Related papers: Statistical Inference of Auto-correlated Eigenvalu…
In the high-dimensional landscape, addressing the challenges of covariance regression with high-dimensional covariates has posed difficulties for conventional methodologies. This paper addresses these hurdles by presenting a novel approach…
Using the replica method, we compute the statistics of the top eigenpair of diluted covariance matrices of the form $\mathbf{J} = \mathbf{X}^T \mathbf{X}$, where $\mathbf{X}$ is a $N\times M$ sparse data matrix, in the limit of large $N,M$…
Diffusion-weighted magnetic resonance imaging (DWI) and fiber tractography are the only methods to measure the structure of the white matter in the living human brain. The diffusion signal has been modelled as the combined contribution from…
We develop a general analytical and numerical framework for estimating intra- and extra-neurite water fractions and diffusion coefficients, as well as neurite orientational dispersion, in each imaging voxel. By employing a set of rotational…
We introduce a new random matrix model called distance covariance matrix in this paper, whose normalized trace is equivalent to the distance covariance. We first derive a deterministic limit for the eigenvalue distribution of the distance…
Mild Traumatic Brain Injury (mTBI) is a significant public health problem. The most troubling symptoms after mTBI are cognitive complaints. Studies show measurable differences between patients with mTBI and healthy controls with respect to…
Estimating treatment effects from observational data is of central interest across numerous application domains. Individual treatment effect offers the most granular measure of treatment effect on an individual level, and is the most useful…
Biophysical modelling of the diffusion MRI signal provides estimates of specific microstructural tissue properties. Although nonlinear optimization such as non-linear least squares (NLLS) is the most widespread method for model estimation,…
Portable, ultra-low-field (ULF) magnetic resonance imaging has the potential to expand access to neuroimaging but currently suffers from coarse spatial and angular resolutions and low signal-to-noise ratios. Diffusion tensor imaging (DTI),…
Purpose: To propose a deep learning-based reconstruction framework for ultrafast and robust diffusion tensor imaging and fiber tractography. Methods: We propose SuperDTI to learn the nonlinear relationship between diffusion-weighted images…
Data driven models for automated diagnosis in radiology suffer from insufficient and imbalanced datasets due to low representation of pathology in a population and the cost of expert annotations. Datasets can be bolstered through data…
Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays…
Diffusion-weighted MRI (DW-MRI) is used to quantitatively characterize the microscopic structure of soft tissue due to the anisotropic diffusion of water in muscle. Applications such as fiber tractography or modeling of tumor spread in soft…
We present the Score-based Autoencoder for Multiscale Inference (SAMI), a method for unsupervised representation learning that combines the theoretical frameworks of diffusion models and VAEs. By unifying their respective evidence lower…
In this paper, we study the asymptotic behavior of the extreme eigenvalues and eigenvectors of the high dimensional spiked sample covariance matrices, in the supercritical case when a reliable detection of spikes is possible. Especially, we…
Purpose: Diffusion Magnetic Resonance Imaging (dMRI) is confounded by its long acquisition duration, thereby thwarting the detection of rapid microstructural changes, especially when diffusivity variations are accompanied by rapid changes…
White matter tract integrity (WMTI) can characterize brain microstructure in areas with highly aligned fiber bundles. Several WMTI biomarkers have now been validated against microscopy and provided promising results in studies of brain…
Computer-aided early diagnosis of Alzheimers Disease (AD) and its prodromal form, Mild Cognitive Impairment (MCI), has been the subject of extensive research in recent years. Some recent studies have shown promising results in the AD and…
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…
Traditional theories of the NMR autocorrelation function for intramolecular dipole pairs assume single-exponential decay, yet the calculated autocorrelation of realistic systems display a rich, multi-exponential behavior resulting in…