Related papers: Statistical Inference of Auto-correlated Eigenvalu…

The correlated Wishart model provides a standard tool for the analysis of correlations in a rich variety of systems. Although much is known for complex correlation matrices, the empirically much more important real case still poses…

We propose denoising diffusion variational inference (DDVI), a black-box variational inference algorithm for latent variable models which relies on diffusion models as flexible approximate posteriors. Specifically, our method introduces an…

Deep learning has shown great potential in accelerating diffusion tensor imaging (DTI). Nevertheless, existing methods tend to suffer from Rician noise and eddy current, leading to detail loss in reconstructing the DTI-derived parametric…

Diffusion magnetic resonance imaging (dMRI) is a crucial non-invasive technique for exploring the microstructure of the living human brain. Traditional hand-crafted and model-based tissue microstructure reconstruction methods often require…

Non-destructive extraction of the target internal part, such as batteries and motors, by cutting surrounding structures is crucial at recycling and disposal sites. However, the diversity of products and the lack of information on…

While Variational Inference (VI) is central to modern generative models like Variational Autoencoders (VAEs) and Denoising Diffusion Models (DDMs), its pedagogical treatment is split across disciplines. In statistics, VI is typically framed…

Diffusion MRI (dMRI) is essential for studying brain microstructure, but high-resolution imaging remains challenging due to the inherent trade-offs between acquisition time and signal-to-noise ratio (SNR). Conventional methods often…

Magnetic Resonance cardiac diffusion tensor imaging (cDTI) and cardiac intravoxel incoherent motion imaging enables probing of in vivo myofiber architecture and myocardial perfusion surrogates. To study the impact of experimental parameters…

Diffusion anisotropy in diffusion tensor imaging (DTI) is commonly quantified with normalized diffusion anisotropy indices (DAIs). Most often, the fractional anisotropy (FA) is used, but several alternative DAIs have been introduced in…

Recent studies on inverse problems have proposed posterior samplers that leverage the pre-trained diffusion models as powerful priors. These attempts have paved the way for using diffusion models in a wide range of inverse problems.…

It is highly desirable to know how uncertain a model's predictions are, especially for models that are complex and hard to understand as in deep learning. Although there has been a growing interest in using deep learning methods in…

Purpose: To propose a domain-conditioned and temporal-guided diffusion modeling method, termed dynamic Diffusion Modeling (dDiMo), for accelerated dynamic MRI reconstruction, enabling diffusion process to characterize spatiotemporal…

Ill-posed imaging inverse problems remain challenging due to the ambiguity in mapping degraded observations to clean images. Diffusion-based generative priors have recently shown promise, but typically rely on computationally intensive…

Axonal damage is the primary pathological correlate of long-term impairment in multiple sclerosis (MS). Previous work has demonstrated a strong, quantitative relationship between decrease in axial diffusivity and axonal damage. In the…

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 statistical analysis of covariance matrix data is considered and, in particular, methodology is discussed which takes into account the non-Euclidean nature of the space of positive semi-definite symmetric matrices. The main motivation…

We performed a PubMed search to find 148 papers published between January 2010 and December 2019 related to human brain, Diffusion Tensor Imaging (DTI), and Machine Learning (ML). The studies focused on healthy cohorts (n = 15), mental…

Diffusion Tensor Cardiac Magnetic Resonance (DT-CMR) is the only in vivo method to non-invasively examine the microstructure of the human heart. Current research in DT-CMR aims to improve the understanding of how the cardiac microstructure…

Efficient schemes for sampling from the eigenvalues of the Wishart distribution have recently been described for both the uncorrelated central case (where the covariance matrix is $\mathbf{I}$) and the spiked Wishart with a single spike…

Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M^\dagger M where M is a complex matrix drawn from a normalized distribution P(M) ~ exp(-\Tr(A M B M^\dagger) with A and B…