Related papers: Varying coefficient model for modeling diffusion t…
Purpose: To estimate fiber-specific $T_1$ values, i.e. proxies for myelin content, in heterogeneous brain tissue. Methods: A diffusion-$T_1$ correlation experiment was carried out on an in vivo human brain using tensor-valued diffusion…
Diffusion MRI (dMRI) is the primary imaging modality used to study brain microstructure in vivo. Reliable and computationally efficient parameter inference for common dMRI biophysical models is a challenging inverse problem, due to factors…
Diffusion-weighted magnetic resonance imaging (D-MRI) is an in-vivo and non-invasive imaging technology to probe anatomical architectures of biological samples. The anatomy of white matter fiber tracts in the brain can be revealed to help…
The purpose of this work is to develop a framework for single-subject analysis of diffusion tensor imaging (DTI) data. This framework (termed TOADDI) is capable of testing whether an individual tract as represented by the major eigenvector…
We propose a new model to describe diffusion processes within active deformable media. Our general theoretical framework is based on physical and mathematical considerations, and it suggests to use diffusion tensors directly coupled to…
Diffusion MRI (dMRI) is a critical non-invasive technique to estimate fiber orientation distribution (FOD) for characterizing white matter integrity. Estimating FOD from single-shell low angular resolution dMRI (LAR-FOD) is limited by…
Tensor regression models, such as CP regression and Tucker regression, have many successful applications in neuroimaging analysis where the covariates are of ultrahigh dimensionality and possess complex spatial structures. The…
Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…
The first part of the paper is devoted to diffraction phenomena that can be expressed by fractional Fourier transforms whose orders are real numbers. According to a scalar theory, diffraction acts on the amplitude of the electric field as…
Brain network analysis plays a crucial role in diagnosing and monitoring neurodegenerative disorders such as Alzheimer's disease (AD). Existing approaches for constructing structural brain networks from diffusion tensor imaging (DTI) often…
The connectivity and structural integrity of the white matter of the brain is nowadays known to be implicated into a wide range of brain-related disorders. However, it was not before the advent of diffusion Magnetic Resonance Imaging (dMRI)…
Background: Diffusion tensor imaging (DTI) has been used to characterize forearm muscle architecture. Since only uniform sampling is performed for seed points rather than fiber tracts, the tracts may be unevenly distributed in the muscle…
Diffusion models have shown incredible capabilities as generative models; indeed, they power the current state-of-the-art models on text-conditioned image generation such as Imagen and DALL-E 2. In this work we review, demystify, and unify…
In neuroscience, functional brain connectivity describes the connectivity between brain regions that share functional properties. Neuroscientists often characterize it by a time series of covariance matrices between functional measurements…
Diffusion Tensor Imaging (DTI) provides the possibility of estimating the location and course of eloquent structures in the human brain. Knowledge about this is of high importance for preoperative planning of neurosurgical interventions and…
We present a novel method for estimation of the fiber orientation distribution (FOD) function based on diffusion-weighted Magnetic Resonance Imaging (D-MRI) data. We formulate the problem of FOD estimation as a regression problem through…
In this paper, we present a mathematical study of wave scattering by a hard elastic obstacle embedded in a soft elastic body in three dimensions. Our contributions are threefold. First, we characterize subwavelength resonances using the…
Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward…
The structure and variability of the brain's connections can be investigated via prediction of non-imaging phenotypes using neural networks. However, known neuroanatomical relationships between input features are generally ignored in…
Let $v$ be a vector field in a bounded open set $G\subset {\mathbb {R}}^d$. Suppose that $v$ is observed with a random noise at random points $X_i, i=1,...,n,$ that are independent and uniformly distributed in $G.$ The problem is to…