相关论文: A Tucker decomposition process for probabilistic m…

Diffusion Magnetic Resonance Imaging (dMRI) is a non-invasive tool for watching the microstructure of fibrous nerve and muscle tissue. From dMRI, it is possible to estimate 2-rank diffusion tensors imaging (DTI) fields, that are widely used…

Diffusion Magnetic Resonance Imaging (dMRI) is an imaging technique with exquisite sensitivity to the microstructural properties of heterogeneous media. The conventionally adopted acquisition schemes involving single pulsed field gradients…

The Tucker decomposition expresses a given tensor as the product of a small core tensor and a set of factor matrices. Apart from providing data compression, the construction is useful in performing analysis such as principal component…

Statistical inference on large-dimensional tensor data has been extensively studied in the literature and widely used in economics, biology, machine learning, and other fields, but how to generate a structured tensor with a target…

In this paper we present a mathematical and numerical framework for a procedure of imaging anisotropic electrical conductivity tensor by integrating magneto-acoutic tomography with data acquired from diffusion tensor imaging.…

Diffusion tensor imaging (DTI) is a widely used method for studying brain white matter development and degeneration. However, standard DTI estimation methods depend on a large number of high-quality measurements. This would require long…

Diffusion magnetic resonance imaging is an imaging technology designed to probe anatomical architectures of biological samples in an in vivo and non-invasive manner through measuring water diffusion. The contribution of this paper is…

Diffusion MRI (dMRI) is an advanced imaging technique characterizing tissue microstructure and white matter structural connectivity of the human brain. The demand for high-quality dMRI data is growing, driven by the need for better…

Statistical analysis of Diffusion Tensor Imaging (DTI) data requires a computational framework that is both numerically tractable (to account for the high dimensional nature of the data) and geometric (to account for the nonlinear nature of…

The Tucker decomposition, an extension of singular value decomposition for higher-order tensors, is a useful tool in analysis and compression of large-scale scientific data. While it has been studied extensively for static datasets, there…

The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional data approximations. In order to represent data with interpretability in data science, researchers develop data-centric skeletonized low…

Quantifying muscle tissue properties is crucial for understanding pathophysiological changes occurring in skeletal muscle (SM). In particular, T2 relaxation and diffusion MRI (dMRI) are promising techniques. However, typical methods measure…

Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…

As parallel computing trends towards the exascale, scientific data produced by high-fidelity simulations are growing increasingly massive. For instance, a simulation on a three-dimensional spatial grid with 512 points per dimension that…

We derive a CUR-type factorization for tensors in the Tucker format based on interpolatory decomposition, which we will denote as Higher Order Interpolatory Decomposition (HOID). Given a tensor $\mathcal{X}$, the algorithm provides a set of…

Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…

We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…

Magnetic resonance imaging (MRI) enables non-invasive 3D thermometry during thermal ablation of cancerous tumors. While T1 or T2 contrast MRI are relatively insensitive to temperature, techniques with greater temperature sensitivity such as…

Medical imaging studies have collected high dimensional imaging data to identify imaging biomarkers for diagnosis, screening, and prognosis, among many others. These imaging data are often represented in the form of a multi-dimensional…

The Tucker decomposition generalizes the notion of Singular Value Decomposition (SVD) to tensors, the higher dimensional analogues of matrices. We study the problem of constructing the Tucker decomposition of sparse tensors on distributed…