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Purpose: To introduce, develop, and evaluate a novel denoising technique for diffusion MRI that leverages non-linear redundancy in the data to boost the SNR while preserving signal information. Methods: We exploit non-linear redundancy of…

We consider the efficient use of an approximation within Markov chain Monte Carlo (MCMC), with subsequent importance sampling (IS) correction of the Markov chain inexact output, leading to asymptotically exact inference. We detail…

In this paper, a novel model-based distributed compressive sensing (DCS) algorithm is proposed. DCS exploits the inter-signal correlations and has the capability to jointly recover multiple sparse signals. Proposed approach is a Bayesian…

We present a Bayesian approach to estimate the parameters of mathematical models of cardiac electrophysiology with quantified uncertainty. Such models capture the dynamics of the electrical signal that coordinates the muscle cell…

In this study, we present a technique that spans multi-scale views (global scale -- meaning brain network-level and local scale -- examining each individual ROI that constitutes the network) applied to resting-state fMRI volumes. Deep…

The ability to reconstruct high-quality images from undersampled MRI data is vital in improving MRI temporal resolution and reducing acquisition times. Deep learning methods have been proposed for this task, but the lack of verified methods…

We introduce a random partition model for Bayesian nonparametric regression. The model is based on infinitely-many disjoint regions of the range of a latent covariate-dependent Gaussian process. Given a realization of the process, the…

Computational neuroimaging involves analyzing brain images or signals to provide mechanistic insights and predictive tools for human cognition and behavior. While diffusion models have shown stability and high-quality generation in natural…

Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC)…

Patient scans from MRI often suffer from noise, which hampers the diagnostic capability of such images. As a method to mitigate such artifact, denoising is largely studied both within the medical imaging community and beyond the community…

Motivated by contemporary and rich applications of anomalous diffusion processes we propose a new statistical test for fractional Brownian motion, which is one of the most popular models for anomalous diffusion systems. The test is based on…

With the great success of diffusion models in image generation, diffusion-based image compression is attracting increasing interests. However, due to the random noise introduced in the diffusion learning, they usually produce…

We consider a nonparametric Bayesian approach to estimate the diffusion coefficient of a stochastic differential equation given discrete time observations over a fixed time interval. As a prior on the diffusion coefficient, we employ a…

Classical parameter-space Bayesian inference for Bayesian neural networks (BNNs) suffers from several unresolved prior issues, such as knowledge encoding intractability and pathological behaviours in deep networks, which can lead to…

A learning-based posterior distribution estimation method, Probabilistic Dipole Inversion (PDI), is proposed to solve quantitative susceptibility mapping (QSM) inverse problem in MRI with uncertainty estimation. A deep convolutional neural…

Functional connectivity (FC) derived from functional magnetic resonance imaging (fMRI) data offers vital insights for understanding brain function and neurological and psychiatric disorders. Unsupervised clustering methods are desired to…

We propose Radial Bayesian Neural Networks (BNNs): a variational approximate posterior for BNNs which scales well to large models while maintaining a distribution over weight-space with full support. Other scalable Bayesian deep learning…

In this paper we consider Bayesian parameter inference for partially observed fractional Brownian motion (fBM) models. The approach we follow is to time-discretize the hidden process and then to design Markov chain Monte Carlo (MCMC)…

Diffusion magnetic resonance imaging is a noninvasive imaging technique that can indirectly infer the microstructure of tissues and provide metrics which are subject to normal variability across subjects. Potentially abnormal values or…

Background: Magneto- and Electro-encephalography record the electromagnetic field generated by neural currents with high temporal frequency and good spatial resolution, and are therefore well suited for source localization in the time and…