Related papers: Statistical Inference of Auto-correlated Eigenvalu…

Objective: Most deep neural network-based diffusion tensor imaging methods require the diffusion gradients' number and directions in the data to be reconstructed to match those in the training data. This work aims to develop and evaluate a…

Deep learning has been successful in predicting neurodegenerative disorders, such as Alzheimer's disease, from magnetic resonance imaging (MRI). Combining multiple imaging modalities, such as T1-weighted (T1) and diffusion-weighted imaging…

The eigenvalue densities of two random matrix ensembles, the Wigner Gaussian matrices and the Wishart covariant matrices, are decomposed in the contributions of each individual eigenvalue distribution. It is shown that the fluctuations of…

Double diffusion encoding (DDE) makes diffusion MRI sensitive to a wide range of microstructural features, and the acquired data can be analysed using different approaches. Correlation tensor imaging (CTI) uses DDE to resolve three…

Wishart random matrices with a sparse or diluted structure are ubiquitous in the processing of large datasets, with applications in physics, biology and economy. In this work we develop a theory for the eigenvalue fluctuations of diluted…

Breast cancer is the second most common type of cancer in women in Canada and the United States, representing over 25\% of all new female cancer cases. As such, there has been immense research and progress on improving screening and…

In this paper, we consider the problem of deriving new eigenvalue distributions of real-valued Wishart matrices that arises in many scientific and engineering applications. The distributions are derived using the tools from the theory of…

We study a discrete denoising diffusion framework that integrates a sample-efficient estimator of single-site conditionals with round-robin noising and denoising dynamics for generative modeling over discrete state spaces. Rather than…

Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality.…

Multivariate time series imputation is fundamental in applications such as healthcare, traffic forecasting, and biological modeling, where sensor failures and irregular sampling lead to pervasive missing values. However, existing…

We present an analytic method to determine spectral properties of the covariance matrices constructed of correlated Wishart random matrices. The method gives, in the limit of large matrices, exact analytic relations between the spectral…

Diffusion models have recently received a surge of interest due to their impressive performance for image restoration, especially in terms of noise robustness. However, existing diffusion-based methods are trained on a large amount of…

We present a concise derivation for several influential score-based diffusion models that relies on only a few textbook results. Diffusion models have recently emerged as powerful tools for generating realistic, synthetic signals --…

For distributed estimations in a sensor network, the consistency and accuracy of an estimator are greatly affected by the unknown correlations between individual estimates. An inconsistent or too conservative estimate may degrade the…

Diffusion MRI (dMRI) provides the ability to reconstruct neuronal fibers in the brain, $\textit{in vivo}$, by measuring water diffusion along angular gradient directions in q-space. High angular resolution diffusion imaging (HARDI) can…

The value of preclinical diffusion MRI (dMRI) is substantial. While dMRI enables in vivo non-invasive characterization of tissue, ex vivo dMRI is increasingly used to probe tissue microstructure and brain connectivity. Ex vivo dMRI has…

The foremost challenge to causal inference with real-world data is to handle the imbalance in the covariates with respect to different treatment options, caused by treatment selection bias. To address this issue, recent literature has…

Alzheimer's disease (AD) progresses heterogeneously across individuals, motivating subject-specific synthesis of follow-up magnetic resonance imaging (MRI) to support progression assessment. While Diffusion Transformers (DiT), an emerging…

Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…

Poor performance of quantitative analysis in histopathological Whole Slide Images (WSI) has been a significant obstacle in clinical practice. Annotating large-scale WSIs manually is a demanding and time-consuming task, unlikely to yield the…