Constrained Maximum Likelihood Estimation of Relative Abundances of Protein Conformation in a Heterogeneous Mixture from Small Angle X-Ray Scattering Intensity Measurements (original) (raw)

A fast schema for parameter estimation in diffusion kurtosis imaging

Computerized medical imaging and graphics : the official journal of the Computerized Medical Imaging Society, 2014

Diffusion kurtosis imaging (DKI) is a new model in magnetic resonance imaging (MRI) characterizing restricted diffusion of water molecules in living tissues. We propose a method for fast estimation of the DKI parameters. These parameters - apparent diffusion coefficient (ADC) and apparent kurtosis coefficient (AKC) - are evaluated using an alternative iteration schema (AIS). This schema first roughly estimates a pair of ADC and AKC values from a subset of the DKI data acquired at 3 b-values. It then iteratively and alternately updates the ADC and AKC until they are converged. This approach employs the technique of linear least square fitting to minimize estimation error in each iteration. In addition to the common physical and biological constrains that set the upper and lower boundaries of the ADC and AKC values, we use a smoothing procedure to ensure that estimation is robust. Quantitative comparisons between our AIS methods and the conventional methods of unconstrained nonlinear ...

Diffusion kurtosis imaging with free water elimination: A bayesian estimation approach

Magnetic resonance in medicine, 2018

Diffusion kurtosis imaging (DKI) is an advanced magnetic resonance imaging modality that is known to be sensitive to changes in the underlying microstructure of the brain. Image voxels in diffusion weighted images, however, are typically relatively large making them susceptible to partial volume effects, especially when part of the voxel contains cerebrospinal fluid. In this work, we introduce the "Diffusion Kurtosis Imaging with Free Water Elimination" (DKI-FWE) model that separates the signal contributions of free water and tissue, where the latter is modeled using DKI. A theoretical study of the DKI-FWE model, including an optimal experiment design and an evaluation of the relative goodness of fit, is carried out. To stabilize the ill-conditioned estimation process, a Bayesian approach with a shrinkage prior (BSP) is proposed. In subsequent steps, the DKI-FWE model and the BSP estimation approach are evaluated in terms of estimation error, both in simulation and real da...

A New Framework for MR Diffusion Tensor Distribution

The ability to characterize heterogeneous and anisotropic water diffusion processes within macro-scopic MRI voxels non-invasively and in vivo is a desideratum in biology, neuroscience, and medicine. While an MRI voxel may contain approximately a microliter of tissue, our goal is to examine intravoxel diffusion processes on the order of picoliters. Here we propose a new theoretical framework and experimental design to describe and measure such intravoxel structural heterogeneity and anisotropy. We assume that a constrained normal tensor-variate distribution (CNTVD) describes the variability of positive definite diffusion tensors within a voxel which extends its applicability to a wide range of b-values unlike existing models. We use a Monte Carlo scheme to synthesize realistic numerical diffusion tensor distribution (DTD) phantoms and invert the MR signal. We show that the signal inversion is well-posed and estimate the CNTVD parameters parsimoniously by exploiting the different symm...