Enhanced Tensor Low-Rank Representation Learning for Hyperspectral Anomaly Detection

Dynamic magnetic resonance imaging (dMRI) strikes a balance between reconstruction speed and image accuracy in medical imaging field. In this paper, an improved robust tensor principal component analysis (RTPCA) method is proposed to reconstruct the dynamic magnetic resonance imaging (MRI) from highly under-sampled K-space data. The MR reconstruction problem is formulated as a high-order low-rank tenor plus sparse tensor recovery problem, which is solved by robust tensor principal component analysis (RTPCA) with a new tensor nuclear norm (TNN). To further exploit the low-rank structures in multi-way data, the core matrix nuclear norm, extracted from the diagonal elements of the core tensor under tensor singular value decomposition (t-SVD) framework, is also integrated into TNN for enforcing the low-rank structure in MRI datasets. The experimental results show that the proposed method outperforms state-of-the-art methods in terms of both MR image reconstruction accuracy and computational efficiency on 3D and 4D experiment datasets, especially for 4D MR image reconstruction. Graphical abstract The flowchart of the proposed method to reconstruct the dynamic magnetic resonance imaging (MRI) from highly under-sampled K-space data in the kth iteration. To further exploit the low-rank structures in multi-way data, the core matrix nuclear norm, extracted from the diagonal elements of the core tensor under tensor singular value decomposition (t-SVD) framework, is also integrated into tensor nuclear norm (TNN) for enforcing the low-rank structure in MRI datasets. In each iteration, the first step is to get low-rank tensor ℓk - 1 by using soft thresholding on the singular values of ℓk - 1 = χk - 1 - ξk - 1, and an improved tensor nuclear norm method is proposed to process the low-rank tensor ℓk - 1 firstly. Then, the shrinkage operator is applied to ξk - 1 = χk - 1 - ℓk - 1 for sparse part ξk - 1. The final reconstructed d-MRI χk is obtained by enforcing data consistency that the residual in K-space is subtracted by the sum of the reconstructed low-rank tensor and sparse tensor.

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.

Probability-weighted tensor robust PCA with CP decomposition for hyperspectral image restoration

The major challenges during the data acquisition process in an environmental wireless sensor network (EWSN) architecture are the presence of outliers and missing data. Outliers and missing data are ubiquitous in EWSN due to sensor failures, external noise, power dwindling, communication failures etc. Robust tensor principal component analysis (RTPCA) decomposes a noisy data tensor into a low-rank tensor and a sparse tensor, which can be exploited for the data recovery in EWSNs, where the low-rank component represents the intrinsic data tensor and the sparse component represents the gross outlier tensor. In this paper, a novel probabilistic outlier modelling scheme using multivariate Chebyshev's inequality hypothesis is proposed, which maps the sample population and the associated magnitudes of outliers with the spatio-temporal correlations in the acquired data. The inherent spatio-temporal and multi-attribute correlations in the EWSN data are established using singular value methods. A tensor nuclear norm (TNN) which extracts more temporal and multi-attribute correlations in the sensory data through block circulant matricization is used as the minimization function in RTPCA. In the forest surveillance scenario, usage of RTPCA results in a reconstruction accuracy of approximately 90% for a dataset with a high missing ratio of 0.95 and the outliers having largest possible magnitudes considered. For oceanographic data, in which the variance is lower, the simulations show similar performance for different outlier contaminations, although RPTCA performs better than other matrix and tensor data completion methods in terms of reconstruction accuracy.

Hyperspectral anomaly detection (HAD) aims to separate subtle anomalies of a given hyperspectral image (HSI) from its background, which is a hot topic as well as a challenging inverse problem. Despite the significant success of the deep learning-based HAD methods, they are hard to interpret due to their black-box nature. Meanwhile, deep learning methods suffer from the identity mapping (IM) problem, referring to the network excessively focusing on the precise reconstruction of the background while neglecting the appropriate representation of anomalies. To this end, this paper proposes a self-attention-aided deep unfolding tensor representation network (SATRNet) for interpretable HAD by solving the tensor representation (TR)-based optimization model within the framework of deep networks. In particular, a Self-Attention Learning Module (SALM) was first designed to extract discriminative features of the input HSI. The HAD problem was then formulated as a tensor representation problem by exploring both the low-rankness of the background and the sparsity of the anomaly. A Weight Learning Module (WLM) exploring local details was also generated for precise background reconstruction. Finally, a deep network was built to solve the TR-based problem through unfolding and parameterizing the iterative optimization algorithm. The proposed SATRNet prevents the network from learning meaningless mappings, making the network interpretable to some extent while essentially solving the IM problem. The effectiveness of the proposed SATRNet is validated on 11 benchmark HSI datasets. Notably, the performance of SATRNet against adversarial attacks is also investigated in the experimentation, which is the first work exploring adversarial robustness in HAD to the best of our knowledge.

Hyperspectral anomaly detection (HAD) is a challenging task since it identifies the anomaly targets without prior knowledge. In recent years, deep learning methods have emerged as one of the most popular algorithms in the HAD. These methods operate on the assumption that the background is well reconstructed while anomalies cannot, and the degree of anomaly for each pixel is represented by reconstruction errors. However, most approaches treat all background pixels of a hyperspectral image (HSI) as one type of ground object. This assumption does not always hold in practical scenes, making it difficult to distinguish between backgrounds and anomalies effectively. To address this issue, a novel deep feature aggregation network (DFAN) is proposed in this paper, and it develops a new paradigm for HAD to represent multiple patterns of backgrounds. The DFAN adopts an adaptive aggregation model, which combines the orthogonal spectral attention module with the background-anomaly category statistics module. This allows effective utilization of spectral and spatial information to capture the distribution of the background and anomaly. To optimize the proposed DFAN better, a novel multiple aggregation separation loss is designed, and it is based on the intra-similarity and inter-difference from the background and anomaly. The constraint function reduces the potential anomaly representation and strengthens the potential background representation. Additionally, the extensive experiments on the six real hyperspectral datasets demonstrate that the proposed DFAN achieves superior performance for HAD. The code is available at https://github.com/ChengXi-1217/DFAN-HAD.

In this study, a hyperspectral anomaly detection method based on Laplacian matrix (HADLAP) is proposed. This paper addresses the problem of determining covariance matrix inversion in high-dimensional data and proposes a new approach for identifying anomalies in hyperspectral images (HSIs). The study’s goals are to find anomalous locations in HSIs and to deal with the problem of calculating the inversion of the covariance matrix of high dimensional data. The method is centered on two main concepts. One of them is decomposition process. The other one is detection process. First, HSI data is decomposed as a low rank and sparse matrices. Second, the sparse component of the data is used to build Mahalanobis Distance (MD). In this study, go decomposition (GoDec) algorithm is employed to decompose the data. Then, the distance is calculated by obtained matrix with aim of detection of anomalous pixels in the HSIs. The method differs from previous studies that covariance matrix in the distance is computed with Laplacian matrix and MD. Experiments conducted on three hyperspectral datasets present the superiority and effectiveness of the proposed framework in terms of detection performance with respect to state-of-the-art methods.

Lately, generative adversarial networks (GAN)-based methods have drawn extensive attention and achieved a promising performance in the field of hyperspectral anomaly detection (HAD) owing to GAN’s powerful data generation capability. However, without considering the background spatial features, most of these methods can not obtain a GAN with a strong background generation ability. Besides, they fail to address the hyperspectral image (HSI) redundant information disturbance problem in the anomaly detection part. To solve these issues, the unsupervised generative adversarial network with background spatial feature enhancement and irredundant pooling (BEGAIP) is proposed for HAD. To make better use of features, spatial and spectral features union extraction idea is also applied to the proposed model. To be specific, in spatial branch, a new background spatial feature enhancement way is proposed to get a data set containing relatively pure background information to train GAN and reconstruct a more vivid background image. In a spectral branch, irredundant pooling (IP) is invented to remove redundant information, which can also enhance the background spectral feature. Finally, the features obtained from the spectral and spatial branch are combined for HAD. The experimental results conducted on several HSI data sets display that the model proposed acquire a better performance than other relevant algorithms.

In this paper we propose novel methods for completion (from limited samples) and de-noising of multilinear (tensor) data and as an application consider 3-D and 4- D (color) video data completion and de-noising. We exploit the recently proposed tensor-Singular Value Decomposition (t-SVD)[11]. Based on t-SVD, the notion of multilinear rank and a related tensor nuclear norm was proposed in [11] to characterize informational and structural complexity of multilinear data. We first show that videos with linear camera motion can be represented more efficiently using t-SVD compared to the approaches based on vectorizing or flattening of the tensors. Since efficiency in representation implies efficiency in recovery, we outline a tensor nuclear norm penalized algorithm for video completion from missing entries. Application of the proposed algorithm for video recovery from missing entries is shown to yield a superior performance over existing methods. We also consider the problem of tensor robust Principal Component Analysis (PCA) for de-noising 3-D video data from sparse random corruptions. We show superior performance of our method compared to the matrix robust PCA adapted to this setting as proposed in [4].

Robust implementation of foreground extraction and vessel segmentation for X-ray coronary angiography image sequence

Anomaly detection in hyperspectral imaging is crucial for remote sensing, driving the development of numerous algorithms. However, systematic studies reveal a dichotomy where algorithms generally excel at either detecting anomalies in specific datasets or generalizing across heterogeneous datasets (i.e., lack adaptability). A key source of this dichotomy may center on the singular and like biases frequently employed by existing algorithms. Current research lacks experimentation into how integrating insights from diverse biases might counteract problems in singularly biased approaches. Addressing this gap, we propose stacking-based ensemble learning for hyperspectral anomaly detection (SELHAD). SELHAD introduces the integration of hyperspectral anomaly detection algorithms with diverse biases (e.g., Gaussian, density, partition) into a singular ensemble learning model and learns the factor to which each bias should contribute so anomaly detection performance is optimized. Additionally, it introduces bootstrapping strategies into hyperspectral anomaly detection algorithms to further increase robustness. We focused on five representative algorithms embodying common biases in hyperspectral anomaly detection and demonstrated how they result in the previously highlighted dichotomy. Subsequently, we demonstrated how SELHAD learns the interplay between these biases, enabling their collaborative utilization. In doing so, SELHAD transcends the limitations inherent in individual biases, thereby alleviating the dichotomy and advancing toward more adaptable solutions.

Deep learning has achieved excellent performance in the field of computer vision and gained attention in the field of hyperspectral anomaly detection (HAD). Convolutional neural networks (CNN) based on pixel pairing features have achieved a certain detection effect, which is limited by background complexity in practical applications. This study proposes an adaptive weighted HAD algorithm that combines an autoencoder (AE) and CNN. Labelled hyperspectral images (HSIs) are used to train a CNN as a binary classifier for similarity discrimination in the data preparation stage, where morphological attribute filtering (MAF) is performed on images in the spatial dimension of the HSIs to highlight anomaly. The spectral angle is used as a measure of reconstruction error to train the AE, and the reconstruction error obtained using the AE is used as an adaptive weight to calculate the anomaly score, which considerably eliminates the blurring of the boundary between the background and anomalies. Through comparisons with some state-of-the-art methods, the effectiveness of the proposed method in improving detection accuracy and increasing background and anomaly discrimination is verified on three real datasets.

Although hyperspectral anomaly detection is commonly conducted in the visible, near-infrared, and shortwave infrared spectral regions, there has been less research on hyperspectral anomaly detection in the longwave infrared (LWIR) hyperspectral region. The radiance of thermal infrared hyperspectral imagery is determined by the temperature and emissivity. To avoid the detection uncertainty caused by the single factor of temperature, emissivity can be introduced to detect anomalies. However, in the emissivity domain, the spectral contrast and signal-to-noise ratio (SNR) are low, which makes it difficult to separate the anomalies from the background. In this paper, an anomaly detection method combining emissivity and a segmented low-rank prior (EaSLRP) is proposed for use with thermal infrared hyperspectral imagery. The EaSLRP method is divided into three parts—1) temperature/emissivity retrieval, 2) extraction of the thermal infrared hyperspectral background information, and 3) Mahalanobis distance detection. A homogeneous region generation method is also proposed to solve the problem of the complex global background leading to inaccurate background estimation. The GoDec method is used for matrix decomposition and background information extraction and to remove some of the noise. The proposed Mahalanobis distance detector then uses the background component and original image for anomaly detection, while highlighting the spectral difference between the anomalies and background. This method can also suppress the influence of noise, to some extent. The experimental results obtained with airborne Fourier transform thermal infrared spectrometer hyperspectral images demonstrate that the EaSLRP method is effective when compared with the Reed–Xiaoli detector (RXD), the segmented RX detector (SegRX), the low-rank and sparse representation-based detector (LRASR), the low-rank and sparse matrix decomposition (LRaSMD)-based Mahalanobis distance method (LSMAD), and the locally enhanced low-rank prior method (LELRP-AD).

Recently, low-rank representation (LRR) methods have been widely applied for hyperspectral anomaly detection, due to their potentials in separating the backgrounds and anomalies. However, existing LRR models generally convert 3-D hyperspectral images (HSIs) into 2-D matrices, inevitably leading to the destruction of intrinsic 3-D structure properties in HSIs. To this end, we propose a novel tensor low-rank and sparse representation (TLRSR) method for hyperspectral anomaly detection. A 3-D TLR model is expanded to separate the LR background part represented by a tensorial background dictionary and corresponding coefficients. This representation characterizes the multiple subspace property of the complex LR background. Based on the weighted tensor nuclear norm and the LF,1 sparse norm, a dictionary is designed to make its atoms more relevant to the background. Moreover, a principal component analysis (PCA) method can be assigned as one preprocessing step to exact a subset of HSI bands, retaining enough the HSI object information and reducing computational time of the postprocessing tensorial operations. The proposed model is efficiently solved by the well-designed alternating direction method of multipliers (ADMMs). A comparison with the existing algorithms via experiments establishes the competitiveness of the proposed method with the state-of-the-art competitors in the hyperspectral anomaly detection task.

Accurately distinguishing between background and anomalous objects within hyperspectral images poses a significant challenge. The primary obstacle lies in the inadequate modeling of prior knowledge, leading to a performance bottleneck in hyperspectral anomaly detection (HAD). In response to this challenge, we put forth a groundbreaking coupling paradigm that combines model-driven low-rank representation (LRR) methods with data-driven deep learning techniques by learning disentangled priors (LDP). LDP seeks to capture complete priors for effectively modeling the background, thereby extracting anomalies from hyperspectral images more accurately. LDP follows a model-driven deep unfolding architecture, where the prior knowledge is separated into the explicit low-rank prior formulated by expert knowledge and implicit learnable priors by means of deep networks. The internal relationships between explicit and implicit priors within LDP are elegantly modeled through a skip residual connection. Furthermore, we provide a mathematical proof of the convergence of our proposed model. Our experiments, conducted on multiple widely recognized datasets, demonstrate that LDP surpasses most of the current advanced HAD techniques, exceling in both detection performance and generalization capability.