Related papers: Analysis of reconstruction from noisy discrete gen…
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…
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…
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…
We study a new class of Radon transforms defined on circular cones called the conical Radon transform. In $\mathbb{R}^3$ it maps a function to its surface integrals over circular cones, and in $\mathbb{R}^2$ it maps a function to its…
Inverse problems are fundamental in fields like medical imaging, geophysics, and computerized tomography, aiming to recover unknown quantities from observed data. However, these problems often lack stability due to noise and…
Deep learning based reconstruction methods deliver outstanding results for solving inverse problems and are therefore becoming increasingly important. A recently invented class of learning-based reconstruction methods is the so-called NETT…
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…
Let $G_{n,r}(\bbK)$ be the Grassmannian manifold of $k$-dimensional $\bbK$-subspaces in $\bbK^n$ where $\bbK=\mathbb R, \mathbb C, \mathbb H$ is the field of real, complex or quaternionic numbers. We consider the Radon, cosine and sine…
A fast implementation of the OPED algorithm, a reconstruction algorithm for Radon data introduced recently, is proposed and tested. The new implementation uses FFT for discrete sine transform and an interpolation step. The convergence of…
In computed tomography (CT), the forward model consists of a linear Radon transform followed by an exponential nonlinearity based on the attenuation of light according to the Beer-Lambert Law. Conventional reconstruction often involves…
Neutron imaging is essential for diagnosing and optimizing inertial confinement fusion implosions at the National Ignition Facility. Due to the required 10-micrometer resolution, however, neutron image require image reconstruction using…
Proton radiography is a technique extensively used to resolve magnetic field structures in high energy density plasmas, revealing a whole variety of interesting phenomena such as magnetic reconnection and collisionless shocks found in…
We propose a variational regularisation approach for the problem of template-based image reconstruction from indirect, noisy measurements as given, for instance, in X-ray computed tomography. An image is reconstructed from such measurements…
The reconstruction of dynamic positron emission tomography (PET) images from noisy projection data is a significant but challenging problem. In this paper, we introduce an unsupervised learning approach, Non-negative Implicit Neural…
We consider the problem of developing a method to reconstruct a potential $q$ from the partial data Dirichlet-to-Neumann map for the Schr\"odinger equation $(-\Delta_g+q)u=0$ on a fixed admissible manifold $(M,g)$. If the part of the…
In optical diffraction tomography (ODT), the three-dimensional scattering potential of a microscopic object rotating around its center is recovered by a series of illuminations with coherent light. Reconstruction algorithms such as the…
Hyperspectral neutron computed tomography enables 3D non-destructive imaging of the spectral characteristics of materials. In traditional hyperspectral reconstruction, the data for each neutron wavelength bin is reconstructed separately.…
The light field reconstruction from the focal stack can be mathematically formulated as an ill-posed integral equation inversion problem. Although the previous research about this problem has made progress both in practice and theory, its…
Within the framework of field-theoretical description of second-order phase transitions via the 3-dimensional O(N) vector model, accurate predictions for critical exponents can be obtained from (resummation of) the perturbative series of…
In this paper, we extend our research concerning the standard and linearized monotonicity methods for the inverse problem of the time harmonic elastic wave equation and introduce the modification of these methods for noisy data. In more…