Tensor-based Method Research Articles

A stable tensor-based method for controlled fluid simulations

The association between fluids and tensors can be observed in some practical situations, such as diffusion tensor imaging and permeable flow. For simulation purposes, tensors may be used to constrain the fluid flow along specific directions. This requires a customized mathematical model for describing fluid motion influenced by tensor. In this work, we propose a formulation for fluid dynamics to locally change momentum, deflecting the fluid along intended paths. Building upon classical computer graphics approaches for fluid simulation, the numerical method is altered to accommodate the new formulation. Gaining control over fluid diffusion can also aid on visualization of tensor fields, where the detection and highlighting of paths of interest is often desired. Experiments show that the fluid adequately follows meaningful paths induced by the underlying tensor field, resulting in a method that is numerically stable and suitable for visualization and animation purposes.

Tensor-Based Method for Residual Water Suppression in 1H Magnetic Resonance Spectroscopic Imaging.

Magnetic resonance spectroscopic imaging (MRSI) signals are often corrupted by residual water and artifacts. Residual water suppression plays an important role in accurate and efficient quantification of metabolites from MRSI. A tensor-based method for suppressing residual water is proposed. A third-order tensor is constructed by stacking the Löwner matrices corresponding to each MRSI voxel spectrum along the third mode. A canonical polyadic decomposition is applied on the tensor to extract the water component and to, subsequently, remove it from the original MRSI signals. The proposed method applied on both simulated and in-vivo MRSI signals showed good water suppression performance. The tensor-based Löwner method has better performance in suppressing residual water in MRSI signals as compared to the widely used subspace-based Hankel singular value decomposition method. A tensor method suppresses residual water simultaneously from all the voxels in the MRSI grid and helps in preventing the failure of the water suppression in single voxels.

A regularized tensor decomposition method with adaptive rank adjustment for Compressed-Sensed-Domain background subtraction

In intelligent video surveillance, Background Subtraction is the foundation and key to the task of Moving Object Detection (MOD). Recently, the development of Compressive Sensing (CS) theory has made the Compressed-Sensed-Domain Background Subtraction (CSDBS) an interesting task and several related models have been proposed. The latest tensor-based method provides the best performance on both reconstructing video and detecting moving objects at present. Unfortunately, it just simply sets the ranks of the tensor video background fixed along all modes, which makes it impossible to obtain accurate background component when the scene is at different time or places. In this paper, we propose a Regularized Tensor Decomposition Method with Adaptive Rank Adjustment (RTDARA) for CSDBS, which can accommodate backgrounds with differently low-rank property in more scenes to a certain extent. In addition, for the model, we use a non-convex surrogate of the rank instead of the convex nuclear norm. Finally, we develop a fast implementation using the alternative direction multiplier method (ADMM) to solve the proposed model. A large number of experimental results have shown that, on the Compressed-Sensed-Domain video in different scenes, our proposed method is superior over the existing state of the art techniques.

Irregular heartbeat classification using Kronecker Product Equations.

Cardiac arrhythmia or irregular heartbeats are an important feature to assess the risk on sudden cardiac death and other cardiac disorders. Automatic classification of irregular heartbeats is therefore an important part of ECG analysis. We propose a tensor-based method for single- and multi-channel irregular heartbeat classification. The method tensorizes the ECG data matrix by segmenting each signal beat-by-beat and then stacking the result into a third-order tensor with dimensions channel × time × heartbeat. We use the multilinear singular value decomposition to model the obtained tensor. Next, we formulate the classification task as the computation of a Kronecker Product Equation. We apply our method on the INCART dataset, illustrating promising results.

Ventricular shape and relative position abnormalities in preterm neonates.

Recent neuroimaging findings have highlighted the impact of premature birth on subcortical development and morphological changes in the deep grey nuclei and ventricular system. To help characterize subcortical microstructural changes in preterm neonates, we recently implemented a multivariate tensor-based method (mTBM). This method allows to precisely measure local surface deformation of brain structures in infants. Here, we investigated ventricular abnormalities and their spatial relationships with surrounding subcortical structures in preterm neonates. We performed regional group comparisons on the surface morphometry and relative position of the lateral ventricles between 19 full-term and 17 preterm born neonates at term-equivalent age. Furthermore, a relative pose analysis was used to detect individual differences in translation, rotation, and scale of a given brain structure with respect to an average. Our mTBM results revealed broad areas of alterations on the frontal horn and body of the left ventricle, and narrower areas of differences on the temporal horn of the right ventricle. A significant shift in the rotation of the left ventricle was also found in preterm neonates. Furthermore, we located significant correlations between morphology and pose parameters of the lateral ventricles and that of the putamen and thalamus. These results show that regional abnormalities on the surface and pose of the ventricles are also associated with alterations on the putamen and thalamus. The complementarity of the information provided by the surface and pose analysis may help to identify abnormal white and grey matter growth, hinting toward a pattern of neural and cellular dysmaturation.

Performance measure of switched control systems based on covariance tensor approach

In this paper, controller performance measure is considered for switched systems. The covariance tensor-based method is proposed for the controller performance measure for this systems evolution with the discrete-valued switching dynamics and local models for continuous dynamics. We define a measurement tensor to construct the measured process outputs data, and employ the data processing technique of higher-order singular value decomposition. Applying the higher-order singular value decomposition, we can obtain the sets of singular values from the measurement tensor, which are used jointly to evaluate the controller performance of the overall switched systems significantly. We develop the covariance tensor-based performance assessment method for the multivariate switched control systems with characteristic information being mined from the measurement tensor and derive the calculation approach base on the sets of singular values from the measurement tensor. It is shown that by applying higher-order singular value decomposition for measured outputs tensor data, the performance assessment results can exactly reflect the controller performance under the overall dynamical process. Finally, two cases study of the numerical simulation examples and a typical industrial process system well demonstrate the effectiveness of the proposed method.

Tensor-Based Dictionary Learning for Spectral CT Reconstruction

Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a tensor-based dictionary learning method for spectral CT reconstruction. In our method, tensor patches are extracted from an image tensor, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a tensor-based dictionary is trained, in which each atom is a rank-one tensor. Then, the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed tensor-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods.

A Tensor Decomposition-Based Approach for Detecting Dynamic Network States From EEG.

The purpose of this paper is to understand the dynamics of FC for understanding the formation and dissolution of networks of the brain. In this paper, we introduce a two-step approach to characterize the dynamics of functional connectivity networks (FCNs) by first identifying change points at which the network connectivity across subjects shows significant changes and then summarizing the FCNs between consecutive change points. The proposed approach is based on a tensor representation of FCNs across time and subjects yielding a four-mode tensor. The change points are identified using a subspace distance measure on low-rank approximations to the tensor at each time point. The network summarization is then obtained through tensor-matrix projections across the subject and time modes. The proposed framework is applied to electroencephalogram (EEG) data collected during a cognitive control task. The detected change-points are consistent with a priori known ERN interval. The results show significant connectivities in medial-frontal regions which are consistent with widely observed ERN amplitude measures. The tensor-based method outperforms conventional matrix-based methods such as singular value decomposition in terms of both change-point detection and state summarization. The proposed tensor-based method captures the topological structure of FCNs which provides more accurate change-point-detection and state summarization.

Joint Channel Estimation for Three-Hop MIMO Relaying Systems

We propose a novel joint channel estimator for a relaying MIMO communication system. Considering a three-hop relaying protocol, our combined alternating least squares (Comb-ALS) algorithm obtains cooperative diversity by fully exploiting the tensor algebraic structures of the available cooperative MIMO links. This is achieved by coupling the tensor data for the different relay-assisted links to iteratively estimate the channel matrices. Simulation results corroborate the effectiveness of the proposed tensor-based joint channel estimator in comparison with a sequential tensor-based method and a sequential LS estimator.

Uncorrelated multiway discriminant analysis for motor imagery EEG classification.

Motor imagery-based brain-computer interfaces (BCIs) training has been proved to be an effective communication system between human brain and external devices. A practical problem in BCI-based systems is how to correctly and efficiently identify and extract subject-specific features from the blurred scalp electroencephalography (EEG) and translate those features into device commands in order to control external devices. In real BCI-based applications, we usually define frequency bands and channels configuration that related to brain activities beforehand. However, a steady configuration usually loses effects due to individual variability among different subjects in practical applications. In this study, a robust tensor-based method is proposed for a multiway discriminative subspace extraction from tensor-represented EEG data, which performs well in motor imagery EEG classification without the prior neurophysiologic knowledge like channels configuration and active frequency bands. Motor imagery EEG patterns in spatial-spectral-temporal domain are detected directly from the multidimensional EEG, which may provide insights to the underlying cortical activity patterns. Extensive experiment comparisons have been performed on a benchmark dataset from the famous BCI competition III as well as self-acquired data from healthy subjects and stroke patients. The experimental results demonstrate the superior performance of the proposed method over the contemporary methods.

Robust Framework of Single-Frame Face Superresolution Across Head Pose, Facial Expression, and Illumination Variations

This paper presents a robust framework to solve the face hallucination problem across multiple factors, i.e., different expressions, head poses, and illuminations. It proposes a redundant transformation with diagonal loading for modeling the mappings among different new face factors, and a local reconstruction with geometry and position constraints for incorporating image details in the new factor spaces. Our proposed redundant and sparse strategies are discussed, and the experiments indicate that it is not necessary to adopt sparse representation in the proposed framework. The experimental results demonstrate that the proposed framework offers robustness when dealing with the inputs that have different expressions, head poses, and illuminations compared with the state-of-the-art methods, can generate high-resolution face images with better image qualities than the hierarchical tensor-based method, and improves the state of the art from single one output to multiple outputs with new factors.

Getting the best value from gravity gradiometry

The critically important steps to get best value from your gravity gradiometry data, assuming your contractor has done his job well in designing and acquiring the data, is the preparation of the representation of the potential field gradients. The ~200 m resolving power of existing gradiometer systems approaches what is necessary for minerals applications. In particular, beyond the aircraft, the topographic surface represents the largest and most proximal density contrast encountered in an airborne survey. Hence terrain effects can have significant impact on AGG data. The critical steps are: Terrain correction and determining ‘best’ terrain densityGridding, using all the measured gradients to constrain the interpolationSmoothing/de-noising by using the 3 rd order tensor constraintsAnti-alias filtering of the gradient signals so that wave lengths are properly represented in all directionsTransformation of the gradients by integration to estimate the gravity or magnetic fieldTerrain corrections are a necessary step in the processing of observed AGG data in rugged terrain, in order to highlight subsurface density variations with a minimal overprint from the terrain. We propose a simple and rapid AGG tensor-based method to estimate an optimum bulk terrain density for subsequent terrain-correction. Each of the currently deployed systems for acquiring gradiometry is evolving driven by competition and the users’ needs. Mining applications of the technology to directly detect ore-bodies that show up as anomalies can now be successful provided the dimensions are of the order of 200 m or more. High resolution 3D geology models of operating mines can be used to calibrate gradiometry surveys

Correlation Analysis for Tensor-based Traffic Data Imputation Method

The phenomenon of missing data in traffic has a great impact on the performance of Intelligent Transportation System (ITS). Many imputation methods have been proposed to estimate the missing traffic data. Recently,a tensor-based traffic volume imputation method has been proposed. In this paper, we focus on the underlying mechanism of tensor-based method from the viewpoint of intrinsic multi-correlations/principle components of the traffic data, and try to recommend suitable tensor pattern for traffic volume imputation. Experiments on PeMS database show that the tensor-based method outperforms matrix-based methods, and using the recommended tensor pattern achieves better performances.

Multiple rank multi-linear SVM for matrix data classification

Matrices, or more generally, multi-way arrays (tensors) are common forms of data that are encountered in a wide range of real applications. How to classify this kind of data is an important research topic for both pattern recognition and machine learning. In this paper, by analyzing the relationship between two famous traditional classification approaches, i.e., SVM and STM, a novel tensor-based method, i.e., multiple rank multi-linear SVM (MRMLSVM), is proposed. Different from traditional vector-based and tensor based methods, multiple-rank left and right projecting vectors are employed to construct decision boundary and establish margin function. We reveal that the rank of transformation can be regarded as a tradeoff parameter to balance the capacity of learning and generalization in essence. We also proposed an effective approach to solve the proposed non-convex optimization problem. The convergence behavior, initialization, computational complexity and parameter determination problems are analyzed. Compared with vector-based classification methods, MRMLSVM achieves higher accuracy and has lower computational complexity. Compared with traditional supervised tensor-based methods, MRMLSVM performs better for matrix data classification. Promising experimental results on various kinds of data sets are provided to show the effectiveness of our method.

A method of two-scale analysis with micro-macro decoupling scheme: application to hyperelastic composite materials

The aim of this study is to propose a strategy for performing nonlinear two-scale analysis for composite materials with periodic microstructures (unit cells), based on the assumption that a functional form of the macroscopic constitutive equation is available. In order to solve the two-scale boundary value problems (BVP) derived within the framework of the homogenization theory, we employ a class of the micro-macro decoupling scheme, in which a series of numerical material tests (NMTs) is conducted on the unit cell model to obtain the data used for the identification of the material parameters in the assumed constitutive model. For the NMTs with arbitrary patterns of macro-scale loading, we propose an extended system of the governing equations for the micro-scale BVP, which is equipped with the external material points or, in the FEM, control nodes. Taking an anisotropic hyperelastic constitutive model for fiber-reinforced composites as an example of the assumed macroscopic material behavior, we introduce a tensor-based method of parameter identification with the `measured' data in the NMTs. Once the macro-scale material behavior is successfully fitted with the identified parameters, the macro-scale analysis can be performed, and, as may be necessary, the macro-scale deformation history at any point in the macro-structure can be applied to the unit cell to evaluate the actual micro-scale response.

White matter fiber tractography: why we need to move beyond DTI

Diffusion-based MRI tractography is an imaging tool increasingly used in neurosurgical procedures to generate 3D maps of white matter pathways as an aid to identifying safe margins of resection. The majority of white matter fiber tractography software packages currently available to clinicians rely on a fundamentally flawed framework to generate fiber orientations from diffusion-weighted data, namely diffusion tensor imaging (DTI). This work provides the first extensive and systematic exploration of the practical limitations of DTI-based tractography and investigates whether the higher-order tractography model constrained spherical deconvolution provides a reasonable solution to these problems within a clinically feasible timeframe. Comparison of tractography methodologies in visualizing the corticospinal tracts was made using the diffusion-weighted data sets from 45 healthy controls and 10 patients undergoing presurgical imaging assessment. Tensor-based and constrained spherical deconvolution-based tractography methodologies were applied to both patients and controls. Diffusion tensor imaging-based tractography methods (using both deterministic and probabilistic tractography algorithms) substantially underestimated the extent of tracks connecting to the sensorimotor cortex in all participants in the control group. In contrast, the constrained spherical deconvolution tractography method consistently produced the biologically expected fan-shaped configuration of tracks. In the clinical cases, in which tractography was performed to visualize the corticospinal pathways in patients with concomitant risk of neurological deficit following neurosurgical resection, the constrained spherical deconvolution-based and tensor-based tractography methodologies indicated very different apparent safe margins of resection; the constrained spherical deconvolution-based method identified corticospinal tracts extending to the entire sensorimotor cortex, while the tensor-based method only identified a narrow subset of tracts extending medially to the vertex. This comprehensive study shows that the most widely used clinical tractography method (diffusion tensor imaging-based tractography) results in systematically unreliable and clinically misleading information. The higher-order tractography model, using the same diffusion-weighted data, clearly demonstrates fiber tracts more accurately, providing improved estimates of safety margins that may be useful in neurosurgical procedures. We therefore need to move beyond the diffusion tensor framework if we are to begin to provide neurosurgeons with biologically reliable tractography information.

A tensor-based method for missing traffic data completion

Missing and suspicious traffic data are inevitable due to detector and communication malfunctions, which adversely affect the transportation management system (TMS). In this paper, a tensor pattern which is an extension of matrix is introduced into modeling the traffic data for the first time, which can give full play to traffic spatial–temporal information and preserve the multi-way nature of traffic data. To estimate the missing value, a tensor decomposition based Imputation method has been developed. This approach not only inherits the advantages of imputation methods based on matrix pattern for estimating missing points, but also well mines the multi-dimensional inherent correlation of traffic data. Experiments demonstrate that the proposed method achieves a better imputation performance than the state-of-the-art imputation approach even when the missing ratio is up to 90%. Furthermore, the experimental results show that the proposed method can address the extreme case where the data of one or several days are completely missing, and additionally it can be employed to recover the missing traffic data in adverse weather as well.

Integrating many co-splicing networks to reconstruct splicing regulatory modules

BackgroundAlternative splicing is a ubiquitous gene regulatory mechanism that dramatically increases the complexity of the proteome. However, the mechanism for regulating alternative splicing is poorly understood, and study of coordinated splicing regulation has been limited to individual cases. To study genome-wide splicing regulation, we integrate many human RNA-seq datasets to identify splicing module, which we define as a set of cassette exons co-regulated by the same splicing factors.ResultsWe have designed a tensor-based approach to identify co-splicing clusters that appear frequently across multiple conditions, thus very likely to represent splicing modules - a unit in the splicing regulatory network. In particular, we model each RNA-seq dataset as a co-splicing network, where the nodes represent exons and the edges are weighted by the correlations between exon inclusion rate profiles. We apply our tensor-based method to the 38 co-splicing networks derived from human RNA-seq datasets and indentify an atlas of frequent co-splicing clusters. We demonstrate that these identified clusters represent potential splicing modules by validating against four biological knowledge databases. The likelihood that a frequent co-splicing cluster is biologically meaningful increases with its recurrence across multiple datasets, highlighting the importance of the integrative approach.ConclusionsCo-splicing clusters reveal novel functional groups which cannot be identified by co-expression clusters, particularly they can grant new insights into functions associated with post-transcriptional regulation, and the same exons can dynamically participate in different pathways depending on different conditions and different other exons that are co-spliced. We propose that by identifying splicing module, a unit in the splicing regulatory network can serve as an important step to decipher the splicing code.

Robust Corner Detection Based on Image Structure

In this paper, we propose a robust corner detection method to improve both detection rate and localization accuracy by modifying the structure tensor-based corner detection method in two ways. First, we introduce a connected component analysis (CCA) method for constructing a CCA structure tensor in order to make the structure tensor adaptive to the structure of the image. Second, the normalized cross-correlation (NCC) method is applied for false corner rejection with the observation that the patch of a true corner has a distinctive characteristic compared with connected neighboring patches. The proposed method is compared with several corner detection methods over a number of images. Experimental results show that the proposed method shows better performance in terms of both detection rate and localization accuracy.

Fictitious domain method and separated representations for the solution of boundary value problems on uncertain parameterized domains

A tensor-based method is proposed for the solution of partial differential equations defined on uncertain parameterized domains. It provides an accurate solution which is explicit with respect to parameters defining the shape of the domain, thus allowing efficient a posteriori probabilistic or parametric analyses. In the proposed method, a fictitious domain approach is first adopted for the reformulation of the parametric problem on a fixed domain, yielding a weak formulation in a tensor product space (product of space functions and parametric functions). The paper is limited to the case of Neumann conditions on uncertain parts of the boundary. The Proper Generalized Decomposition method is then introduced for the construction of a tensor product approximation (separated representation) of the solution. It can be seen as an a priori model reduction technique which automatically captures reduced bases of space functions and parametric functions which are optimal for the representation of the solution. This tensor-based method is made computationally tractable by introducing separated representations of variational forms, resulting from separated representations of the parameterized indicator function of the uncertain domain. For this purpose, a method is proposed for the construction of a constrained tensor product approximation which preserves positivity and therefore ensures well-posedness of problems associated with approximate indicator functions. Moreover, a regularization of the geometry is introduced to speed up the convergence of these tensor product approximations.