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Multiband synthetic aperture radar (SAR) image fusion combines the scattering characteristics of targets from different bands to provide a comprehensive and informative output. However, the conventional SAR denoise and fusion separation framework often encounters the loss of fine details. This problem arises due to the inherent conflict between noise filtering and edge preservation. To address this issue, this article proposes the joint tensor-based low-rank total variation (TLRTV) dual-band SAR image denoise–fusion strategy. The proposed strategy formulates the denoise–fusion problem by integrating the LR and TV models. Furthermore, this problem is extended to a high-dimensional form using tensor representation. To effectively solve the TLRTV problem, an optimization method is developed based on the alternating direction method of multipliers. This method decomposes the TLRTV problem into a series of subproblems, allowing for an efficient and accurate solution. To evaluate the performance of the proposed TLRTV method, the real measurement dual-band SAR images obtained from our developed airborne multiband SAR system are utilized to compare with other existing denoise and fusion separation methods. The extensive experimental results demonstrate the superiority of the TLRTV approach achieving better fusion results, particularly in the presence of noise interference.

With the evolution of the sixth generation (6G) mobile communication technology, the terahertz (THz) spectrum has attracted much attention in wireless communication applications due to its high bandwidth and low signal transmission delay. However, the introduction of the THz spectrum leads to higher path transmission losses and complex signal attenuation. This makes user sensing and localization in THz massive multiple-input multiple-output (MIMO) systems more challenging. In this paper, we investigate the user sensing and localization problem in THz massive MIMO systems with the assistance of reconfigurable intelligent surfaces (RIS). Firstly, the received signal is modeled as a tensor, and a parallel factor (PARAFAC) method is proposed. The minimum description length (MDL) is then utilized to detect the number of scattering paths in the channel. On this basis, the alternating least squares (ALS) algorithm is employed to estimate the factor matrices, followed by the utilization of a straightforward correlation-based approach to obtain channel parameter information. Finally, the positions of users and scattering points are estimated based on the geometric relationship between channel parameters and location coordinates. The simulation results have verified the effectiveness of the proposed scheme compared to the existing competitive algorithms, and indicate that the proposed scheme exhibits superior parameter estimation performance and can achieve localization accuracy at the decimeter level.

Utilizing unmanned aerial vehicle (UAV) technology in communication holds promise for meeting the increasing data rate demands in future wireless systems due to its flexibility. Meanwhile, reconfigurable intelligent surface (RIS) has garnered increased attention for their potential to enhance wireless communication performance through intelligent control of the transmission environment. In this paper, we first combine the UAV and the RISs to construct an Internet of Things (IoT) uplink transmission system, where the UAV serves as an aerial relay to collect data from IoT terminal (IT) and forward it to base stations (BS), while RISs assist communication to reduce congestion. Then, a parallel factor (PARAFAC) tensor model is formulated at the BS. At last, the iterative alternating least squares (ALS) algorithm and the closed-form singular value decomposition (SVD) algorithm are derived to fit the constructed tensor model for joint channel estimation and symbol detection. Compared with the competitive algorithms, the two proposed algorithms offer lower computational complexity and superior channel estimation performance. Furthermore, the proposed algorithms exhibit good symbol detection capabilities even at higher transmission rates. The numerical results demonstrate the effectiveness of the proposed algorithms.

In real life, only partial information of samples is available everywhere, this makes Incomplete multi-view clustering (IMVC) becomes a significant research topic to handle data loss situations. Recently, several methods leverage the anchor strategy by selecting fixed anchors to handle the challenging large-scale IMVC. However, all of them ignore the guidance of prior information hidden in the bipartite graph. Therefore, we propose a novel Anchor Pseudo-supervise Large-scale Incomplete Multi-view Clustering (AP-LIMC) method by introducing a prior indicator matrix as a pseudo-supervise anchor learning paradigm. Specifically, the prior indicator matrix is first introduced to control the distribution of anchors in each cluster. Then, an anchor pseudo-supervise learning framework is designed to generate high-quality anchors and a unified bipartite graph with prior indicator supervision. In addition, we design an optimized process with linear computational and extensive experiments on multiple public datasets with recent advances to validate the effectiveness, superiority, and efficiency. For example, on the Stl10 dataset, the performance of the proposed AP-LIMC improved by 23.95%,15.71%,27.39%, and 18.24% in terms of four evaluation metrics, respectively.

Millimeter Wave (mmWave) massive multiple-input multiple-output (MIMO) systems with hybrid analog-digital architectures can greatly increase system capacity and communicate with multiple users at the same time. Accurate channel estimation is crucial for multi-user communications, but its accuracy is limited as the number of antennas and users increases. In the matrix high-dimensional operation for multi-user channel estimation, not only is it computationally intensive, but also the estimation accuracy is low. It makes our work turn to channel estimation of the user group within a certain region to improve the accuracy of estimation. In this paper, we propose a tensor dictionary manifold learning method for channel estimation and interference elimination of the multi-user mmWave massive MIMO system. A multi-user digital-analog mixed received signal model is presented. The tensor dictionary manifold learning scheme is proposed to model the received signal as a third-order low-rank tensor to handle the high-dimensional user, antenna, and channel. After segmentation, clustering and manifold learning, multiple tensor dictionary manifold models containing a group of user signals are fitted. Tensor dictionary manifold learning can take advantage of the inherent multi-domain properties of signals in the frequency, time, code and spatial domains to maintain inter-user correlation within a user group while reducing the high-dimensional channels of the user group. Using the convex relaxation property of the tensor alternating direction method, we propose a strategy to eliminate interference from other groups. And with the help of the multi-signal classification method, the channel parameters of user groups are obtained to improve the accuracy of multi-user channel estimation. This method can perform channel estimation for multiple users with only a few pilots, and improve the performance of the system. Numerical results confirm the good performance of this method.

In recent years, numerous studies have adopted rs-fMRI to construct dynamic functional connectivity networks (DFCNs) and applied them to the diagnosis of brain diseases, such as epilepsy and schizophrenia. Compared with the static brain networks, the DFCNs have a natural advantage in reflecting the process of brain activity due to the time information contained in it. However, most of the current methods for constructing DFCNs fail to aggregate the brain topology structure and temporal variation of the functional architecture associated with brain regions, and often ignore the inherent multi-dimensional feature representation of DFCNs for classification. In order to address these issues, we propose a novel DFCNs construction and representation method and apply it to brain disease diagnosis. Specifically, we fuse the blood oxygen level dependent (BOLD) signal and interactions between brain regions to distinguish the brain topology within each time domain and across different time domains, by embedding block structure in the adjacency matrix. After that, a sparse tensor decomposition method with sparse local structure preserving regularization is developed to extract DFCNs features from a multi-dimensional perspective. Finally, the kernel discriminant analysis is employed to provide the decision result. We validate the proposed method on epilepsy and schizophrenia identification tasks, respectively. The experimental results show that the proposed method outperforms several state-of-the-art methods in the diagnosis of brain diseases. [ABSTRACT FROM AUTHOR]

Channel estimation is a challenging issue for millimeter wave (mmWave) and massive multiple-input multiple-output (MIMO) in the future sixth generation (6G) wireless systems, where the conventional estimation schemes may fail to track the fast varying channels, especially in high-speed mobile scenarios. In this paper, a novel tensor-based uplink channel estimation scheme is proposed for multi-user MIMO (MU-MIMO) systems over time-varying channels. In the proposed scheme, a low-overhead pilot transmission scheme is designed to track the varying channel. The received uplink signal at the base station (BS) is formulated as a third-order tensor which admits a CANDECOMP/PARAFAC (CP) model. The CP decomposition issue is then solved using blind matrix decomposition, in which the special structures of signals in the time dimension and the matrix subspace are utilized. By exploiting low-rank structure of the signal tensor, the channel parameters (angles of arrival/departure, path gains, and Doppler shifts) are estimated from the factor matrices. Moreover, the proposed scheme is theoretically analyzed and it is guaranteed with low pilot overhead. Simulation results verify that the proposed scheme can outperform the compressed sensing (CS) based scheme and the iteration-based scheme in terms of accuracy and stability. The uniqueness of the proposed scheme is also verified in our simulation. [ABSTRACT FROM AUTHOR]

Heterogeneous Information Network (HIN) collecitve classification studies the problem of predicting labels for one type of nodes in a HIN which contains multiple types of nodes multiple types of links among them. Previous studies have revealed that exploiting relative importance of links is quite useful to improve node classification performance as connected nodes tend to have similar labels. Most existing approaches exploit the relative importance of links either by directly counting the number of connections among nodes or by learning the weight of each type of link from labeled data only. However, these approaches either neglect the importance of types of links to the class labels or may lead to overfitting problem. We propose a Tensor-based Markov chain (T-Mark) approach, which is able to automatically and simultaneously predict the labels for unlabeled nodes and give the relative importance of types of links that actually improve the classification accuracy. Specifically, we build two tensor equations by using the HIN and features of nodes from both labeled and unlabeled data. A Markov chain-based model is proposed and it is solved by an iterative process to obtain the stationary distributions. Theoretical analyses of the existence and uniqueness of such probability distributions are given. Extensive experimental results demonstrate that T-Mark is able to achieve superior performance in the comparison and obtain reasonable relative importance of links. [ABSTRACT FROM AUTHOR]

Reconfigurable intelligent surface (RIS) is a revolutionary technology and can be used to assist communication systems by adaptively manipulating the wireless environment. In this paper, we propose a novel cascaded channel estimation algorithm for the RIS-assisted multiple-input multiple-output orthogonal frequency division multiplexing systems. Inspired by the channel compression idea, we can obtain a sub-sampled channel by turning off a fraction of RIS elements and then extrapolate it to the complete one, by which the pilot overhead is greatly reduced. The problem of channel extrapolation is transformed into recovering the physical parameters of the cascaded channel from the partial channel observations and is then formulated by the sparse Bayesian learning (SBL) framework. In order to circumvent the curse of high dimensional matrices inversion in the vector-matrix system, we further introduce the tensor structure into the SBL framework. Specially, by leveraging of the channel sparsity over the angle domain and delay domain, we derive the virtual channel expression in tensor form and model a Kronecker-structured prior distribution for the virtual channels. The multi-domain sparse properties of the virtual channel tensor can be effectively captured by a group of low-dimensional hyper-parameters, and thus reduce the computational complexity. In addition, the Cramer-Rao lower bound is derived for the proposed channel extrapolation. Simulation results show the superior performance of the proposed scheme. [ABSTRACT FROM AUTHOR]

Human-oriented and machine-generated data in cyber-physical-social systems are often complicated graph-structured. Graph-powered learning methods are conducive to discovering valuable knowledge from large-scale graph data and improving decision-making processes. However, due to the neglect of diverse relations among things, most existing knowledge reasoning studies are inherently flawed and inefficient in processing the heterogeneous graphs with high-order connectivity. Tensor, as a powerful and effective tool to model high-level semantic interactions between various things, can provide high-order Internet of things graph with new perspectives and possibilities. Therefore, this article innovatively proposes a collaborative artificial intelligence of things data analysis and application framework based on Boolean tensors, which supports the expression and fusion of heterogeneous graph and ultimately promotes the AI processing. In this context, we focus on developing an incremental Boolean tensor factorization (IBTF) approach for efficient knowledge reasoning to meet the requirements of real-time and high-level quality demands for intelligent services. To the best of our knowledge, we are the first to do this work. More concretely, we present factors update and binary features merge algorithms for the integrated graph tensors to avoid numerous repeated calculations of historical data. Experimental results on general synthetic datasets demonstrate that the IBTF approach proposed in this article guarantees nearly equal approximate accuracy while reducing execution time by dozens and even more of times. Furthermore, experimental evaluations and interpretability analysis on real-world datasets verify the practicality of the proposed framework and approach. [ABSTRACT FROM AUTHOR]

The so-called block-term decomposition (BTD) tensor model, especially in its rank- $(L_{r},L_{r},1)$ version, has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of blocks of rank higher than one, a scenario encountered in numerous and diverse applications. Uniqueness conditions and fitting methods have thus been thoroughly studied. Nevertheless, the challenging problem of estimating the BTD model structure, namely the number of block terms, $R$ , and their individual ranks, $L_{r}$ , has only recently started to attract significant attention, mainly through regularization-based approaches which entail the need to tune the regularization parameter(s). In this work, we build on ideas of sparse Bayesian learning (SBL) and put forward a fully automated Bayesian approach. Through a suitably crafted multi-level hierarchical probabilistic model, which gives rise to heavy-tailed prior distributions for the BTD factors, structured sparsity is jointly imposed. Ranks are then estimated from the numbers of blocks ($R$) and columns ($L_{r}$) of non-negligible energy. Approximate posterior inference is implemented, within the variational inference framework. The resulting iterative algorithm completely avoids hyperparameter tuning, which is a significant defect of regularization-based methods. Alternative probabilistic models are also explored and the connections with their regularization-based counterparts are brought to light with the aid of the associated maximum a-posteriori (MAP) estimators. We report simulation results with both synthetic and real-word data, which demonstrate the merits of the proposed method in terms of both rank estimation and model fitting as compared to state-of-the-art relevant methods. [ABSTRACT FROM AUTHOR]

Accurate load modeling is critical for credible power system stability analysis. Because of the increasing complexity in modern system load, establishing a more comprehensive load model and performing accurate parameter estimation are the two biggest challenges in composite load modeling. In this paper, an induction motor with variable frequency drive (IM-VFD) together with the traditional ZIP+IM model is utilized to describe the dynamic characteristics of the system load. We estimate the time-varying probabilistic distributions of all states and parameters to describe their stochastic characteristics, thereby representing the real-time varying features of an actual load. The Fokker-Planck operator is applied to linearize the updated load model in tensor format. We then use tensor decomposition to reduce the computational and storage costs for calculating load model parameters. A sensitivity indicator is used to analyze the sensitivities of the estimated parameter distributions for subsequent model reduction. Simulations demonstrate that the updated load model has better performance than the traditional ZIP+IM model. [ABSTRACT FROM AUTHOR]

Sparse-view scanning has great potential for realizing ultra-low-dose computed tomography (CT) examination. However, noise and artifacts in reconstructed images are big obstacles, which must be handled to maintain the diagnosis accuracy. Existing sparse-view CT reconstruction algorithms were usually designed for circular imaging geometry, whereas the helical imaging geometry is commonly adopted in the clinic. In this paper, we show that the sparse-view helical CT (SHCT) images contain not only noise and artifacts but also severe anatomical distortions. These troubles reduce the applicability of existing sparse-view CT reconstruction algorithms. To deal with this problem, we analyzed the three-dimensional (3D) anatomical structure sparsity in SHCT images. Based on the analyses, we proposed a tensor decomposition and anisotropic total variation regularization model (TDATV) for SHCT reconstruction. Specifically, the tensor decomposition works on nonlocal cube groups to exploit the anatomical structure redundancy; the anisotropic total variation works on the whole volume to exploit the structural piecewise-smooth. Finally, an alternating direction method of multipliers is developed to solve the TDATV model. To our knowledge, the paper presents the first work investigating the reconstruction of sparse-view helical CT. The TDATV model was validated through digital phantom, physical phantom, and clinical patient studies. The results reveal that SHCT could serve as a potential solution for reducing HCT radiation dose to ultra-low level by using the proposed TDATV model.

A smartphone contains many critical components that are produced in highly automated and precisely monitored facilities throughout the complex manufacturing process. Even with the rapid development in the smartphone manufacturing industry today, the physical buttons are still existing on the smartphone because of the crucial importance of both in terms of their functionality and role. The smartphone’s physical buttons are small in size and have non-planar and shiny surfaces that lead to difficulty in detecting defects not only with human eyes but also with most AOI systems. Besides, most defects are tiny, with low contrast which is a huge challenge for deep learning models-based defect detection. To overcome these challenges, we propose a novel framework based on machine vision named highlight defect region by using higher-order singular value decomposition of wavelet subband-based tensor (HHoWST) for real-time smartphone’s physical buttons quality inspection. First, a modern image acquisition system is designed to obtain a high-quality smartphone’s physical button image dataset with a total of 500 images containing 13,472 samples of six defect types. Next, a wavelet subband-based third-order tensor of the smartphone’s physical button color image is constructed. Finally, higher-order singular value decomposition is proposed to estimate the components that contain the global illumination information and highlight the defective regions of the image. The experiments performed on HHoWST images reveal that our proposed method significantly improves the defect detection efficiency of deep learning models, such as SSD, Faster R-CNN, and YOLOv5, especially the performance in detecting the tiny defect types.

Multi-Spectral Image(MSI) denoising is an important preprocessing procedure to improve the performance of high-level processing. Tensor-based approach is one of the most popular methods for MSI denoising, since MSIs can be seen as multi-dimension arrays containing both spatial and spectral information. There are two main information in MSI, Global Correlation along Spectrum(GCS) and Nonlocal Self Similarity across space(NSS). Most tensor based approaches exploited these two characteristics by low-rank regularizations, mainly based on CANDERCOMP/PARAFAC(CP) decomposition and Tucker decomposition. However, they did not show a clear physical meaning. In this paper, we exploit the fact that pixels in MSI often cover several different materials and so that tensor data is mixed. Based on this, we divide tensor into several sub-tensors and propose a novel low rank regularization called Whole and Sub-Sparsity(WSS): GCS is modeled in the sub-tensors and NSS is modeled in the original tensor, which shows a clear physical meaning. Besides, to solve our model, we develop the corresponding algorithm by employing alternating direction method of multipliers(ADMM) framework. Experiment results show that our method is competitive compared to all state of the art MSI denoising methods.

A formulation that determines the permittivity and permeability tensors of a 3-D array of obstacles is presented. The formulation uses the reflection and transmission properties of a single layer with respect to Floquet modal fields, followed by eigenmode expansion of the fields. The eigenmodal fields together with Maxwell’s equations yield the permittivity and permeability tensors. The numerical results compare well with the available data in the literature. Interesting results of meander line obstacles are shown and discussed. [ABSTRACT FROM AUTHOR]

In this paper, we propose to extend the standard Convolutional Dictionary Learning problem to a tensor representation where the activations are constrained to be “low-rank” through a Canonical Polyadic decomposition. We show that this additional constraint increases the robustness of the CDL with respect to noise and improve the interpretability of the final results. In addition, we discuss in detail the advantages of this representation and introduce two algorithms, based on ADMM or FISTA, that efficiently solve this problem. We show that by exploiting the low rank property of activations, they achieve lower complexity than the main CDL algorithms. Finally, we evaluate our approach on a wide range of experiments, highlighting the modularity and the advantages of this tensorial low-rank formulation. [ABSTRACT FROM AUTHOR]

The recent availability of high-resolution multiview ZY-3 satellite images, with angular information, can provide an opportunity to capture 3-D structural features for classification. In high-resolution image classification over urban areas, objects with diverse vertical structures make urban landscape more heterogeneous in 3-D space and consequently can make the classification challenging. In this article, a novel multiangle gray-level cooccurrence tensor feature is proposed based on the multiview bands of the ZY-3 imagery, namely, GLCMMA–T. The GLCMMA–T feature captures the distributions of the gray-level spatial variation under different viewing angles, which can depict the 3-D textures and structures of urban objects. The spectral and GLCMMA–T tensor features are interpreted by two 3-D convolutional neural network (CNN) streams and then concatenated as the input to the fully connected layer. This novel multispectral and multiangle 3-D convolutional neural network (M2-3-DCNN) combines the spectral and angular information, and the fused feature has the potential to provide a comprehensive description of urban objects with complex vertical structures. The experimental results on ZY-3 multiview images from four test areas indicate that the proposed method can significantly improve the classification accuracy when compared with several state-of-the-art multiangle features and deep-learning-based image classification methods. [ABSTRACT FROM AUTHOR]

Fingerprint image enhancement is a key aspect of an automated fingerprint identification system. This paper describes an effective algorithm based on a novel lighting compensation scheme. The scheme involves the use of adaptive higher-order singular value decomposition on a tensor of wavelet subbands of a fingerprint (AHTWF) image to enhance the quality of the image. The algorithm consists of three stages. The first stage is the decomposition of an input fingerprint image of size 2M × 2N into four subbands at the first level by applying a two-dimensional discrete wavelet transform. In the second stage, we construct a tensor in ℝM×N×4 space. The tensor contains four wavelet subbands that serve as four frontal planes. Furthermore, the tensor is decomposed through higher-order singular value decomposition to separate the fingerprint's wavelet subbands into detailed individual components. In the third stage, a compensated image is produced by adaptively obtaining the compensation coefficient for each frontal plane of the tensor-based on the reference Gaussian template. The experimental results indicated that the quality of the AHTWF image was higher than that of the original image. The proposed algorithm not only improves the clarity and continuity of ridge structures but also removes the background and blurred regions of a fingerprint image. Therefore, this algorithm can achieve higher fingerprint classification accuracy than related methods can.

In edge computing, for dimensionality reduction and core data extraction, both edge computing node (ECN) and cloud server may implement a high-order singular value decomposition (HOSVD) algorithm before data are passed to local computing models. However, at present, many edge computing systems regard the two HOSVD procedures as two independent parts, which leads to repeated calculations in the cloud. In this paper, we propose an aggregative HOSVD method by reusing intermediate results of subtensor HOSVD in ECNs to reduce the HOSVD computing cost of the merged tensor in the cloud server. First, two equivalence lemmas of singular value decomposition (SVD) are proven. Second, the SVD left mergence algorithm (SVDLM), hierarchical-SVDLM (H-SVDLM) algorithm and aggregative HOSVD (AHOSVD) algorithm are proposed to obtain the HOSVD result of the merged tensor by efficiently merging the unfolded matrix SVD results of the subtensors. Finally, the efficiency and accuracy between the HOSVD and the AHOSVD are compared, and the experimental results validate that the proposed AHOSVD algorithm improves efficiency compared with the HOSVD algorithm in circumstances with comparable accuracy results with the HOSVD algorithm.

Traffic signal control has long been considered as a critical topic in intelligent transportation systems. Most existing related methods either suffer from inefficient training or mainly focus on isolated intersections. This article aims at the cooperative control for multi-intersection traffic signal, in which a novel end-to-end learning model is established and an efficient training method is proposed analogously, which is capable of adapting to large-scale scenarios. In the proposed method, the input traffic status in multi-intersection are expressed by a tensor without information loss, which significantly reduces model complexity than using a huge matrix, since additional convolutional layers can be required to extract features from a huge matrix. For the output, a multidimensional boolean vector is employed to simplify the control policy with abiding the practical phase changing rules, and then a multi-task learning structure is used to get the cooperative policy. Instead of only using the reinforcement learning to train the model, we employ imitation learning to integrate a rule based model to do the pre-training, which greatly accelerates the convergence. Afterwards, the reinforcement learning method is adopted to continue the fine training, where proximal policy optimization algorithm is incorporated to solve the policy collapse problem in multi-dimensional output situation. Numerical experiments demonstrate the distinctive advantages of the proposed method with comparison to the efficiency and accuracy of the related state-of-the-art methods.

Discriminant analysis is an important tool in machine learning. One of the motivations of this paper is to judge whether a dataset is suitable for discriminant analysis. At present, tensor data are becoming more and more popular in machine learning. Another motivation is to propose a dimensionality reduction algorithm of tensor data which facilitates discriminant analysis of tensor data. The first contribution of this paper is to propose a criterion to measure the potential ability of discriminant analysis of a dataset, and the criterion is called Maximum Discriminant Difference (MDD). The second contribution is to propose a dimensionality reduction algorithm of tensor data based on the mode product of tensor and MDD, called MDD-TDR for short. The first innovation of this paper is that, although MDD is inspired by Linear discriminant analysis (LDA), MDD is a criterion, not an algorithm. MDD can be applied to many applications, not just dimensionality reduction. Furthermore, MDD can be applied to both supervised and unsupervised learning. The second innovation is that, unlike many other tenor dimensionality reduction algorithms that are linear and align tenor into a vector for processing, MDD-TDR is nonlinear and iterative, and in each iteration, each dimension of a tensor is dimensionally reduced separately. The experimental results on 5 widely-used landmark datasets show MDD-TDR outperforms 7 related algorithms published in top academic journals in recent years.

Tensors and multiway analysis aim to explore the relationships between the variables used to represent the data and find a summarization of the data with models of reduced dimensionality. However, although in this context a great attention was devoted to this problem, dimension reduction of high-order tensors remains a challenge. The aim of this article is to provide a nonlinear dimensionality reduction approach, named principal tensor embedding (PTE), for unsupervised tensor learning, that is able to derive an explicit nonlinear model of data. As in the standard manifold learning (ML) technique, it assumes multidimensional data lie close to a low-dimensional manifold embedded in a high-dimensional space. On the basis of this assumption a local parametrization of data that accurately captures its local geometry is derived. From this mathematical framework a nonlinear stochastic model of data that depends on a reduced set of latent variables is obtained. In this way the initial problem of unsupervised learning is reduced to the regression of a nonlinear input-output function, i.e. a supervised learning problem. Extensive experiments on several tensor datasets demonstrate that the proposed ML approach gives competitive performance when compared with other techniques used for data reconstruction and classification.

Dimension reduction (DR) addresses the problem known as the curse of dimensionality in myriad hyperspectral imagery applications. Although the spatial pattern may assist in the distinction between different land covers that have close spectral signatures, it is often neglected by the current DR methods. In order to overcome this defect, two solutions: patch-based and tensor-patch-based, are studied in this article for a group of graph-based DR methods. To date, only a few attempts have been made in the patch- and tensor-patch-based variations for the graph-based DR methods. This article proposed two weight modified tensor-patch-based methods, namely weight modified tensor locality preserving projections and weight modified tensor neighborhood preserving embedding. Specifically, as graph-based DR methods heavily rely on the construction of adjacency graphs, this paper proposes a new use of the weighted region covariance matrix in the calculation of adjacency graphs. We found that the two proposed tensor-patch methods outperform the up-to-date methods.

In finance, it is believed that market information, namely, fundamentals and news information, affects stock movements. Such media-aware stock movements essentially comprise a multimodal problem. Two unique challenges arise in processing these multimodal data. First, information from one data mode will interact with information from other data modes. A common strategy is to concatenate various data modes into one compound vector; however, this strategy ignores the interactions among different modes. The second challenge is the heterogeneity of the data in terms of sampling time. Specifically, fundamental data consist of continuous values sampled at fixed time intervals, whereas news information emerges randomly. This heterogeneity can cause valuable information to be partially missing or can distort the feature spaces. In addition, the study of media-aware stock movements in previous work has focused on the one-to-one problem, in which it is assumed that news affects only the performance of the stocks mentioned in the reports. However, news articles also impact related stocks and cause stock co-movements. In this article, we propose a tensor-based event-driven LSTM model to address these challenges. Experiments performed on the China securities market demonstrate the superiority of the proposed approach over state-of-the-art algorithms, including AZFinText, eMAQT, and TeSIA. [ABSTRACT FROM AUTHOR]

Medical hyperspectral imagery has recentlyattracted considerable attention. However, for identification tasks, the high dimensionality of hyperspectral images usually leads to poor performance. Thus, dimensionality reduction (DR) is crucial in hyperspectral image analysis. Motivated by exploiting the underlying structure information of medical hyperspectral images and enhancing the discriminant ability of features, a discriminant tensor-based manifold embedding (DTME) is proposed for discriminant analysis of medical hyperspectral images. Based on the idea of manifold learning, a new discriminant similarity metric is designed, which takes into account the tensor representation, sparsity, low-rank and distribution characteristics. Then, an inter-class tensor graph and an intra-class tensor graph are constructed using the new similarity metric to reveal intrinsic manifold of hyperspectral data. Dimensionality reduction is achieved by embedding this supervised tensor graphs into the low-dimensional tensor subspace. Experimental results on membranous nephropathy and white bloodcells identification tasks demonstrate the potential clinical value of the proposed DTME. [ABSTRACT FROM AUTHOR]

Sparse unmixing is an important technique for analyzing and processing hyperspectral images (HSIs). Simultaneously exploiting spatial correlation and sparsity improves substantially abundance estimation accuracy. In this article, we propose to exploit nonlocal spatial information in the HSI for the sparse unmixing problem. Specifically, we first group similar patches in the HSI, and then unmix each group by imposing simultaneous a low-rank constraint and joint sparsity in the corresponding third-order abundance tensor. To this end, we build an unmixing model with a mixed regularization term consisting of the sum of the weighted tensor trace norm and the weighted tensor $\ell _{2,1}$ -norm of the abundance tensor. The proposed model is solved under the alternating direction method of multipliers framework. We term the developed algorithm as the nonlocal tensor-based sparse unmixing algorithm. The effectiveness of the proposed algorithm is illustrated in experiments with both simulated and real hyperspectral data sets. [ABSTRACT FROM AUTHOR]

The procedure of establishing the correspondence between two sets of feature points is important in computer vision applications. In this article, an elastic net constraint-based tensor model is proposed for high-order graph matching. To control the tradeoff between the sparsity and the accuracy of the matching results, an elastic net constraint is introduced into the tensor-based graph matching model. Then, a nonmonotone spectral projected gradient (NSPG) method is derived to solve the proposed matching model. During the optimization of using NSPG, we propose an algorithm to calculate the projection on the feasible convex sets of elastic net constraint. Further, the global convergence of solving the proposed model using the NSPG method was proved. The superiority of the proposed method is verified through experiments on the synthetic data and natural images. [ABSTRACT FROM AUTHOR]

Tucker decomposition has been widely used to extract meaningful and underlying data from heterogeneous data generated by different kinds of devices in a wide range of industrial Internet of Things (IIoT) applications. IIoT data uploaded to the cloud contain personal and sensitive information; thus, there is a growing concern about data privacy. Current existing data analysis solutions, however, assume that the data are reliably and securely collected from different IIoT data providers, an assumption that is not always true in the real world. To address the issues, in this article we propose a privacy-preserving tucker train decomposition based on gradient descent over blockchain-based encrypted IIoT data. Specifically, we use blockchain techniques to enable IIoT data providers to reliably and securely share their data by encrypting them locally before recording them in the blockchain. We use tensor train (TT) theory to build an efficient TT-based tucker decomposition based on gradient descent that tremendously reduces the number of elements to be updated during the tucker decomposition. We utilize the massive resources of fogs and clouds to implement an efficient privacy-preserving tucker train decomposition scheme. We use homomorphic encryption to build our scheme that does complete tucker train decomposition without the involvement of users. Results from a series of extensive experiments on synthetic datasets and real-world datasets demonstrate that our proposed scheme is efficient. [ABSTRACT FROM AUTHOR]

Natural images often have self-similarity, which can be used to remove noise. Therefore, many current denoising methods denoise by processing similar image block matrix. Aiming at the problem that these methods will destroy the two-dimensional structure of image blocks when they are expanded into one-dimensional column vectors, a new image denoising method based on high-order singular value decomposition is proposed. Several similar image blocks are stacked into three-dimensional arrays and treated as a third-order tensor; then, higher-order singular value decomposition can be performed. For the core tensor obtained by decomposition, an iterative algorithm with adaptive hard threshold coefficient shrinkage is proposed. The experimental results show that the proposed method outperforms the state-of-the-art methods in peak-signal-to-noise ratio, structural similarity, and visual effects.

The local structure feature of the target in synthetic aperture radar (SAR) image and the inner correlation among multiple SAR images of the same target can effectively improve the recognition performance. In order to utilize these two kinds of information, we propose the multi-view tensor sparse representation (MTSR) model for SAR target recognition. In the proposed model, the SAR image is treated as tensor and represented by the dictionaries on each dimension of the image and corresponding sparse representation coefficient tensor (SRCT). For multi-view SAR images of one target, we design the proposed model by letting the SRCTs of those images have the same structure, which means that the non-zero elements of those SRCTs have the same coordinates. In order to solve the proposed model, we propose the joint tensor orthogonal matching pursuit (JT-OMP) algorithm to calculate the SRCTs of multiple views. JT-OMP ensures that all the SRCTs have the same structure by looking for the atoms of dictionaries that can contribute the total maximum energy for all multi-view tensors in every iteration. To achieve recognition, we construct two dictionaries for each class and compare the total sparse representation error of multi-view SAR images in each class. The experiments conducted on the moving and stationary target acquisition recognition database (MSTAR) verify the performance of the proposed algorithm.

Several features have been developed to characterize the land cover in synthetic aperture radar (SAR) data with speckle noise. Feature extraction has become an essential task for SAR image processing. However, how to preserve the original intrinsic structural information and enhance the discriminant ability to reduce the impact of noise is still a challenge in this area. In this paper, using a clustering method to maintain the nonlocal information in images and tensors with the ability to preserve spatial neighborhood structure information, a new cluster-based tensorial semisupervised discriminant analysis (CTSDA) method is proposed for feature extraction of SAR images. In the CTSDA, the block clustering algorithm is employed to generate several high-order clustering tensors of multifeature SAR images, which preserves the intrinsic nonlocal spatial information and neighborhood structure. In the multiple manifold structures of the cluster tensors, the improved discriminant analysis enhances the feature discrimination by considering the local structure and labeled and unlabeled information through the Laplace matrix, and the fusion of tensor algebraic analysis and improved discriminant analysis produces multiple new projection directions of the cluster tensors. Finally, feature extraction is achieved by rearranging the projected cluster tensors. The experimental results on the simulated SAR data and four real SAR images demonstrate the superiority of the proposed method over several state-of-the-art approaches.

Non-local self-similarity (NLSS) is widely used as prior information in an image restoration method. In particular, a low-rankness-based prior has a significant effect on performance. On the other hand, a number of color extensions of NLSS-based grayscale image restoration methods have been developed. These extensions focus on the pixel-wise correlation among color channels. However, a natural color image also has a complex dependency, known as an inter-channel dependency, among local regions from different color channels. As a result, color artifacts appear in a denoised image obtained by using the existing methods. In this paper, we propose a novel non-local and inter-channel dependency-aware prior called the weighted tensor nuclear norm (WTNN). The proposed prior is derived by incorporating inter-channel dependency to low-rank-based NLSS prior. The WTNN is a low-rankness-of-the-third-order patch tensor, and we apply it to the tensors constructed with non-local similar patches. It enables us to naturally represent the higher-order dependencies among similar color patches. We propose an image denoising algorithm using the WTNN and image restoration algorithm by using a non-trivial generalization of this algorithm. The experimental results clearly show that the proposed WTNN-based color image denoising and restoration algorithms outperform state-of-the-art methods.

Alternating least squares (ALS) and its variations are the most commonly used algorithms for the PARAFAC decomposition of a tensor. However, it is still troubled for one how to accelerate the ALS algorithm with the reduced computational complexity. In this paper, a new acceleration method for the ALS with a matrix polynomial predictive model (MPPM) is proposed. In the MPPM, a matrix-valued function is first approximated by a matrix polynomial. It is shown that the future value of the function can be predicted by an FIR filter with the coefficients determined offline. By viewing each factor matrix of a tensor as a matrix-valued function, a new ALS algorithm, the ALS-MPPM algorithm, is then given. Analyses show that our ALS-MPPM algorithm is of low computational complexity and a close relation with the existing ALS algorithms. Moreover, to further accelerate the convergence of the proposed algorithm, a new technique called the multi-model (MM) prediction is also introduced. While the analytical results are verified by the numerical simulations, it is also shown that our ALS-MPPM outperforms the existing ALS-based algorithms in terms of the rate of convergence.

Heterogeneous network entity classification is to predict the labels of entities in a heterogeneous network which consists of multiple types of relations and multiple types of entities. The existing studies have shown that relations information is critical for improving entity classification performance. The relation information is often exploited by clustering the entities into groups based on relation density or constructing relation features by counting the number of different relations. However, these methods only consider the relation information but neglect the importance of different relations in the network. In practice, different relations may have different degrees of importance w.r.t different entities. To this end, we propose a Random walk Tensor Model (RTM) to reveal the relation importance and classify the entities in the heterogeneous network, simultaneously. In RTM, the heterogeneous network is represented as a multi-relational network using a three-way tensor. The tensor is also used to compute the transition probability for the random walk among entities. We build a Markov chain model and use an iterative algorithm to solve the Markov chain equations in the model to obtain the random walk stationary distributions and compute the entity classification and relation ranking results based on such distributions. The theoretical analyses are given to show the rationality and interpretability of the model. The experimental results demonstrate that the RTM can achieve superior classification performance compared with several state-of-the-art methods and obtain a reasonable relation ranking.

We consider the joint estimation of direction-of-arrival (DOA) and polarization of constant modulus (CM) signals based on an electromagnetic vector-sensor (EMVS) array. Two algebraic algorithms for canonical polyadic decomposition (CPD) with CM constraint are proposed in two scenarios, in which the source signals are fully and partially CM, respectively. The proposed algorithms use the analytic CM algorithm in the first step to calculate the source matrix, and then exploit the CPD structure of the data tensor to compute the remaining factor matrices, from which the DOA and polarization parameters can finally be obtained. Due to the algebraic nature, the proposed algorithms are faster and more stable than the optimization based algorithms, and can be used to effectively initialize the latter. We have shown that the proposed algorithms have more relaxed uniqueness conditions than unconstrained CPD, and thus can be applied in highly underdetermined cases where the number of source signals greatly exceeds that of the EMVSs. Simulation results are provided to illustrate the performance of the proposed algorithms.

In the area of subspace clustering, methods combining self-representation and spectral clustering are predominant in recent years. For dealing with tensor data, most existing methods vectorize them into vectors and lose most of the spatial information. For removing noise of the data, most existing methods focus on the input space and lack consideration of the projection space. Aiming at preserving the spatial information of tensor data, we incorporate tensor mode-d product with low-rank matrices for self-representation. At the same time, we remove noise of the data in both the input space and the projection space, and obtain a robust affinity matrix for spectral clustering. Extensive experiments on several popular subspace clustering datasets show that the proposed method outperforms both traditional subspace clustering methods and recent state-of-the-art deep learning methods.

Vibration signal analysis is one of the most effective approaches for detecting faults in bearings. A bearing compound-fault signal always consists of multiple signatures and stochastic noise. The separation of multi-fault signals from them is not only crucial but also very challenging. In order to solve this issue, a novel multiple faults detecting technique has been developed based on tensor factorization. The original multi-channel vibration signals are formulated as a 3-way tensor via the temporal signal, spectra, and channel information in a high-dimensional space. The PARAFAC decomposition is used to analyze the tensor model, and then, principal component analysis (PCA) is introduced to find the numbers of the rank-one tensor. Finally, the tensor model is solved by alternating least squares (ALSs) approach combined with PCA technique. The performance of the detection method has been proven by simulation analysis of the multi-channel compound faults signals. The experimental results obtained using the developed technique also demonstrated that compound-fault signatures can be effectively and clearly identified.

A novel deep architecture, the sparse deep tensor extreme learning machine (SDT-ELM), is presented as a tool for pattern classification. In extending the original ELM, the proposed SDT-ELM gains the theoretical advantage of effectively reducing the number of hidden-layer parameters by using tensor operations, and using a weight tensor to incorporate higher-order statistics of the hidden feature. In addition, the SDT-ELM gains the implementation advantage of enabling the random hidden nodes to be added block by block, with all blocks having the same hidden layer configuration. Moreover, an SDT-ELM without randomness can also achieve better learning accuracy. Extensive experiments with three widely used classification datasets demonstrate that the proposed algorithm achieves better generalization performance.

Accuracy is extensively considered a key issue for traffic big data prediction in a vehicular cyber-physical system (VCPS). Deep learning with super performance has been successfully applied to traffic prediction for feature learning. However, uncertain traffic big data pose a remarkable challenge on current deep learning models, which work in a vector space in a deterministic manner and fail to learn the features of uncertain traffic data. This study solves the problem of citywide traffic flow prediction to satisfy the accuracy requirement of the VCPS from the perspective of users. In this study, a tensor-train fuzzy deep convolution (TFDC) approach is first proposed to satisfy the accuracy requirements of traffic flow prediction. Moreover, the Tucker deep computation (T-TFDC) approach for TFDC is proposed to satisfy the prediction accuracy requirements with low computational complexity. The TFDC model is built upon the fuzzy deep convolutional network, which uses unified tensor data representation for spatio-temporal traffic flow data. The key idea of the T-TFDC is to introduce Tucker decomposition into the TFDC model to compress parameters for traffic flow feature learning. Furthermore, learning algorithms for training TFDC and T-TFDC model parameters are devised on the basis of the back-propagation strategy. Experimental results on the TaxiBJ and BikeNYC data sets verify the effectiveness and efficiency of the proposed approaches over state-of-the-art methods.

Tensor-based dimensionality reduction (DR) of hyperspectral images is a promising research topic. However, patch-based tensorization usually adopts a squared neighborhood with fixed window size, which may be inaccurate in modeling the local spatial information in a hyperspectral image scene. In this work, we propose a novel shape-adaptive tensor factorization (SATF) model for dimensionality reduction and classification of hyperspectral images. Firstly, shape-adaptive patch features are extracted to build fourth-order tensors. Secondly, multilinear singular value decomposition (MLSVD) is adopted for tensor factorization and latent features are extracted via mode-i tensor-matrix product. Finally, classification is conducted by using a sparse multinomial logistic regression (SMLR) model. Experimental results, conducted with two popular hyperspectral data sets collected over the Indian Pines and the University of Pavia, respectively, indicate that the proposed method outperforms the other traditional and tensor-based DR methods.

The so-called block-term decomposition (BTD) tensor model has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of blocks of rank higher than one, a scenario encountered in numerous and diverse applications. Its uniqueness and approximation have thus been thoroughly studied. Nevertheless, the challenging problem of estimating the BTD model structure, namely the number of block terms and their individual ranks, has only recently started to attract significant attention. In this paper, a novel method of BTD model selection and computation is proposed, based on the idea of imposing column sparsity jointly on the factors and in a hierarchical manner and estimating the ranks as the numbers of factor columns of non-negligible magnitude. Following a block successive upper bound minimization (BSUM) approach for the proposed optimization problem is shown to result in an alternating hierarchical iteratively reweighted least squares (HIRLS) algorithm, which is fast converging and enjoys high computational efficiency, as it relies in its iterations on small-sized sub-problems with closed-form solutions. Simulation results for both synthetic examples and a hyper-spectral image denoising application are reported, which demonstrate the superiority of the proposed scheme over the state-of-the-art in terms of success rate in rank estimation as well as computation time and rate of convergence while attaining a comparable tensor approximation performance. [ABSTRACT FROM AUTHOR]

Reducing cost and power consumption while maintaining high network access capability is a key physical-layer requirement of massive Internet of Things (mIoT) networks. Deploying a hybrid array is a cost- and energy-efficient way to meet the requirement, but would penalize system degree of freedom (DoF) and channel estimation accuracy. This is because signals from multiple antennas are combined by a radio frequency (RF) network of the hybrid array. This article presents a novel hybrid uniform circular cylindrical array (UCyA) for mIoT networks. We design a nested hybrid beamforming structure based on sparse array techniques and propose the corresponding channel estimation method based on the second-order channel statistics. As a result, only a small number of RF chains are required to preserve the DoF of the UCyA. We also propose a new tensor-based two-dimensional (2-D) direction-of-arrival (DoA) estimation algorithm tailored for the proposed hybrid array. The algorithm suppresses the noise components in all tensor modes and operates on the signal data model directly, hence improving estimation accuracy with an affordable computational complexity. Corroborated by a Cramér-Rao lower bound (CRLB) analysis, simulation results show that the proposed hybrid UCyA array and the DoA estimation algorithm can accurately estimate the 2-D DoAs of a large number of IoT devices. [ABSTRACT FROM AUTHOR]

Industrial Internet-of-Things (IIoT) has revolutionized almost every aspect of industrial manufacturing through industrial intelligence by incorporating production equipment, mobile terminals, and smart devices with wireless or wired networks. However, industrial visual information, such as images, videos, graphs, and texts, generated and collected from the industrial processes, contains various kinds of hidden value for industrial intelligence. Therefore, for the trend of providing ubiquitous industrial intelligence, new paradigms of perception and processing technologies of visual information such as recognition methods are required. However, industrial visual information is heterogeneous and complex with multiattributes, which presents significant challenges on visual information perception and processing technologies such as multiattributes recognition method. In this article, to provide industrial intelligence, a tensor-based visual feature recognition method is used to recognize the object from the perspective of multiattributes with the combination of attributes. To demonstrate its practical implementation, a case study about the industrial intelligence on the faulty location and diameter of bearings in the IIoT is described. Also, experiments on object recognition are carried out on the public image set COIL-100 to demonstrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, we investigate effective sketching schemes via sparsification for high dimensional multilinear arrays or tensors. More specifically, we propose a novel tensor sparsification algorithm that retains a subset of the entries of a tensor in a judicious way, and prove that it can attain a given level of approximation accuracy in terms of tensor spectral norm with a much smaller sample complexity when compared with existing approaches. In particular, we show that for a kth order $ {d}\times \cdots \times {d}$ cubic tensor of stable rank $ {r}_{ {s}}$ , the sample size requirement for achieving a relative error $\varepsilon $ is, up to a logarithmic factor, of the order $ {r}_{ {s}}^{1/2} {d}^{ {k}/2} /\varepsilon $ when $\varepsilon $ is relatively large, and $ {r}_{ {s}} {d} /\varepsilon ^{2}$ and essentially optimal when $\varepsilon $ is sufficiently small. It is especially noteworthy that the sample size requirement for achieving a high accuracy is of an order independent of k. To further demonstrate the utility of our techniques, we also study how higher order singular value decomposition (HOSVD) of large tensors can be efficiently approximated via sparsification. [ABSTRACT FROM AUTHOR]

Data-driven problem solving in many real-world applications involves analysis of time-dependent multivariate data, for which dimensionality reduction (DR) methods are often used to uncover the intrinsic structure and features of the data. However, DR is usually applied to a subset of data that is either single-time-point multivariate or univariate time-series, resulting in the need to manually examine and correlate the DR results out of different data subsets. When the number of dimensions is large either in terms of the number of time points or attributes, this manual task becomes too tedious and infeasible. In this paper, we present MulTiDR, a new DR framework that enables processing of time-dependent multivariate data as a whole to provide a comprehensive overview of the data. With the framework, we employ DR in two steps. When treating the instances, time points, and attributes of the data as a 3D array, the first DR step reduces the three axes of the array to two, and the second DR step visualizes the data in a lower-dimensional space. In addition, by coupling with a contrastive learning method and interactive visualizations, our framework enhances analysts' ability to interpret DR results. We demonstrate the effectiveness of our framework with four case studies using real-world datasets. [ABSTRACT FROM AUTHOR]

Hyperspectral image (HSI) has been widely used in target detection and classification. However, various kinds of noise in HSIs affect the applications of HSIs. In this paper, we propose a low-rank (LR) tensor recovery model to remove noise. Considering that the HSI is a 3-D HSI data, and the underlying LR tensor property is used in the model. Then, according to the similarity of adjacent bands images, the regularization on the difference of adjacent bands images is considered. The experiments of removing noise from different noisy HSIs show that our method can achieve better performance on removing sparse noise, especially for strips removal.

Thousands of long non-coding RNAs (lncRNAs) are encoded by mammalian genomes and play important roles in various biological processes, including the regulation of gene transcription. Through these relationships, lncRNAs can participate in proliferation, differentiation, and cytoprotective programs, which implies their critical roles in human diseases, especially cancers. Therefore, there is an urgent need to study the relationships between lncRNAs and genes in human diseases, which will help uncover the mechanisms underlying disease progression. In this paper, we explore the relationships between lncRNAs and genes in various diseases through a tensor completion-based approach (TCA). The results of performance evaluation suggest that TCA can obtain a significantly better performance than the baseline method. Moreover, top ranked relationships with highest average scores in all diseases corroborate the effectiveness of TCA and the reliability of the predicted results. Case study of hepatocellular carcinoma (HCC) indicates that the elements of the top ranked relationships may be functionally implicated in HCC. Furthermore, three lncRNAs (HULC, MALAT1, and BANCR) and gene HOXB7 are found to be important in HCC, which are consistent with the newest reports and existing literatures.

In this brief, a separable maximum correntropy criterion (SMCC) algorithm is developed by exploiting the typical separability property of tensors. Utilizing the separability property, a great number savings are obtained along with accelerated learning rate and improved estimate accuracy. In the proposed SMCC, a correntropy scheme is used to construct a adaptive algorithm to combat the impulsive noise and outliers in non-Gaussian environment. The complexity and convergence analysis of the SMCC are presented and discussed. Examples with two-way matrix and three-way tensor are carried out to verify the performance of the proposed SMCC algorithm under mixture Gaussian and Student’s t noises. [ABSTRACT FROM AUTHOR]

Magnetic anomaly detection is an effective method for detecting ferromagnetic targets. The practical application of target detection by measuring the magnetic gradient has been confirmed in many studies, and its suppression of background noise has been widely recognized. However, the variation of the unidirectional magnetic field gradient is very small in a short distance, and the amplitude of the signal is also affected by the direction of the target’s magnetic moment and the shaking of the sensor platform itself. These make it difficult to extract the signal from complex background interference. In order to solve these problems, this paper is devoted to use the variation of three axial magnetic gradients in the geomagnetic coordinate system caused by the presence of magnetic target (we call it full magnetic gradient) to construct the magnetic anomaly characteristic of the target. A set of orthonormal basis functions is further derived to linearly describe this characteristic, which improves the signal-to-noise ratio (SNR) of the signal from the perspective of signal energy. The present work main contribution is to propose a full magnetic gradient orthonormal basis function (FMG-OBF) method to effectively characterize magnetic anomaly of magnetic targets. Compared with the traditional one-direction magnetic gradient orthonormal basis function method, the SNR of this method is greatly improved, and it is not affected by a change in the target magnetic moment’s direction nor by the shaking of the sensor carrier platform. Therefore, it has great value in the practical application of aeromagnetic detection. [ABSTRACT FROM AUTHOR]