Related papers: Limited data problems for the generalized Radon tr…
In this paper we present a general forward fitting method for multichannel image restoration based on regularized chi2. We introduce separable regularizations that account for the dynamic of the model and take advantage of the continuities…
We reduce boundary determination of an unknown function and its normal derivatives from the (possibly weighted and attenuated) broken ray data to the injectivity of certain geodesic ray transforms on the boundary. For determination of the…
The Learned Primal Dual (LPD) method has shown promising results in various tomographic reconstruction modalities, particularly under challenging acquisition restrictions such as limited viewing angles or a limited number of views. We…
The reconstruction of an unknown function $f$ from its line sums is the aim of discrete tomography. However, two main aspects prevent reconstruction from being an easy task. In general, many solutions are allowed due to the presence of the…
High resolution reconstruction of complicated objects from incomplete and noisy data can be achieved by solving modulation equations iteratively under physical constraints. This direct demodulation method is a powerful technique for dealing…
One important property of imaging modalities and related applications is the resolution of image reconstructions which relies on various factors such as instrumentation or data processing. Restrictions in resolution can have manifold…
Here we present a new non-parametric approach to density estimation and classification derived from theory in Radon transforms and image reconstruction. We start by constructing a "forward problem" in which the unknown density is mapped to…
In the present article we consider the uniqueness problem for the generalized Radon transform arising in a mathematical model of production. We prove uniqueness theorems for this transform and for the profit function in the corresponding…
Recovering a function from integrals over conical surfaces recently got significant interest. It is relevant for emission tomography with Compton cameras and other imaging applications. In this paper, we consider the weighted conical Radon…
Limited-angle X-ray tomography reconstruction is an ill-conditioned inverse problem in general. Especially when the projection angles are limited and the measurements are taken in a photon-limited condition, reconstructions from classical…
The most common problem in data reconstruction is to fit a function based on the observations of some sample (guiding) points. This paper provides a methodological point of view of digital-discrete surface reconstruction. We explain our…
Neural implicit representations have shown substantial improvements in efficiently storing 3D data, when compared to conventional formats. However, the focus of existing work has mainly been on storage and subsequent reconstruction. In this…
In this paper, we consider linear ill-posed problems in Hilbert spaces and their regularization via frame decompositions, which are generalizations of the singular-value decomposition. In particular, we prove convergence for a general class…
Radon transform is widely used in physical and life sciences and one of its major applications is the X-ray computed tomography (X-ray CT), which is significant in modern health examination. The Radon inversion or image reconstruction is…
In this work, we explore a change of paradigm to build Precomputed Radiance Transfer (PRT) methods in a data-driven way. This paradigm shift allows us to alleviate the difficulties of building traditional PRT methods such as defining a…
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…
We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…
Fix $n \geq 2$ an integer, and $F$ be a totally real number field. We reduce the shifted convolution problem for $L$-function coefficients of $\operatorname{GL}_n({\bf{A}}_F)$-automorphic forms to the better-understood setting of…
Let $\sigma$ be arc-length measure on $S^1\subset \mathbb R^2$ and $\Theta$ denote rotation by an angle $\theta \in (0, \pi]$. Define a model bilinear generalized Radon transform, $$B_{\theta}(f,g)(x)=\int_{S^1} f(x-y)g(x-\Theta y)\,…
The classical $\overline \partial$-method has been generalized recently [lnv], [lnv2] to be used in the presence of exceptional points. We apply this generalization to solve Dirac inverse scattering problem with weak assumptions on…