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Gaussian graphical regressions have emerged as a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which, unlike traditional Gaussian graphical models, can help determine how graphs are…

In electrocardiography, the "classic" inverse problem is the reconstruction of electric potentials at a surface enclosing the heart from remote recordings at the body surface and an accurate description of the anatomy. The latter being…

The heart's contraction is caused by electrical excitation which propagates through the heart muscle. It was recently shown that the electrical excitation can be computed from the contractile motion of a simulated piece of heart muscle…

We consider the problem of recovering random graph signals from nonlinear measurements. For this case, closed-form Bayesian estimators are usually intractable and even numerical evaluation of these estimators may be hard to compute for…

Segmentation of cardiac magnetic resonance images (MRI) is crucial for the analysis and assessment of cardiac function, helping to diagnose and treat various cardiovascular diseases. Most recent techniques rely on deep learning and usually…

Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…

Cardiac parametric mapping is useful for evaluating cardiac fibrosis and edema. Parametric mapping relies on single-shot heartbeat-by-heartbeat imaging, which is susceptible to intra-shot motion during the imaging window. However, reducing…

Deep neural networks have shown great potential in image reconstruction problems in Euclidean space. However, many reconstruction problems involve imaging physics that are dependent on the underlying non-Euclidean geometry. In this paper,…

Blood flow reconstruction in the vasculature is important for many clinical applications. However, in clinical settings, the available data are often quite limited. For instance, Transcranial Doppler ultrasound (TCD) is a noninvasive…

The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as…

Trained generative models have shown remarkable performance as priors for inverse problems in imaging -- for example, Generative Adversarial Network priors permit recovery of test images from 5-10x fewer measurements than sparsity priors.…

Electroanatomical mapping, a keystone diagnostic tool in cardiac electrophysiology studies, can provide high-density maps of the local electric properties of the tissue. It is therefore tempting to use such data to better individualize…

Signal processing over graphs has recently attracted significant attentions for dealing with structured data. Normal graphs, however, only model pairwise relationships between nodes and are not effective in representing and capturing some…

Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…

In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…

Electroencephalogram (EEG) signals are frequently used in brain-computer interfaces (BCIs), but they are easily contaminated by artifacts and noises, so preprocessing must be done before they are fed into a machine learning algorithm for…

This paper proposes a new methodology for performing Bayesian inference in imaging inverse problems where the prior knowledge is available in the form of training data. Following the manifold hypothesis and adopting a generative modelling…

Deep Gaussian processes have recently been proposed as natural objects to fit, similarly to deep neural networks, possibly complex features present in modern data samples, such as compositional structures. Adopting a Bayesian nonparametric…

Cardiac cells exhibit variability in the shape and duration of their action potentials in space within a single individual. To create a mathematical model of cardiac action potentials (AP) which captures this spatial variability and also…

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…