Tucker Tensor Research Articles

Coordinated, multicellular patterns of transcriptional variation that stratify patient cohorts are revealed by tensor decomposition.

Tissue-level and organism-level biological processes often involve the coordinated action of multiple distinct cell types. The recent application of single-cell assays to many individuals should enable the study of how donor-level variation in one cell type is linked to that in other cell types. Here we introduce a computational approach called single-cell interpretable tensor decomposition (scITD) to identify common axes of interindividual variation by considering joint expression variation across multiple cell types. scITD combines expression matrices from each cell type into a higher-order matrix and factorizes the result using the Tucker tensor decomposition. Applying scITD to single-cell RNA-sequencing data on 115 persons with lupus and 83 persons with coronavirus disease 2019, we identify patterns of coordinated cellular activity linked to disease severity and specific phenotypes, such as lupus nephritis. scITD results also implicate specific signaling pathways likely mediating coordination between cell types. Overall, scITD offers a tool for understanding the covariation of cell states across individuals, which can yield insights into the complex processes that define and stratify disease.

Tucker tensor decomposition with rank estimation for sparse hyperspectral unmixing

ABSTRACT Hyperspectral image unmixing gives increasing focus on the structural integrity of the spatial-spectral information. A large number of methods exploit the sparse and low-rank properties of the abundance vectors, abundance matrices and abundance maps, which are first-order or second-order structures, and are hard to preserve the integrated structure of the abundance. The abundance tensor formed by overlapping the abundance maps of endmembers sequentially is a more appropriate expression of the abundance. However, hyperspectral unmixing studies based on the abundance tensor are still in the minority, and most of these methods either inherently degrade the tensor structure to some extent, which is hard to distinguish the low-rankness of different dimensions; or are based on tensor decomposition methods, which always require a pre-estimation of the tensor rank, thus the unmixing accuracy depends on the rank estimation. In this article, we propose an unmixing model on tensor framework, in which the abundance tensor is approximated by a truncated Tucker tensor decomposition (TTD). Since the generated factor matrices are relatively low-rank, the low-rankness exploration of the abundance tensor is achieved potentially by this way. Moreover, we further improve the unmixing performance by a suitable rank estimation. The more flexible algorithm Tucker tensor decomposition with rank estimation for sparse hyperspectral unmixing (TTDRE) is proposed to differentiate the low-rankness of different dimensions of the abundance tensor while preserving the structural integrity. Experiments on synthetic and real data illustrate the effectiveness of our method.

Tucker Tensor Approach for Accelerating Fock Exchange Computations in a Real-Space Finite-Element Discretization of Generalized Kohn-Sham Density Functional Theory.

The evaluation of Fock exchange is often the computationally most expensive part of hybrid functional density functional theory calculations in a systematically improvable, complete basis. In this work, we employ a Tucker tensor based approach that substantially accelerates the evaluation of the action of Fock exchange by transforming three-dimensional convolutional integrals into a tensor product of one-dimensional convolution integrals. Our numerical implementation uses a parallelization strategy that balances the memory and communication bottlenecks, alongside overlapping compute and communication operations to enhance computational efficiency and parallel scalability. The accuracy and computational efficiency are demonstrated on various systems, including Pt clusters of various sizes and a TiO2 cluster with 3684 electrons.

Constructing low-rank Tucker tensor approximations using generalized completion

Abstract The projected gradient method for matrix completion is generalized towards the higher-dimensional case of low-rank Tucker tensors. It is shown that an operation order rearrangement in the common projected gradient approach provides a complexity improvement. An even better algorithm complexity can be obtained by replacing the completion operator by a general operator that satisfies restricted isometry property; however, such a replacement transforms the completion algorithm into an approximation algorithm.

A DEIM Tucker tensor cross algorithm and its application to dynamical low-rank approximation

We introduce a Tucker tensor cross approximation method that constructs a low-rank representation of a d-dimensional tensor by sparsely sampling its fibers. These fibers are selected using the discrete empirical interpolation method (DEIM). Our proposed algorithm is referred to as DEIM fiber sampling (DEIM-FS). For a rank-r approximation of an O(Nd) tensor, DEIM-FS requires access to only dNrd−1 tensor entries, a requirement that scales linearly with the tensor size along each mode. We demonstrate that DEIM-FS achieves an approximation accuracy close to the Tucker-tensor approximation obtained via higher-order singular value decomposition at a significantly reduced cost. We also present DEIM-FS (iterative) that does not require access to singular vectors of the target tensor unfolding and can be viewed as a black-box Tucker tensor algorithm. We employ DEIM-FS to reduce the computational cost associated with solving nonlinear tensor differential equations (TDEs) using dynamical low-rank approximation (DLRA). The computational cost of solving DLRA equations can become prohibitive when the exact rank of the right-hand side tensor is large. This issue arises in many TDEs, especially in cases involving non-polynomial nonlinearities, where the right-hand side tensor has full rank. This necessitates the storage and computation of tensors of size O(Nd). We show that DEIM-FS results in significant computational savings for DLRA by constructing a low-rank Tucker approximation of the right-hand side tensor on the fly. Another advantage of using DEIM-FS is to significantly simplify the implementation of DLRA equations, irrespective of the type of TDEs. We demonstrate the efficiency of the algorithm through several examples including solving high-dimensional partial differential equations.

Unsupervised Anomaly Detection of Intermittent Demand for Spare Parts Based on Dual-Tailed Probability

The quick development of machine learning techniques provides a superior capability for manufacturing enterprises to make effective decisions about inventory management based on spare parts demand (SPD) data. Since SPD sequences in practical maintenance applications usually show an intermittent distribution, it is not easy to represent the demand pattern of such sequences. Meanwhile, there are some aspects like manual report errors, environmental interference, sudden project changes, etc., that bring large and unexpected fluctuations to SPD sequences, i.e., anomalous demands. The inventory decision made based on the SPD sequences with anomalous demands is not trusted by enterprise engineers. For such SPD data, there are two great concerns, i.e., false alarms in which sparse demands are recognized to be anomalous and missing alarms in which the anomalous demands are categorized as normal due to their adjacent demands having extreme values. To address these concerns, a new unsupervised anomaly-detection method for intermittent time series is proposed based on a dual-tailed probability. First, the multi-way delay embedding transform (MDT) was applied on the raw SPD sequences to obtain higher-order tensors. Through Tucker tensor decomposition, the disturbance of extreme demands can be effectively reduced. For the reconstructed SPD sequences, then, the tail probability at each time point, as well as the empirical cumulative distribution function were calculated based on the probability of the demand occurrence. Second, to lessen the disturbance of sparse demand, the non-zero demand sequence was distilled from the raw SPD sequence, with the tail probability at each time point being calculated. Finally, the obtained dual-tailed probabilities were fused to determine the anomalous degree of each demand. The proposed method was validated on the two actual SPD datasets, which were collected from a large engineering manufacturing enterprise and a large vehicle manufacturing enterprise in China, respectively. The results demonstrated that the proposed method can effectively lower the false alarm rate and missing alarm rate with no supervised information provided. The detection results were trustworthy enough and, more importantly, computationally inexpensive, showing significant applicability to large-scale after-sales parts management.

A low-rank isogeometric solver based on Tucker tensors

We propose an isogeometric solver for Poisson problems that combines (i) low-rank tensor techniques to approximate the unknown solution and the system matrix, as a sum of a few terms having Kronecker product structure, (ii) a Truncated Preconditioned Conjugate Gradient solver to keep the rank of the iterates low, and (iii) a novel low-rank preconditioner, based on the Fast Diagonalization method where the eigenvector multiplication is approximated by the Fast Fourier Transform. Although the proposed strategy is written in arbitrary dimension, we focus on the three-dimensional case and adopt the Tucker format for low-rank tensor representation, which is well suited in low dimension. We show by numerical tests that this choice guarantees significant memory saving compared to the full tensor representation. We also extend and test the proposed strategy to linear elasticity problems.

A scalogram tensor decomposition based ECG quality assessment

ECG quality assessment is crucial for reducing false alarms and physician strain in automated diagnosis of cardiovascular diseases. Recent researches have focused on constructing an automatic noisy ECG record rejection mechanism. This work develops a noisy ECG record rejection system using scalogram and Tucker tensor decomposition. The system can reject ECG records, which cannot be analyzed or diagnosed. Scalogram of all 12‑lead ECG signals per subject are stacked to form a 3-way tensor. Tucker tensor decomposition is applied with empirical settings to obtain the core tensor. The core tensor is reshaped to form the latent features set. When tested using the PhysioNet challenge 2011 dataset in five-fold cross validation settings, the RusBoost ensemble classifier proved to be a very reliable option, producing an accuracy of 92.4% along with sensitivity of 87.1% and specificity of 93.5%. According to the experimental findings, combining the scalogram with Tucker tensor decomposition yields competitive performance and has the potential to be used in actual evaluation of ECG quality.

Tensor-Based Joint Beamforming with Ultrasonic and RIS-Assisted Dual-Hop Hybrid FSO mmWave Massive MIMO of V2X

Reconfigurable intelligent surface (RIS)-assisted millimeter-wave (mmWave) communication systems relying on hybrid beamforming structures are capable of achieving high spectral efficiency at a low hardware complexity and with low power consumption. Tensor-based joint beamforming with low-cost ultrasonic and RIS-assisted Dual-Hop Hybrid free space optical (FSO) mm Wave massive Multiple Input Multiple Output (MIMO) of vehicle-to-everything (V2X) is proposed. To address the occlusion problem for high-speed mobility of the vehicle, an RIS-assisted mixed FSO-MIMO V2X system is proposed. The low-cost ultrasonic array signal model is developed to solve the accurate direction-of-arrival (DOA) estimation. The ultrasonic-assisted RIS phase shift matrix based on subspace self-organizing iterations is designed to track the beam direction between RIS and vehicle. Specifically, the associated bandwidth-efficiency maximization problem is transformed into a series of subproblems, where the subarray of phase shifters and RIS elements is jointly optimized to maximize each subarray’s rate. The vehicle motion state is transformed into a two-dimensional model for prior distribution to calculate the particle weights of the RIS phase. Multi-vehicle Tucker tensor decomposition is used to describe the high-dimensional beam space. We conceive a multi-vehicle joint optimization method for designing the hybrid beamforming matrix of the base station (BS) and the passive beamforming matrix of the RIS. A cascaded channel decomposition method based on Singular Value Decomposition (SVD) is used to obtain the combined matrix beamforming of BS and vehicle. Our simulation results demonstrate the superiority of the proposed method compared to its traditional counterparts.

Faster quantum state decomposition with Tucker tensor approximation

Faster quantum state decomposition with Tucker tensor approximation

Joint range, angle and polarization estimation in polarimetric FDA-MIMO radar based on Tucker tensor decomposition

Frequency diverse array multiple-input multiple-output (FDA-MIMO) radar is an emerging technology to offer range-angle-dependent beampattern. Polarimetric FDA-MIMO radar can sense additional polarization information to improve target identification capability. In this article, we investigate the problem of joint range, angle and polarization parameter estimation in a monostatic polarimetric FDA-MIMO radar with an FDA at transmitter and a cross-dipole array at receiver. Unlike the conventional methods in which the multidimensional data structure is rearranged into vectors or matrices by stacking operation, we propose a Tucker tensor decomposition-based scheme, which can reserve the original data structure and avoid spoiling the inherent characteristics of interest, especially when the number of snapshots is small. The third-order tensor model of the observed data is constructed. Two approaches named as Tucker covariance reconstruction and Tucker signal subspace are presented using the fourth-order covariance tensor decomposition. The Cramér–Rao bound for range, angle and polarization estimation is also provided. Numerical experiments demonstrate the superiorities of the proposed approaches. Specifically, two targets with identical range and close angles are effectively distinguished.

High Performance Hierarchical Tucker Tensor Learning Using GPU Tensor Cores

Extracting information from large-scale high-dimensional data is a fundamentally important task in high performance computing, where the hierarchical Tucker (HT) tensor learning approach (learning a tensor-tree structure) has been widely used in many applications. However, HT tensor learning algorithms are compute-intensive due to the “ <i>curse of dimensionality</i> ,” i.e., the time complexity grows exponentially with the order of the data tensor. The computation of HT tensor learning algorithms boils down to tensor primitives, which are amenable to computing on GPU tensor cores. Existing work does not support HT tensor learning using GPU tensor cores. There are three main challenges to address: 1) to accelerate tensor learning primitives using GPU tensor cores; 2) to implement the tensor learning algorithms using GPU tensor cores and multiple GPUs; 3) to support large-scale data tensors exceeding the GPU memory capacity. In this paper, we present efficient HT tensor learning primitives using GPU tensor cores and demonstrate three applications. First, we utilize GPU tensor cores to optimize HT tensor learning primitives, including tensor contractions, tensor matricizations and tensor singular value decomposition (SVD). We employ the optimized primitives to optimize HT tensor decomposition algorithms for Big Data analysis. Second, we propose a novel HT tensor layer for deep neural networks, whose training process only involves a forward pass without back propagation. The forward pass consists of tensor operations, thus further exploiting the computing power of GPU tensor cores. Third, we apply the optimized primitives to develop a tensor-tree structured quantum machine learning algorithm <i>tree-tensor network (TTN)</i> . Compared with TensorLy and TensorNetwork on NVIDIA A100 GPUs, our third-order HT tensor decomposition algorithm achieves up to <inline-formula><tex-math notation="LaTeX">$8.92 \times$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$6.42 \times$</tex-math></inline-formula> speedups, respectively, and our high-order case achieves up to <inline-formula><tex-math notation="LaTeX">$32.67 \times$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$23.97 \times$</tex-math></inline-formula> speedups, respectively. Our HT tensor layer for a fully connected neural network achieves <inline-formula><tex-math notation="LaTeX">$49.2 \times$</tex-math></inline-formula> compression at the cost of 0.5% drops in accuracy and <inline-formula><tex-math notation="LaTeX">$1.42 \times$</tex-math></inline-formula> speedup compared with the implementation on CUDA cores; for the AlexNet, our HT tensor layer achieves <inline-formula><tex-math notation="LaTeX">$9.45 \times$</tex-math></inline-formula> compression at the cost of 0.8% drops in accuracy and <inline-formula><tex-math notation="LaTeX">$1.87 \times$</tex-math></inline-formula> speedup compared with the implementation on CUDA cores. Our TTN algorithm achieves up to <inline-formula><tex-math notation="LaTeX">$11.17\times$</tex-math></inline-formula> speedup compared with TensorNetwork, indicating the potential of optimized tensor learning primitives for the classical simulation of quantum machine learning algorithms.

Editorial: Tensor numerical methods and their application in scientific computing and data science

Editorial: Tensor numerical methods and their application in scientific computing and data science

Tucker Decomposition Based on a Tensor Train of Coupled and Constrained CP Cores

Many real-life signal-based applications use the Tucker decomposition of a high dimensional/order tensor. A well-known problem with the Tucker model is that its number of entries increases exponentially with its order, a phenomenon known as the “curse of the dimensionality”. The Higher-Order Orthogonal Iteration (HOOI) and Higher-Order Singular Value Decomposition (HOSVD) are known as the gold standard for computing the range span of the factor matrices of a Tucker Decomposition but also suffer from the curse. In this paper, we propose a new methodology with a similar estimation accuracy as the HOSVD with non-exploding computational and storage costs. If the noise-free data follows a Tucker decomposition, the corresponding Tensor Train (TT) decomposition takes a remarkable specific structure. More precisely, we prove that for a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> -order Tucker tensor, the corresponding TT decomposition is constituted by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q-3$</tex-math></inline-formula> 3-order TT-core tensors that follow a Constrained Canonical Polyadic Decomposition. Using this new formulation and the coupling property between neighboring TT-cores, we propose a JIRAFE-type scheme for the Tucker decomposition, called TRIDENT. Our numerical simulations show that the proposed method offers a drastically reduced complexity compared to the HOSVD and HOOI while outperforming the Fast Multilinear Projection (FMP) method in terms of estimation accuracy.

Combined Deep Priors With Low-Rank Tensor Factorization for Hyperspectral Image Restoration

Mixed noise pollution severely disturbs hyperspectral image (HSI) processing and applications. Plenty of algorithms have been developed to address this issue via two strategies: model-driven or data-driven strategy. However, model-driven methods exist in the highly time-consuming weakness of iterative optimization and unstable sensitivity of setting parameters. Data-driven methods usually perform poor due to the overfitting effects. To solve these issues, we combine both the deep denoising priors with low-rank tensor factorization (DP-LRTF) for HSI restoration. The proposed method uses Tucker tensor factorization to depict the global spectral low-rank constraint. Then the spectral orthogonal basis and spatial reduced factor are optimized by two deep denoising priors, respectively. Through this integrated strategy, we can simultaneously exploit the intrinsic low-rank property of HSI, and utilize the powerful feature extraction ability by deep learning for HSI restoration. Compared with model-driven and data-driven methods, DP-LRTF outperforms on HSI mixed noise removal and execution efficiency for various simulated/real experiments.

Tucker network: Expressive power and comparison

Deep neural networks have achieved great success in solving many machine learning and computer vision problems. In this paper, we propose a deep neural network called the Tucker network derived from the Tucker format and analyze its expressive power. The results demonstrate that the Tucker network has exponentially higher expressive power than the shallow network. In other words, a shallow network with an exponential width is required to realize the same score function as that computed by the Tucker network. Moreover, we discuss the expressive power between the hierarchical Tucker tensor network (HT network) and the proposed Tucker network. To generalize the Tucker network into a deep version, we combine the hierarchical Tucker format and Tucker format to propose a deep Tucker tensor decomposition. Its corresponding deep Tucker network is presented. Experiments are conducted on three datasets: MNIST, CIFAR-10 and CIFAR-100. The results experimentally validate the theoretical results and show that the Tucker network and deep Tucker network have better performance than the shallow network and HT network.

Data compression for advanced monitoring infrastructure information in power systems based on tensor decomposition

In this paper, an innovative data compression methodology based on Tucker tensor decomposition is presented. The proposed approach exploits the benefits of organizing time series in multidimensional arrays (tensors) in order to achieve higher compression ratios of the original data while preserving most of their properties and, in this form, achieving a low reconstruction error. This reorganization of the data into the tensor allows the creation of correlation for heterogeneous data. Furthermore, it reduces the direct relationship between the number of columns and rows with the final size of the compressed file when the data is compressed using algorithms based on matrix-based dimensional reduction techniques, such as the Singular Value Decomposition (SVD). At the same time, the problem of missing data can be overcome since the problem is formulated as an iterative process. To demonstrate the effectiveness of the innovative algorithm proposed, two study cases from electrical networks are presented. First, the compression of real synchrophasor data acquired from one commercial Phasor Measurement Unit (PMU) measuring 3-phase voltages and frequency measurements from the electrical system of Continental Europe is presented, where a significant CR is achieved for apparently no correlated data. Then, an application to real Smart Meter measurements from the electrical utility ERCOT in the USA is also provided. Here the clustering of the data is obtained as an additional outcome of the proposed algorithm. To underline the benefits of the innovative proposed methodology in contrast to other more common decompositions such as SVD, the compression ratios and reconstruction error achieved using these two different techniques are compared. The results indicate that using Tucker decomposition, not only higher compression can be achieved, but also it is demonstrated that for SM data, additional attributes can be obtained, such as clustering.

TTDFT: A GPU accelerated Tucker tensor DFT code for large-scale Kohn-Sham DFT calculations

We present the Tucker tensor DFT (TTDFT) code which uses a tensor-structured algorithm with graphic processing unit (GPU) acceleration for conducting ground-state DFT calculations on large-scale systems. The Tucker tensor DFT algorithm uses a localized Tucker tensor basis computed from an additive separable approximation to the Kohn-Sham Hamiltonian. The discrete Kohn-Sham problem is solved using Chebyshev filtered subspace iteration method that relies on matrix-matrix multiplications of a sparse symmetric Hamiltonian matrix and a dense wavefunction matrix, expressed in the localized Tucker tensor basis. These matrix-matrix multiplication operations, which constitute the most computationally intensive step of the solution procedure, are GPU accelerated providing ∼8-fold GPU-CPU speedup for these operations on the largest systems studied. The computational performance of the TTDFT code is presented using benchmark studies on aluminum nano-particles and silicon quantum dots with system sizes ranging up to ∼7,000 atoms. Program summaryProgram Title: TTDFT: Tucker tensor density functional theory codeCPC Library link to program files:https://doi.org/10.17632/8dgmcs8ys2.1Licensing provisions: LGPLProgramming language: C/C++External routines/libraries: TuckerMPI (https://gitlab.com/tensors/TuckerMPI), cuBLAS (https://docs.nvidia.com/cuda/cublas/index.html), cuSparse (https://docs.nvidia.com/cuda/cusparse/index.html), ALGLIB (http://www.alglib.net/), Boost (https://www.boost.org/), BLAS (http://www.netlib.org/blas/), LAPACK (http://www.netlib.org/lapack/), PETSc (https://www.mcs.anl.gov/petsc), SLEPc (http://slepc.upv.es)Nature of problem: Real-space Kohn-Sham density functional theory calculations using localized Tucker tensor basis.Solution method: We present a real-space Kohn-Sham density functional theory code based on tensor-structured techniques with GPU acceleration. Tensor-structured techniques are adopted for computing a Tucker tensor basis, representing the eigenfunctions of an additive separable approximation to the Kohn-Sham Hamiltonian. The Tucker tensor basis is further localized using L1 regularization to improve the sparsity of the Kohn-Sham Hamiltonian matrix, and improve the computational efficiency and parallel scalability of the proposed algorithm. The solution to the Kohn-Sham problem in the localized Tucker tensor basis is computed using the Chebyshev filtered subspace iteration (ChFSI) method.Additional comments including restrictions and unusual features: The code works with Troullier-Martin (TM) pseudopotentials in Kleinman-Bylander form. The current release supports only non-periodic DFT calculations with the local density approximation (LDA) for exchange-correlation functional.This TTDFT project uses GitHub via Git, a free distributed version control software. The archived version at the time of submission of this work can be found on the CPC program library through program files DOI provided above. The GitHub repository of this project can be found on https://github.com/ttdftdev/ttdft_public.

A Hybrid Tucker-VQ Tensor Sketch decomposition model for coding and streaming real world light fields using stack of differently focused images

• Lightfield representation, coding and streaming schemes using a stack of focal images. • Layer pattern optimization from focal stack for efficient streaming on tensor display. • Hybrid Tucker Tensor Sketch Scheme with Vector Quantization for low-rank modeling. • A single integrated, adaptable and flexible system to realize a range of bitrates. Computational multi-view displays involving light fields are a fast emerging choice for 3D presentation of real-world scenes. Tensor autostereoscopic glasses-free displays use just few light attenuating layers in front of a backlight to output high quality light field. We propose three novel schemes, Focal Stack - Hybrid Tucker-TensorSketch Vector Quantization (FS-HTTSVQ), Focal Stack - Tucker-TensorSketch (FS-TTS), and Focal Stack - Tucker Alternating Least-Squares (FS-TALS), for efficient representation, streaming and coding of light fields using a stack of differently focused images. Working with a focal stack instead of the entire light field majorly reduces the data acquisition cost as well as the computation and processing cost. Extensive experiments with real world light field focal stacks demonstrate that proposed novel one-pass Tucker decomposition using TensorSketch with hybrid vector quantization in FS-HTTSVQ, compactly represents the approximated focal stack in codebook form for better transmission and streaming. Encoding with High Efficiency Video Coding (HEVC) eliminates all intrinsic redundancies present in the approximated focal stack. Resultant low-rank approximated and coded focal stack is then employed to analytically optimize layer patterns for the tensor display. The complete end-to-end light field processing pipelines flexibly work for multiple bitrates and are adaptable for a variety of multi-view autostereoscopic platforms. Our schemes exhibit note-worthy performances on focal stacks compared to direct encoding of an entire light field using a standard codec like HEVC.

A sparse and spectral smooth regularized low-rank tensor decomposition method for hyperspectral target detection

ABSTRACT In recent years, hyperspectral target detection methods have been widely used in military or civilian fields. Many high-performance hyperspectral target detection methods have been proposed, and tensor decomposition-based methods have attracted the attention of researchers. However, the non-uniqueness of tensor rank and the interference of noise will reduce the effect of target detection. In order to solve these problems, a sparse and spectral smooth regularized low-rank tensor decomposition method for hyperspectral target detection is proposed in this paper. The proposed method adds the low-rank regularization to the factor matrix of the tensor decomposition framework, which can reduce the adverse effect of information redundancy on the detection effect of the algorithm. Furthermore, the spectral smooth regularization is added to the spectral factor matrix to suppress noise and the sparse regularization is added to the core tensor to solve the problems of non-uniqueness of the Tucker tensor decomposition, which can improve the effect of target detection. On this basis, it simplifies the calculation process and reduces the complexity of the algorithm by using the conjugate gradient algorithm and the tensor Kronecker product. In this paper, the algorithm is tested on four real hyperspectral data sets and compared with six state-of-the-art algorithms. The experimental results show that targets detected by the proposed method are more obvious and the background is more pure.