Higher Order Singular Value Decomposition Research Articles

Denoise ultra-low-field 3D magnetic resonance images using a joint signal-image domain filter

Ultra-low-field magnetic resonance imaging (MRI) could suffer from heavy uncorrelated noise, and its removal could be a critical post-processing task. As a primary source of interference, Gaussian noise could corrupt the sampled MR signal (k-space data), especially at lower B0 field strength. For this reason, we consider both signal and image domains by proposing a new joint filter characterized by a Kalman filter with linear prediction and a nonlocal mean filter with higher-order singular value decomposition (HOSVD) for denoising 3D MR data. The Kalman filter first attenuates the noise in k-space, and then its reconstruction images are used to guide HOSVD denoising process with exploring self-similarity among 3D structures. The clearer prefiltered images could also generate improved HOSVD learned bases used to transform the noise corrupted patch groups in the original MR data. The flexibility of proposed method is also demonstrated by integrating other k-space filters into the algorithm scheme. Experimental data includes simulated MR images with the varying noise level and real MR images obtained from our 50 mT MRI scanner. The results reveal that our method has a better noise-removal ability and introduces lesser unexpected artifacts than other related MRI denoising approaches.

Optical coherence tomography image despeckling based on edge feature-guided higher-order singular value decomposition

As an emerging tomographic technique, optical coherence tomography (OCT) has been widely used in clinical practice in a short period of time. Unfortunately, the quality of OCT images is inevitably deteriorated by the coherent noise known as speckle noise. To effectively reduce the speckle noise in OCT images while preserving local structures, we present a speckle noise reduction method based on feature-guided higher-order singular value decomposition (HOSVD). Specifically, the grouped 3D tensors are first decomposed by HOSVD. And then, the corresponding core tensors are thresholded according to the Eckart-Young-Mirsky theorem and are shrunk by the dectected edge features, which are defined as the local mean absolute deviation (LMAD). Finally, the filtered OCT images can be obtained by the inverse transform and an aggregation strategy. Compared with several state-of-the-art methods, the proposed method has better performance on despeckling OCT images in terms of both speckle noise reduction and edge preservation.

Compression of Hyper Spectral Images using Tensor Decomposition Methods

Tensor decomposition methods have beenrecently identified as an effective approach for compressing high-dimensional data. Tensors have a wide range of applications in numerical linear algebra, chemo metrics, data mining, signal processing, statics, and data mining and machine learning. Due to the huge amount of information that the hyper spectral images carry, they require more memory to store, process and send. We need to compress the hyper spectral images in order to reduce storage and processing costs. Tensor decomposition techniques can be used to compress the hyper spectral data. The primary objective of this work is to utilize tensor decomposition methods to compress the hyper spectral images. This paper explores three types of tensor decompositions: Tucker Decomposition (TD_ALS), CANDECOMP/PARAFAC (CP) and Tucker_HOSVD (Higher order singular value Decomposition) and comparison of these methods experimented on two real hyper spectral images: the Salinas image (512 x 217 x 224) and Indian Pines corrected (145 x 145 x 200). The PSNR and SSIM are used to evaluate how well these techniques work. When compared to the iterative approximation methods employed in the CP and Tucker_ALS methods, the Tucker_HOSVD method decomposes the hyper spectral image into core and component matrices more quickly. According to experimental analysis, Tucker HOSVD's reconstruction of the image preserves image quality while having a higher compression ratio than the other two techniques.

High-order singular value decomposition of contrast pulsing sequences for improved clutter suppression

Contrast-enhanced ultrasound is a diagnostic tool used to visualize blood flow in the cardiovascular system. The use of ultrasound contrast agent (microbubbles) in combination with contrast pulsing scheme (CPS) improves the sensitivity and specificity of ultrasound flow imaging by enhancing the signal in the blood compartment. The commonly used CPS are pulse inversion (PI), amplitude modulation (AM), and amplitude-modulated pulse inversion (AMPI). Using differences in phase or amplitude of multiple pulses, the linear tissue clutter signal can be suppressed. However, this process can be degraded by motion or non-linear propagation of the ultrasound wave. These effects cause the cancellation of linear clutter signal to be ineffective We propose using higher-order singular value decomposition (HOSVD) with spatial, temporal, and pulsing dimensions as the input to improve clutter suppression under the conditions of motion and non-linear propagation. We performed systematic in-vitro- experiment emulating these conditions, as well as in-vivo cardiac measurements. The results showed that HOSVD increases the clutter suppression of all the 3 CPS compared to the conventional linear processing. The improvement of clutter reduction could be beneficial to various cardiac evaluation like myocardial perfusion or intra ventricular flow assessment.

Long-Term Postoperative Pain Prediction Using Higher-Order Singular Value Decomposition of Intraoperative Physiological Responses: Prospective Cohort Study.

BackgroundLong-term postoperative pain (POP) and patient responses to pain relief medications are not yet fully understood. Although recent studies have developed an index for the nociception level of patients under general anesthesia based on multiple physiological parameters, it remains unclear whether these parameters correlate with long-term POP outcomes.ObjectiveThis study aims to extract unbiased and interpretable descriptions of how the dynamics of physiological parameters change over time and across patients in response to surgical procedures and intraoperative medications using a multivariate-temporal analysis. We demonstrated that there is an association (correlation) between the main features of intraoperative physiological responses and long-term POP, which has a predictive value, even without claiming causality.MethodsWe proposed a complex higher-order singular value decomposition method to accurately decompose patients’ physiological responses into multivariate structures evolving over time. We used intraoperative vital signs of 175 patients from a mixed surgical cohort to extract three interconnected, low-dimensional, complex-valued descriptions of patients’ physiological responses: multivariate factors, reflecting subphysiological parameters; temporal factors, reflecting common intrasurgery temporal dynamics; and patients’ factors, describing interpatient changes in physiological responses.ResultsAdoption of the complex higher-order singular value decomposition method allowed us to clarify the dynamic correlation structure included in the intraoperative physiological responses. Instantaneous phases of the complex-valued physiological responses of 242 patients within the subspace of principal descriptors enabled us to discriminate between mild and not-mild (moderate-severe) levels of pain at postoperative days 30 and 90. Following rotation of physiological responses before projection to align with the common multivariate-temporal dynamic, the method achieved an area under curve for postoperative day 30 and 90 outcomes of 0.81 and 0.89 for thoracic surgery, 0.87 and 0.83 for orthopedic surgery, 0.87 and 0.88 for urological surgery, 0.86 and 1 for colorectal surgery, 1 and 1 for transplant surgery, and 0.83 and 0.92 for pancreatic surgery, respectively.ConclusionsBy categorizing patients into different surgical groups, we identified significant surgery-related principal descriptors. Each of them potentially encodes different surgical stimulation. The dynamics of patients’ physiological responses to these surgical events were linked to long-term POP development.

Array antenna failure robust compensation via tensor Hankelization in MIMO radar for DOA estimation

Utilizing low-rank tensor completion (LRTC) provides great success in the recovery of missing entries by exploiting the multidimensional structure. However, the assumption of most LRTC methods that the observed samples are randomly distributed is violated in multiple-input multiple-output (MIMO) radar under antenna failure, in which some fibers or slices are missing in the third-order measurement tensor. An antenna failure compensation method based on Hankel low-rank tensor recovery is proposed for robust direction-of-arrival (DOA) estimation in MIMO radar. To reduce computational burdens and noise sensitivity, we first use higher-order singular value decomposition (HOSVD) to lower the dimensions of the observations. Then, each frontal slice of the reduced-dimensional tensor is mapped into twofold Hankel structure to better reveal the relationship among different fibers. We further explore the Hankelization operation in a tensor manner to constitute high-dimensional structured Hankel tensor by concatenating the subtensors to capture the slice correlations. Because of the stronger low-rank property and the lack of entirely missing fibers or slices, the LRTC method can be applied to this structured Hankel tensor to recover structurally incomplete tensor. Simulation experiments verify that the proposed method achieves the robust compensation of faulty antennas in MIMO radar, ensuring remarkable DOA estimation performance.

Tensor Dictionary Self-Taught Learning Classification Method for Hyperspectral Image

Precise object classification based on Hyperspectral imagery with limited training data presents a challenging task. We propose a tensor-based dictionary self-taught learning (TDSL) classification method to provide some insight into these challenges. The idea of TDSL is to utilize a small amount of unlabeled data to improve the supervised classification. The TDSL trains tensor feature extractors from unlabeled data, extracts joint spectral-spatial tensor features and performs classification on the labeled data set. These two data sets can be gathered over different scenes even by different sensors. Therefore, TDSL can complete cross-scene and cross-sensor classification tasks. For training tensor feature extractors on unlabeled data, we propose a sparse tensor-based dictionary learning algorithm for three-dimensional samples. In the algorithm, we initialize dictionaries using Tucker decomposition and update these dictionaries based on the K higher-order singular value decomposition. These dictionaries are feature extractors, which are used to extract sparse joint spectral-spatial tensor features on the labeled data set. To provide classification results, the support vector machine as the classifier is applied to the tensor features. The TDSL with the majority vote (TDSLMV) can reduce the misclassified pixels in homogenous regions and at the edges of different homogenous regions, which further refines the classification. The proposed methods are evaluated on Indian Pines, Pavia University, and Houston2013 datasets. The classification results show that TDSLMV achieves as high as 99.13%, 99.28%, and 99.76% accuracies, respectively. Compared with several state-of-the-art methods, the classification accuracies of the proposed methods are improved by at least 2.5%.

Tensor Network Calculation of the Logarithmic Correction Exponent in the XY Model

We study the logarithmic correction to the scaling of the first Lee-Yang (LY) zero in the classical $XY$ model on square lattices by using tensor renormalization group methods. In comparing the higher-order tensor renormalization group (HOTRG) and the loop-optimized tensor network renormalization (LoopTNR), we find that the entanglement filtering in LoopTNR is crucial to gaining high accuracy for the characterization of the logarithmic correction, while HOTRG still proposes approximate bounds for the zero location associated with two different bond-merging algorithms of the higher-order singular value decomposition and the oblique projectors. Using the LoopTNR data computed up to the system size of $L=1024$ in the $L \times L$ lattices, we estimate the logarithmic correction exponent $r = -0.0643(9)$ from the extrapolation of the finite-size effective exponent, which is comparable to the renormalization group prediction of $r = -1/16$.

Nonintrusive model order reduction for cross-diffusion systems

In this paper, we investigate tensor based nonintrusive reduced-order models (ROMs) for parametric cross-diffusion equations. The full-order model (FOM) consists of ordinary differential equations (ODEs) in matrix or tensor form resulting from finite difference discretization of the differential operators by taking the advantage of Kronecker structure. The matrix/tensor differential equations are integrated in time with the implicit–explicit (IMEX) Euler method. The reduced bases, relying on a finite sample set of parameter values, are constructed in form of a two-level approach by applying higher-order singular value decomposition (HOSVD) to the space–time snapshots in tensor form, which leads to a large amount of computational and memory savings. The nonintrusive reduced approximation for an arbitrary parameter value is obtained through tensor product of the reduced basis by the parameter dependent core tensor that contains the reduced coefficients. The reduced coefficients for new parameter values are computed with the radial basis functions. The efficiency of the proposed method is illustrated through numerical experiments for two-dimensional Schnakenberg and three-dimensional Brusselator cross-diffusion equations. The spatiotemporal patterns are accurately predicted by the reduced-order models with speedup factors of orders two and three over the full-order models.

Accelerating Dynamic MRI Reconstruction Using Adaptive Sequentially Truncated Higher-Order Singular Value Decomposition.

Dynamic magnetic resonance imaging (dMRI) plays an important role in cardiac perfusion and functional clinical exams. However, further applications are limited by the speed of data acquisition. A low-rank plus sparse decomposition approach is often introduced for reconstructing dynamic magnetic resonance imaging (dMRI) from highly under-sampling K-space data. In this paper, the reconstruction problem of DMR is transformed into a low-rank tensor plus sparse tensor recovery problem. A sequentially truncated higher-order singular value decomposition method is proposed to quickly approximate the low-rank tensor space structure and learn sparse components by adding a tensor kernel norm to the low-rank tensor and a l1 norm to the sparse tensor to constrain the two parts at the same time. The optimization problem is solved by using the iterative soft-thresholding algorithm; therefore, under the premise of ensuring the accuracy of the data, the amount of computation can be effectively reduced. Compared with the state-of-the-art methods, the experimental results show that the proposed method can achieve better performance in terms of reconstruction speed and reconstruction quality on 3D and 4D dMRI datasets. The multidimensional MRI time series is represented by the tensor tool and decomposed into low rank tensor terms and sparse tensor terms. The low rank spatial structure is captured by the adaptive ST-HOSVD for fast approximation and the sparse component is constrained efficiently with a sparsity transform and l1 norm. The optimization problem is solved by an iterative soft-thresholding algorithm. Through extensive 3D and 4D dMRI experiments, it is demonstrated that our method can achieve superior reconstruction performance and efficiency compared with the other three state-of-theart methods reported in the literature.

Compressed sensing based dynamic MR image reconstruction by using 3D-total generalized variation and tensor decomposition: k-t TGV-TD

PurposeCompressed Sensing Magnetic Resonance Imaging (CS-MRI) is a promising technique to accelerate dynamic cardiac MR imaging (DCMRI). For DCMRI, the CS-MRI usually exploits image signal sparsity and low-rank property to reconstruct dynamic images from the undersampled k-space data. In this paper, a novel CS algorithm is investigated to improve dynamic cardiac MR image reconstruction quality under the condition of minimizing the k-space recording.MethodsThe sparse representation of 3D cardiac magnetic resonance data is implemented by synergistically integrating 3D total generalized variation (3D-TGV) algorithm and high order singular value decomposition (HOSVD) based Tensor Decomposition, termed k-t TGV-TD method. In the proposed method, the low rank structure of the 3D dynamic cardiac MR data is performed with the HOSVD method, and the localized image sparsity is achieved by the 3D-TGV method. Moreover, the Fast Composite Splitting Algorithm (FCSA) method, combining the variable splitting with operator splitting techniques, is employed to solve the low-rank and sparse problem. Two different cardiac MR datasets (cardiac perfusion and cine MR datasets) are used to evaluate the performance of the proposed method.ResultsCompared with the state-of-art methods, such as k-t SLR, 3D-TGV, HOSVD based tensor decomposition and low-rank plus sparse method, the proposed k-t TGV-TD method can offer improved reconstruction accuracy in terms of higher peak SNR (PSNR) and structural similarity index (SSIM). The proposed k-t TGV-TD method can achieve significantly better and stable reconstruction results than state-of-the-art methods in terms of both PSNR and SSIM, especially for cardiac perfusion MR dataset.ConclusionsThis work proved that the k-t TGV-TD method was an effective sparse representation way for DCMRI, which was capable of significantly improving the reconstruction accuracy with different acceleration factors.

Tensor product model HOSVD based polytopic LPV controller for suspension anti-vibration system

This paper presents a polytopic linear parameter varying (LPV) controller design methodology for nonlinear anti-vibration suspension based on stochastic road identification. As the main nonlinear component in semi-active suspension, the continuous damping control (CDC) damper value is mapped by damping velocity and control current through a bench experiment. linear parameter varying gain-scheduled method is applied for dealing with the nonlinear deterministic model. As the uncertainties caused by road stochastic excitation to suspension cannot be ignored, it is essential to identify the excitation signal as a measurable variable parameter. Empirical-mode-decomposition (EMD) and support vector machine (SVM) are utilized to identify and classify the road stochastic signal input into standard level, so polytopic LPV controller can be designed with CDC damper velocity, control current, and road level as variable parameters. Meanwhile the exponential increase of high-order plant elements in multi-parameter LPV model makes it too complicated for real-time computing. Hence the tensor product model transformation is utilized to identify the orthogonal basis of system plant so that low-rank approximation of it can be implemented by truncated high-order singular value decomposition (T−HOSVD) method. Real-time simulation shows the performance and feasibility of controller, which can efficaciously identify the road stochastic excitation as measurable variable parameters for nonlinear suspension polytopic LPV control.

Unsupervised and Self-Supervised Tensor Train for Change Detection in Multitemporal Hyperspectral Images

Remote sensing change detection (CD) using multitemporal hyperspectral images (HSIs) provides detailed information on spectral–spatial changes and is useful in a variety of applications such as environmental monitoring, urban planning, and disaster detection. However, the high dimensionality and low spatial resolution of HSIs do not only lead to expensive computation but also bring about inter-class homogeneity and inner-class heterogeneity. Meanwhile, labeled samples are difficult to obtain in reality as field investigation is expensive, which limits the application of supervised CD methods. In this paper, two algorithms for CD based on the tensor train (TT) decomposition are proposed and are called the unsupervised tensor train (UTT) and self-supervised tensor train (STT). TT uses a well-balanced matricization strategy to capture global correlations from tensors and can therefore effectively extract low-rank discriminative features, so the curse of the dimensionality and spectral variability of HSIs can be overcome. In addition, the two proposed methods are based on unsupervised and self-supervised learning, where no manual annotations are needed. Meanwhile, the ket-augmentation (KA) scheme is used to transform the low-order tensor into a high-order tensor while keeping the total number of entries the same. Therefore, high-order features with richer texture can be extracted without increasing computational complexity. Experimental results on four benchmark datasets show that the proposed methods outperformed their tensor counterpart, the tucker decomposition (TD), the higher-order singular value decomposition (HOSVD), and some other state-of-the-art approaches. For the Yancheng dataset, OA and KAPPA of UTT reached as high as 98.11% and 0.9536, respectively, while OA and KAPPA of STT were at 98.20% and 0.9561, respectively.

An Efficient Transform based Low Rank Tensor Completion to Extreme Visual Recovery

Objective: To propose an optimization approach in recovering of the corrupted tensors in the high dimensional real time data. Methods: The recovering of corrupted tensors is performed by low-rank tensor completion methods. The tensor decomposition methods are used in tensor completion methods. These Tensor decomposition methods; candecomp / parafac (CP), tucker and higher-order Singular Value Decomposition (HoSVD) are used to minimize the rank of a tensor data. The limitations are in finding the rank of a tensor. Findings: The recovered data using the lifting transform induced tensor- Singular Value Decomposition (t-SVD) technique were assessed utilizing the Peak Signal to Noise Ratio (PSNR), Structural Similarity (SSIM), Naturalness Image Quality Evaluator (NIQE), and Perceptual Image Quality Evaluator (PIQE). When compared to state-of-the-art approaches, the low rank assumption condition with the lifting transform consideration gave good data recovery for every missing ratio. Novelty: The missing data is calculated by lifting polyphase structures by utilizing the available data. The polyphase structures are splitting the value into equivalent multiple triangular matrices, these are processed with the t-SVD to have the better approximation tensor rank. Keywords: Tensor Completion; Transformbased Optimization; 5/3 Lifting Wavelet Transform; Lowrank tensor completion; tSVD

An Ultrasonic Reverse Time Migration Imaging Method Based on Higher-Order Singular Value Decomposition.

An ultrasonic reverse time migration imaging method, based on high-order singular value decomposition, is proposed in the study to solve the problems of low signal-to-noise ratio (SNR) and excessive artifacts in defect ultrasonic detection imaging results of materials with high noise levels. In this method, based on the 3D structural properties of the ultrasonic full-matrix capture data, higher-order singular value decomposition is directly performed with the 3D data. The method overcomes the difficulty in selecting the number of singular values in the original singular value decomposition noise-reduction algorithm and realizes the one-step noise reduction processing of all the signals. Subsequently, the reverse time migration imaging is performed in the frequency domain, and high-quality acoustic images are obtained. The effects of the number of array elements, the center frequency of the excitation signal, and the number of defects on the denoising effect of the algorithm are investigated. It was experimentally demonstrated that the method could suppress the interference of noise signals and significantly improve the imaging SNR compared with total focusing method and the reverse time migration.

A weighted sparse coding model on product Grassmann manifold for video-based human gesture recognition.

It is a challenging problem to classify multi-dimensional data with complex intrinsic geometry inherent, such as human gesture recognition based on videos. In particular, manifold structure is a good way to characterize intrinsic geometry of multi-dimensional data. The recently proposed sparse coding on Grassmann manifold shows high discriminative power in many visual classification tasks. It represents videos on Grassmann manifold using Singular Value Decomposition (SVD) of the data matrix by vectorizing each image in videos, while vectorization destroys the spatial structure of videos. To keep the spatial structure of videos, they can be represented as the form of data tensor. In this paper, we firstly represent human gesture videos on product Grassmann manifold (PGM) by Higher Order Singular Value Decomposition (HOSVD) of data tensor. Each factor manifold characterizes features of human gesture video from different perspectives and can be understood as appearance, horizontal motion and vertical motion of human gesture video respectively. We then propose a weighted sparse coding model on PGM, where weights can be understood as modeling the importance of factor manifolds. Furthermore, we propose an optimization algorithm for learning coding coefficients by embedding each factor Grassmann manifold into symmetric matrices space. Finally, we give a classification algorithm, and experimental results on three public datasets show that our method is competitive to some relevant excellent methods.

Deep Learning-Based Diffusion-Weighted Magnetic Resonance Imaging in the Diagnosis of Ischemic Penumbra in Early Cerebral Infarction.

The prefiltered image was imported into the local higher-order singular value decomposition (HOSVD) denoising algorithm (GL-HOSVD)-optimized diffusion-weighted imaging (DWI) image, which was compared with the deviation correction nonlocal mean (NL mean) and low-level edge algorithm (LR + edge). Regarding the peak signal-to-noise ratio (PSNR), root mean square error (RMSE), sensitivity, specificity, accuracy, and consistency, the application effect of the GL-HOSVD algorithm in DWI was investigated, and its adoption effect in the examination of ischemic penumbra (IP) of early acute cerebral infarction (ACI) patients was evaluated. A total of 210 patients with ACI were selected as the research subjects, who were randomly rolled into two groups. Those who were checked by conventional DWI were set as the control group, and those who used DWI based on the GL-HOSVD denoising algorithm were set as the observation group, with 105 people in each. Positron emission tomography (PET) test results were set as the gold standard to evaluate the application value of the two examination methods. It was found that under different noise levels, the peak signal-to-noise ratio (PSNR) of the GL-HOSVD algorithm and the root mean square error (RMSE) of the FA parameter were better than those of the nonlocal means (NL-means) of deviation correction and low-rank edge algorithm (LR + edge). The sensitivity, specificity, accuracy, and consistency (8.76%, 81.25%, 87.62%, and 0.52) of the observation group were higher than those of the control group (57.78%, 53.33%, 57.14%, and 0.35) (P < 0.05). Moreover, the apparent diffusion coefficient (ADC) of the DWI images of the observation group was basically consistent with that of the PET images, while the control group had a poor display effect and low definition. In summary, under different noise levels, the GL-HOSVD algorithm had a good denoising effect and greatly reduced fringe artifacts. DWI after denoising had high sensitivity, specificity, accuracy, and consistency in the detection of IP, which was worthy of clinical application and promotion.

High-fidelity noise-reconstructed empirical mode decomposition for mechanical multiple and weak fault extractions

The premise to ensure the safe operation of rotating machinery is to accurately and timely capture all kinds of damages and fault signatures, whose challenging issues are the multiple and weak faults. Ensemble noise-reconstructed empirical mode decomposition (ENEMD) is a smart method of adaptively decomposing and denoising for mechanical fault diagnosis. However, the original ENEMD and its derivative methods suffer from the drawbacks of critical noise estimation on the high accuracy, leading to the powerless capability for accurate multiple and weak fault signature extraction. Thus, high-fidelity noise-reconstructed empirical mode decomposition (HNEMD) is proposed to overcome the drawbacks, whose compositions include: (1) The cepstral neighboring coefficient editing is proposed to obtain the pre-whitening signal with the actual white noise, from which the major noise can be well purified by the minimax thresholding. (2) The high order singular value decomposition (HOSVD) local reconstruction is developed to estimate the minor noise from the pre-characterizing signal, where the tensor with the reasonable singular order is constructed by the sliding window and Hankel matrix. (3) The high-fidelity noise recovered by the major noise and the minor noise is reconstructed and combined with the basic ENEMD algorithm for accurate signature extraction, especially for the multiple or/and weak fault ones. Three repeatable simulations are analyzed to illustrate the signature extraction capability and noise estimation process of this method. Moreover, the effective detections of weak and multiple faults from a hot strip finishing mill gearbox and an aerospace bearing further validate the feasibility of the proposed method.

Highly undersampling dynamic cardiac MRI based on low-rank tensor coding

Dynamic cardiac magnetic resonance imaging (CMRI) is an important tool for the non-invasive assessment of cardiovascular disease. However, dynamic CMRI suffers from long acquisition times due to the need of obtaining images with high temporal and spatial resolution, whole-heart coverage. Conventionally, a multidimensional dataset in dynamic CMRI is treated as a series of two-dimensional matrices, and then various matrix/vector transforms are used to explore the sparsity of MR images. In this paper, we propose a low-rank tensor coding (LRTC) model with tensor sparsity for the application of compressive sensing (CS) in dynamic CMRI. In this framework, each group of 3D similar patches extracted from high-dimensional images is considered to be a low-rank tensor. LRTC can better capture the sparse part of dynamic CMRI and make full use of the redundancy between the feature vectors of adjacent positions. ADMM technique is introduced to tackle the proposed model, where soft threshold operator is used to solving the l1 norm relaxation. Higher-order singular value decomposition (HOSVD) is exploited to process high-dimensional tensors and mine correlations in space-time dimensions. Validations based on cardiac cine and myocardial perfusion datasets indicate that the proposed method achieved comparable reconstruction accuracy with the low-rank matrix recovery methods, and outperformed the conventional sparse recovery methods.

Distributed Monitoring of Power System Oscillations Using Multiblock Principal Component Analysis and Higher-order Singular Value Decomposition

The primary goal in the analysis of hierarchical distributed monitoring and control architectures is to study the spatiotemporal patterns of the interactions between areas or subsystems. In this paper, a novel conceptual framework for distributed monitoring of power system oscillations using multi-block principal component analysis (MB-PCA) and higher-order singular value decomposition (HOSVD) is proposed to understand, characterize, and visualize the global behavior of the power system. The proposed framework can be used to evaluate the influence of a given area or utility on the oscillatory behavior, uncover low-dimensional structures from high-dimensional data, and analyze the effects of heterogeneous data on the modal characteristics and interpretation of power system. The metrics are then investigated to examine the relationships between the dynamic patterns and participation of individual data blocks in the global behavior of the system. Practical Application of these techniques is demonstrated by case studies of two systems: a 14-machine test system and a 5449-bus 635-generator equivalent model of a large power system.