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Denoising diffusion models (DDMs) offer a flexible framework for sampling from high dimensional data distributions. DDMs generate a path of probability distributions interpolating between a reference Gaussian distribution and a data…
A key challenge in maximizing the benefits of Magnetic Resonance Imaging (MRI) in clinical settings is to accelerate acquisition times without significantly degrading image quality. This objective requires a balance between under-sampling…
The purpose of this study is to propose a brain tissue-selective, optimized slice-by-slice B0 field shimming for high-resolution brain diffusion MRI. We incorporated actual gradient fields of X, Y, and Z gradient coils in the calculation of…
Reducing acquisition time is of fundamental importance in various imaging modalities. The concept of variable density sampling provides a nice framework to achieve this. It was justified recently from a theoretical point of view in the…
Many diffusion MRI researchers, including the Human Connectome Project (HCP), acquire data using multishell (e.g., WU-Minn consortium) and diffusion spectrum imaging (DSI) schemes (e.g., USC-Harvard consortium). However, these data sets are…
Propagation characteristics of a wave are defined by the dispersion relationship, from which the governing partial differential equation (PDE) can be recovered. PDEs are commonly solved numerically using the finite-difference (FD) method,…
We develop an efficient numerical scheme for the 3D mean-field spherical dynamo equation. The scheme is based on a semi-implicit discretization in time and a spectral method in space based on the divergence-free spherical harmonic…
A popular approach to sample a diffusion-based generative model is to solve an ordinary differential equation (ODE). In existing samplers, the coefficients of the ODE solvers are pre-determined by the ODE formulation, the reverse discrete…
From a mathematical perspective, the extraordinary properties of metamaterials are often reflected in the coefficients of the governing partial differential equations (PDEs). These coefficients may fall outside the assumptions of classical…
Diffusion-Weighted Magnetic Resonance Imaging (DWI) is widely used for early cerebral infarct detection caused by ischemic stroke. Manual segmentation is done by a radiologist as a common clinical process, nonetheless, challenges of…
3D medical imaging is in high demand and essential for clinical diagnosis and scientific research. Currently, diffusion models (DMs) have become an effective tool for medical imaging reconstruction thanks to their ability to learn rich,…
One-shot medical image segmentation (MIS) is crucial for medical analysis due to the burden of medical experts on manual annotation. The recent emergence of the segment anything model (SAM) has demonstrated remarkable adaptation in MIS but…
In this paper, an online multiscale model reduction method is presented for stochastic partial differential equations (SPDEs) with multiplicative noise, where the diffusion coefficient is spatially multiscale and the noise perturbation…
Two inverse scattering schemes were recently developed in \cite{LiLiuShangSun} for locating multiple electromagnetic (EM) scatterers, respectively, of small size and regular size compared to the detecting EM wavelength. Both schemes make…
This paper presents a novel efficient method for gridless line spectrum estimation problem with single snapshot, namely the gradient descent least squares (GDLS) method. Conventional single snapshot (a.k.a. single measure vector or SMV)…
We discuss R package SQUAREM for accelerating iterative algorithms which exhibit slow, monotone convergence. These include the well-known expectation-maximization algorithm, majorize-minimize (MM), and other EM-like algorithms such as…
The energy spectral efficiency maximization (ESEM) problem of a multi-user, multi-relay, multi-cell system is considered, where all the network nodes are equipped with multi-antenna transceivers. To deal with the potentially excessive…
Coherent diffractive imaging (CDI) provides new opportunities for high resolution X-ray imaging with simultaneous amplitude and phase contrast. Extensions to CDI broaden the scope of the technique for use in a wide variety of experimental…
We propose SERUM: an intriguingly simple yet highly effective method for marking images generated by diffusion models (DMs). We only add a unique watermark noise to the initial diffusion generation noise and train a lightweight detector to…
Undersampling is a common method in Magnetic Resonance Imaging (MRI) to subsample the number of data points in k-space, reducing acquisition times at the cost of decreased image quality. A popular approach is to employ undersampling…