Related papers: Bayesian Uncertainty-Aware MRI Reconstruction

Magnetic Resonance Imaging (MRI) is a noninvasive imaging technique that provides exquisite soft-tissue contrast without using ionizing radiation. The clinical application of MRI may be limited by long data acquisition times; therefore, MR…

In this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. Then a common general forward modeling for them is given and the corresponding…

For linear inverse problems with a large number of unknown parameters, uncertainty quantification remains a challenging task. In this work, we use Krylov subspace methods to approximate the posterior covariance matrix and describe efficient…

Atlas-based approaches allow high-quality, patient-specific shape reconstructions of cardiac anatomy from sparse and/or noisy data such as point clouds. However, these methods are mainly prior-driven, so the impact of uncertainty can be…

Computed tomography is a method for synthesizing volumetric or cross-sectional images of an object from a collection of projections. Popular reconstruction methods for computed tomography are based on idealized models and assumptions that…

Most existing MRI reconstruction methods perform tar-geted reconstruction of the entire MR image without tak-ing specific tissue regions into consideration. This may fail to emphasize the reconstruction accuracy on im-portant tissues for…

Recently, diffusion models have attracted considerable attention for magnetic resonance image reconstruction due to their high sample quality. However, most existing methods rely on large networks with opaque time-conditioning mechanisms,…

Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…

Hyperspectral unmixing is a blind source separation problem which consists in estimating the reference spectral signatures contained in a hyperspectral image, as well as their relative contribution to each pixel according to a given mixture…

Efficiently quantifying predictive uncertainty in medical images remains a challenge. While Bayesian neural networks (BNN) offer predictive uncertainty, they require substantial computational resources to train. Although Bayesian…

The Planck satellite, along with several ground based telescopes, have mapped the cosmic microwave background (CMB) at sufficient resolution and signal-to-noise so as to allow a detection of the subtle distortions due to the gravitational…

Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…

We propose the first Bayesian encoder for metric learning. Rather than relying on neural amortization as done in prior works, we learn a distribution over the network weights with the Laplace Approximation. We actualize this by first…

Stress and material deformation field predictions are among the most important tasks in computational mechanics. These predictions are typically made by solving the governing equations of continuum mechanics using finite element analysis,…

Bayesian inference requires determining the posterior distribution, a task that becomes particularly challenging when the dimension of the parameter space is large and unknown. This limitation arises in many physics problems, such as…

A well known identifiability issue in factor analytic models is the invariance with respect to orthogonal transformations. This problem burdens the inference under a Bayesian setup, where Markov chain Monte Carlo (MCMC) methods are used to…

The Bayesian Conjugate Gradient method (BayesCG) is a probabilistic generalization of the Conjugate Gradient method (CG) for solving linear systems with real symmetric positive definite coefficient matrices. Our CG-based implementation of…

Deep learning-based image reconstruction approaches have demonstrated impressive empirical performance in many imaging modalities. These approaches usually require a large amount of high-quality paired training data, which is often not…

In ill-posed inverse problems, it is commonly desirable to obtain insight into the full spectrum of plausible solutions, rather than extracting only a single reconstruction. Information about the plausible solutions and their likelihoods is…

This paper addresses the statistical estimation of Gaussian Mixture Models (GMMs) with unknown diagonal covariances from independent and identically distributed samples. We employ the Beurling-LASSO (BLASSO), a convex optimization framework…