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This book presents the core principles that have guided the development of diffusion models, tracing their origins and showing how diverse formulations arise from shared mathematical ideas. Diffusion modeling starts by defining a forward…
Many developmental processes, such as plasticity and aging, or pathological processes such as neurological diseases are characterized by modulations of specific cellular types and their microstructures. Diffusion-weighted Magnetic Resonance…
Pseudo-healthy image inpainting is an essential preprocessing step for analyzing pathological brain MRI scans. Most current inpainting methods favor slice-wise 2D models for their high in-plane fidelity, but their independence across slices…
Tractography fiber clustering using diffusion MRI (dMRI) is a crucial strategy for white matter (WM) parcellation. Current methods primarily use the geometric information of fibers (i.e., the spatial trajectories) to group similar fibers…
Since the 1970s, analogies between laser dynamics and fluid systems have provided insight into phenomena such as chaos, multistability, and turbulence. Building on this perspective, we model the optical field as an energy fluid and…
We review, systematize and discuss models of diffusion in neuronal tissue, by putting them into an overarching physical context of coarse-graining over an increasing diffusion length scale. From this perspective, we view research on…
Diffusion MRI (dMRI) is sensitive to microstructural barriers, yet most existing methods either assume impermeable boundaries or estimate voxel-level parameters without recovering explicit interfaces. We present Spinverse, a…
This study introduces a novel approach for image reconstruction based on a diffusion model conditioned on the native data domain. Our method is applied to multi-coil MRI and quantitative MRI reconstruction, leveraging the domain-conditioned…
Probing the transport of fluids within confined domains is important in many areas including material science, catalysis, food science, and cell biology. The diffusion propagator fully characterizes the diffusion process, which is highly…
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…
Deformable image registration aims to precisely align medical images from different modalities or times. Traditional deep learning methods, while effective, often lack interpretability, real-time observability and adjustment capacity during…
The brain white matter consists of a set of tracts that connect distinct regions of the brain. Segmentation of these tracts is often needed for clinical and research studies. Diffusion-weighted MRI offers unique contrast to delineate these…
Modeling radio frequency (RF) signal propagation is essential for understanding the environment, as RF signals offer valuable insights beyond the capabilities of RGB cameras, which are limited by the visible-light spectrum, lens coverage,…
Brownian motion of water molecules provides an essential length scale, the diffusion length, commensurate with cell dimensions in biological tissues. Measuring the diffusion coefficient as a function of diffusion time makes in vivo…
In porous material research, one main interest of nuclear magnetic resonance (NMR) diffusion experiments is the determination of the exact shape of pores. It has been a longstanding ques-tion if this is achievable in principle. In this…
We propose a multi-shell sampling grid and develop corresponding transforms for the accurate reconstruction of the diffusion signal in diffusion MRI by expansion in the spherical polar Fourier (SPF) basis. The transform is exact in the…
Detail features of magnetic resonance images play a cru-cial role in accurate medical diagnosis and treatment, as they capture subtle changes that pose challenges for doc-tors when performing precise judgments. However, the widely utilized…
Diffusion tensor imaging provides important information on tissue structure and orientation of fiber tracts in brain white matter in vivo. It results in diffusion tensors, which are $3\times3$ symmetric positive definite (SPD) matrices,…
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.…
We present an algorithm to estimate fast and accurate depth maps from light fields via a sparse set of depth edges and gradients. Our proposed approach is based around the idea that true depth edges are more sensitive than texture edges to…