Data augmentation in Rician noise model and Bayesian Diffusion Tensor Imaging

Dario Gasbarra; Jia Liu; Juha Railavo

Home/Archive/arXiv

arXiv · 1403.5065

Data augmentation in Rician noise model and Bayesian Diffusion Tensor Imaging

Dario Gasbarra·Jia Liu·Juha Railavo

View original source ↗Read source document ↗Export metadata ↓

Abstract

Mapping white matter tracts is an essential step towards understanding brain function. Diffusion Magnetic Resonance Imaging (dMRI) is the only noninvasive technique which can detect in vivo anisotropies in the 3-dimensional diffusion of water molecules, which correspond to nervous fibers in the living brain. In this process, spectral data from the displacement distribution of water molecules is collected by a magnetic resonance scanner. From the statistical point of view, inverting the Fourier transform from such sparse and noisy spectral measurements leads to a non-linear regression problem. Diffusion tensor imaging (DTI) is the simplest modeling approach postulating a Gaussian displacement distribution at each volume element (voxel). Typically the inference is based on a linearized log-normal regression model that can fit the spectral data at low frequencies. However such approximation fails to fit the high frequency measurements which contain information about the details of the displacement distribution but have a low signal to noise ratio. In this paper, we directly work with the Rice noise model and cover the full range of $b$-values. Using data augmentation to represent the likelihood, we reduce the non-linear regression problem to the framework of generalized linear models. Then we construct a Bayesian hierarchical model in order to perform simultaneously estimation and regularization of the tensor field. Finally the Bayesian paradigm is implemented by using Markov chain Monte Carlo.

Explore related subjects

stat.CO stat.AP stat.ME

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Dario Gasbarra, Jia Liu, Juha Railavo. 2014-03-20. Data augmentation in Rician noise model and Bayesian Diffusion Tensor Imaging. https://arxiv.org/abs/1403.5065

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Wasserstein mixing of a systematic-scan random rotation sampler

We study the mixing time of a systematic-scan analogue of Kac's walk that was proposed as a fast surrogate for Haar-distributed orthogonal matrices in randomized high-dimensional algorithms and was conjectured to approach Haar measure after only logarithmically many sweeps. We show that this conjectured speed-up does not occur for convergence of the full matrix law to Haar measure in Frobenius Wasserstein distance. At fixed normalized accuracy, the mixing time lies between order $n/\log n$ and order $n$ sweeps; at fixed absolute Frobenius accuracy, the corresponding bounds are between order $n$ and order $n\log n$. More strongly, below the scale $n/\log n$, the normalized Wasserstein distance remains asymptotically at its extremal value. We also show that the output law is singular with respect to Haar measure for fewer than $n/2$ sweeps. Thus the sampler may provide effective application-specific randomization without exhibiting the much faster full-Haar mixing.

stat.CO↗

arXiv2026

Bayesian Calibration with Functional Outputs Using Elastic Partial Matching

Calibrating a simulation model involves estimating its parameters by comparing model outputs with experimental data, so that simulation results faithfully reproduce the experimental observations. When the outputs are functions of time, there are multiple ways to quantify the discrepancy between experimental and simulated curves. A recent approach based on elastic functional data analysis decomposes a functional output into two components: a function temporally aligned to a template, and the corresponding warping function. This decomposition splits the problem into two independent calibration tasks, thereby addressing functional misalignment. However, it assumes that experimental and simulated curves share the same temporal support, an assumption often violated in practice when initial or end times are themselves uncertain or depend on the calibration parameters. In this work, we reinterpret the decomposition step as an approximation to a more general Bayesian calibration problem that incorporates an error term on the time axis. This perspective allows us to naturally extend the framework to a broader family of time warpings with varying initial or end times, using partial elastic alignment. We illustrate the method on a synthetic test case, comparing it with existing Bayesian calibration methods and demonstrating improved surrogate performance and error modeling. We then apply the proposed approach to the calibration of an equation of state (a thermodynamic equation relating the state variables of a material).

stat.CO↗

arXiv2026

Delayed Acceptance Slice Sampling

Slice sampling is a well-established Markov chain Monte Carlo method for approximate sampling of target distributions which are only known up to a normalizing constant. The method is based on choosing a new state on a slice, i.e., a superlevel set of the given unnormalized target density (with respect to a reference measure). However, slice sampling algorithms usually require per step multiple evaluations of the target density, and thus can become computationally expensive. This is particularly the case for Bayesian inference with costly likelihoods. In this paper, we exploit deterministic approximations of the target density, which are relatively cheap to evaluate, and propose delayed acceptance versions of several common (hybrid) slice samplers. We show ergodicity of the resulting slice sampling methods, discuss the superiority of delayed acceptance (ideal) slice sampling over delayed acceptance Metropolis-Hastings algorithms, and illustrate the benefits of our novel approach in terms of improved computational efficiency in numerical experiments.

stat.CO↗