相关论文: Some theoretical results on tensor elliptical dist…

A fundamental problem in statistics is estimating the shape matrix of an Elliptical distribution. This generalizes the familiar problem of Gaussian covariance estimation, for which the sample covariance achieves optimal estimation error.…

This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…

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.…

This paper concerns the reconstruction of an anisotropic conductivity tensor in an elliptic second-order equation from knowledge of the so-called power density functionals. This problem finds applications in several coupled-physics medical…

Tensors are multidimensional arrays of numerical values and therefore generalize matrices to multiple dimensions. While tensors first emerged in the psychometrics community in the $20^{\text{th}}$ century, they have since then spread to…

Magnetic resonance imaging (MRI) is a crucial tool to identify brain abnormalities in a wide range of neurological disorders. In focal epilepsy MRI is used to identify structural cerebral abnormalities. For covert lesions, machine learning…

Diffusion kurtosis imaging is an extension of diffusion tensor imaging that provides scientifically and clinically valuable information about brain tissue microstructure but suffers from poor robustness to noise, especially in voxels…

The envelope of an elliptical Gaussian complex vector, or equivalently, the amplitude or norm of a bivariate normal random vector has application in many weather and signal processing contexts. We explicitly characterize its distribution in…

Magnetic resonance imaging (MRI) is the method of choice for noninvasive studies of micrometer-scale structures in biological tissues via their effects on the time/frequency-dependent ("restricted") and anisotropic self-diffusion of water.…

In past few decades, tensor algebra also known as multi-linear algebra has been developed and customized as a tool to be used for various engineering applications. In particular, with the help of a special form of tensor contracted product,…

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…

Asymptotic efficiency of targeted maximum likelihood estimators (TMLE) of target features of the data distribution relies on a a second order remainder being asymptotically negligible. In previous work we proposed a nonparametric MLE termed…

While low-rank matrix prior has been exploited in dynamic MR image reconstruction and has obtained satisfying performance, tensor low-rank models have recently emerged as powerful alternative representations for three-dimensional dynamic MR…

The estimation of the mean matrix of the multivariate normal distribution is addressed in the high dimensional setting. Efron-Morris-type linear shrinkage estimators based on ridge estimators for the precision matrix instead of the…

We propose a new distribution, called the soft tMVN distribution, which provides a smooth approximation to the truncated multivariate normal (tMVN) distribution with linear constraints. An efficient blocked Gibbs sampler is developed to…

Tractography is typically performed for each subject using the diffusion tensor imaging (DTI) data in its native subject space rather than in some space common to the entire study cohort. Despite performing tractography on a population…

The purpose of the present paper is to give unified expressions to the characteristic functions of all elliptical and related distributions. Those distributions including the multivariate elliptical symmetric distributions and some…

Thin ferromagnetic films with an interfacially induced DMI exhibit nontrivial asymmetric dispersion relations that lead to unique and useful magnonic properties. Here we derive an analytical expression for the magnon propagation angle…

This paper proposes the density and characteristic functions of a general matrix quadratic form $\mathbf{X}^{*}\mathbf{AX}$, when $\mathbf{A} = \mathbf{A}^{*}$, $\mathbf{X}$ has a matrix multivariate elliptical distribution and…

We theoretically and experimentally investigate tensor-based regression and classification. Our focus is regularization with various tensor norms, including the overlapped trace norm, the latent trace norm, and the scaled latent trace norm.…