Related papers: Using the Notion of Copula in Tomography
This paper studies the multi-reference alignment (MRA) problem of estimating a signal function from shifted, noisy observations. Our functional formulation reveals a new connection between MRA and deconvolution: the signal can be estimated…
Low-dose Computed Tomography is a common issue in reality. Current reduction, sparse sampling and limited-view scanning can all cause it. Between them, limited-view CT is general in the industry due to inevitable mechanical and physical…
In geosciences, the use of classical Euclidean methods is unsuitable for treating and analyzing some types of data, as this may not belong to a vector space. This is the case for correlation matrices, belonging to a subfamily of symmetric…
Recovering a function from its integrals over circular cones recently gained significance because of its relevance to novel medical imaging technologies such emission tomography using Compton cameras. In this paper we investigate the case…
We consider recently developed Cohomological Field Theory soliton counting diagram technique for Khovanov and Khovanov-Rozansky invariants [1,2]. Although the expectation to obtain a new way for computing the invariants has not yet come…
The problem of using proximity (similarity or dissimilarity) data for the purpose of "adding a point to a vector diagram" was first studied by J.C. Gower in 1968. Since then, a number of methods -- mostly kernel methods -- have been…
Perturbation theory (PT) is often used to model statistical observables capturing the translation and rotation-invariant information in cosmological density fields. PT produces higher-order corrections by integration over linear statistics…
In this paper we study the reconstruction of moving object densities from undersampled dynamic X-ray tomography in two dimensions. A particular motivation of this study is to use realistic measurement protocols for practical applications,…
We study multilinear generalized Radon transforms using a graph-theoretic paradigm that includes the widely studied linear case. These provide a general mechanism to study Falconer-type problems involving $(k+1)$-point configurations in…
Indirect imaging problems in biomedical optics generally require repeated evaluation of forward models of radiative transport, for which Monte Carlo is accurate yet computationally costly. We develop a novel approach to reduce this…
In this paper we refer to the reconstruction formulas given in L.-E. Andersson's On the determination of a function from spherical averages, which are often used in applications such as SAR and SONAR. We demonstrate that the first one of…
We consider the imaging of cosmic strings by using Cosmic Microwave Background (CMB) data. Mathematically, we study the inversion of an X-ray transform in Lorentzian geometry, called the light ray transform. The inverse problem is highly…
In probability and statistics, copulas play important roles theoretically as well as to address a wide range of problems in various application areas. In this paper, we introduce the concept of multivariate discrete copulas, discuss their…
We consider a formulation of Cauchy problem for Kolmogorov equation which corresponds a localized source of particles to be scattered by medium with given scattering amplitude density. The multiple scattering amplitudes are introduced and…
Deep learning (DL) has shown unprecedented performance for many image analysis and image enhancement tasks. Yet, solving large-scale inverse problems like tomographic reconstruction remains challenging for DL. These problems involve…
X-ray computed tomography (CT) is one of widely used diagnostic tools for medical and dental tomographic imaging of the human body. However, the standard filtered backprojection reconstruction method requires the complete knowledge of the…
An explicit series solution is proposed for the inversion of the spherical mean Radon transform. Such an inversion is required in problems of thermo- and photo- acoustic tomography. Closed-form inversion formulae are currently known only…
The spherical Radon transform (SRT) is an integral transform that maps a function to its integrals over concentric spherical shells centered at specified sensor locations. It has several imaging applications, including synthetic aperture…
We develop an approach to generate random graphs to a target level of assortativity by using copula structures in graphons. Unlike existing random graph generators, we do not use rewiring or binning approaches to generate the desired random…
In many tomographic imaging problems the data consist of integrals along lines or curves. Increasingly we encounter "rich tomography" problems where the quantity imaged is higher dimensional than a scalar per voxel, including vectors…