefore been an active area of research for decades. This paper is based on what anomaly detection is, the main areas of application for anomaly detection, and the challenges of anomaly detection at this stage. Deep learning-based anomaly detection is proposed based on the unpredictability, diversity, and sparsity that exist in anomaly detection, and deep learning anomaly detection algorithms are classified into unsupervised deep anomaly detection algorithms and semi-supervised deep anomaly detection algorithms based on the use of anomaly labels. This paper reviews and analyses the research on these two algorithms, and elaborates on the advantages and disadvantages of each type of anomaly detection algorithm when applied. Deep anomaly detection is also applied to the anomaly detection of charging data and is classified according to the different types of charging data, into deep anomaly detection for electric vehicles, deep anomaly detection for charging stations, and deep anomaly detection for charging poles. Finally, we provide an outlook on various algorithms for anomaly detection and future applications of anomaly detection in charging data.

In this paper, collaborative representation is proposed for anomaly detection in hyperspectral imagery. The algorithm is directly based on the concept that each pixel in background can be approximately represented by its spatial neighborhoods, while anomalies cannot. The representation is assumed to be the linear combination of neighboring pixels, and the collaboration of representation is reinforced by l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm minimization of the representation weight vector. To adjust the contribution of each neighboring pixel, a distance-weighted regularization matrix is included in the optimization problem, which has a simple and closed-form solution. By imposing the sum-to-one constraint to the weight vector, the stability of the solution can be enhanced. The major advantage of the proposed algorithm is the capability of adaptively modeling the background even when anomalous pixels are involved. A kernel extension of the proposed approach is also studied. Experimental results indicate that our proposed detector may outperform the traditional detection methods such as the classic Reed-Xiaoli (RX) algorithm, the kernel RX algorithm, and the state-of-the-art robust principal component analysis based and sparse-representation-based anomaly detectors, with low computational cost.

Cluttered environments with partial object occlusions pose significant challenges to robot manipulation. In settings composed of one dominant object type and various undesirable contaminants, occlusions make it difficult to both recognize and isolate undesirable objects. Spatial features alone are not always sufficiently distinct to reliably identify anomalies under multiple layers of clutter, with only a fractional part of the object exposed. We create a multi-modal data representation of cluttered object scenes pairing depth data with a registered hyperspectral data cube. Hyperspectral imaging provides pixel-wise Visible Near-Infrared (VNIR) reflectance spectral curves which are invariant in similar material types. Spectral reflectance data is grounded in the chemical-physical properties of an object, making spectral curves an excellent modality to differentiate inter-class material types. Our approach proposes a new automated method to perform hyperspectral anomaly detection in cluttered workspaces with the goal of improving robot manipulation. We first assume the dominance of a single material class, and coarsely identify the dominant, non-anomalous class. Next these labels are used to train an unsupervised autoencoder to identify anomalous pixels through reconstruction error. To tie our anomaly detection to robot actions, we then apply a set of heuristically-evaluated motion primitives to perturb and further expose local areas containing anomalies. The utility of this approach is demonstrated in numerous cluttered environments including organic and inorganic materials. In each of our four constructed scenarios, our proposed anomaly detection method is able to consistently increase the exposed surface area of anomalies. Our work advances robot perception for cluttered environments by incorporating multi-modal anomaly detection aided by hyperspectral sensing into detecting fractional object presence without need for laboriously curated labels.

Anomaly detection is a fundamental task in hyperspectral image (HSI) processing. However, most existing methods rely on pixel feature vectors and overlook the relational structure information between pixels, limiting the detection performance. In this article, we propose a novel approach to hyperspectral anomaly detection that characterizes the HSI data using a vertex- and edge-weighted graph with the pixels as vertices. The constructed graph encodes rich structural information in an affinity matrix. A crucial innovation of our method is the ability to obtain internal relations between pixels at multiple topological scales by processing different powers of the affinity matrix. This power processing is viewed as a graph evolution, which enables anomaly detection using vertex extraction formulated as a quadratic programming problem on graphs of varying topological scales. We also design a hierarchical guided filtering architecture to fuse multiscale detection results derived from graph evolution, which significantly reduces the false alarm rate. Our approach effectively characterizes the topological properties of HSIs, leveraging the structural information between pixels to improve anomaly detection accuracy. Experimental results on four real HSIs demonstrate the superior detection performance of our proposed approach compared to some state-of-the-art hyperspectral anomaly detection methods.