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An approach to diffraction tomography is investigated for two-dimensional image reconstruction of objects surrounded by an arbitrarily-shaped curve of sources and receivers. Based on the integral theorem of Helmholtz and Kirchhoff, the…
The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…
Many naturally-occuring models in the sciences are well-approximated by simplified models, using multiscale techniques. In such settings it is natural to ask about the relationship between inverse problems defined by the original problem…
Graphical models are powerful tools to investigate complex dependency structures in high-throughput datasets. However, most existing graphical models make one of the two canonical assumptions: (i) a homogeneous graph with a common network…
Score-based generative models (SGMs) have gained prominence in sparse-view CT reconstruction for their precise sampling of complex distributions. In SGM-based reconstruction, data consistency in the score-based diffusion model ensures close…
In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…
We study iterative signal reconstruction in computed tomography (CT), wherein measurements are produced by a linear transformation of the unknown signal followed by an exponential nonlinear map. Approaches based on pre-processing the data…
Abdominal aortic aneurysms (AAAs) are progressive dilatations of the abdominal aorta that, if left untreated, can rupture with lethal consequences. Imaging-based patient monitoring is required to select patients eligible for surgical…
Demographic studies suggest that changes in the retinal vasculature geometry, especially in vessel width, are associated with the incidence or progression of eye-related or systemic diseases. To date, the main information source for width…
Many modern applications of Bayesian inference, such as in cosmology, are based on complicated forward models with high-dimensional parameter spaces. This considerably limits the sampling of posterior distributions conditioned on observed…
Computational fluid dynamics (CFD) based simulation of coronary blood flow provides valuable hemodynamic markers, such as pressure gradients, for diagnosing coronary artery disease (CAD). However, CFD is computationally expensive,…
The Sudden Approximation is applied to invert structural data on randomly corrugated surfaces from inert atom scattering intensities. Several expressions relating experimental observables to surface statistical features are derived. The…
In this paper, we propose a new flexible family of distributions for data that consist of three angles, two angles and one linear component, or one angle and two linear components. To achieve this, we equip the recently proposed trivariate…
Coronary CT angiography (CCTA) has established its role as a non-invasive modality for the diagnosis of coronary artery disease (CAD). The CAD-Reporting and Data System (CAD-RADS) has been developed to standardize communication and aid in…
In decision theoretic estimation of parameters in Euclidean space $\mathbb{R}^p$, the action space is chosen to be the convex closure of the estimand space. In this paper, the concept has been extended to the estimation of circular…
We present an iterative framework to improve the amortized approximations of posterior distributions in the context of Bayesian inverse problems, which is inspired by loop-unrolled gradient descent methods and is theoretically grounded in…
Stochastic minimax optimization has drawn much attention over the past decade due to its broad applications in machine learning, signal processing and game theory. In some applications, the probability distribution of uncertainty depends on…
Appropriate models for spatially autocorrelated data account for the fact that observations are not independent. A popular model in this context is the simultaneous autoregressive (SAR) model that allows to model the spatial dependency…
Echocardiography plays a fundamental role in the extraction of important clinical parameters (e.g. left ventricular volume and ejection fraction) required to determine the presence and severity of heart-related conditions. When deploying…
Angular observations, or observations lying on the unit circle, arise in many disciplines and require special care in their description, analysis, interpretation and visualization. We provide methods to construct concentric circular boxplot…