Related papers: Thermoacoustic tomography - implementation of exac…
The correct insertion of virtual objects in images of real-world scenes requires a deep understanding of the scene's lighting, geometry and materials, as well as the image formation process. While recent large-scale diffusion models have…
Single photon emission computed tomography (SPECT) is a well established clinical tool for functional imaging. A limitation of current SPECT systems is the use of mechanical collimation, where only a small fraction of the emitted photons is…
This is a continuation of two recent publications of the authors about reconstruction procedures for 3-d phaseless inverse scattering problems. The main novelty of this paper is that the Born approximation for the case of the wave-like…
The inverse Radon transform allows to obtain partonic double distributions from (extended) generalized parton distributions. We express the extension of generalized parton distributions by their dual parts, generalized distribution…
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…
We study properties of the general integral transform defined for a family of hypersurfaces in a smooth manifold. Estimates of Sobolev norms, range conditions and approximation theorem for the kernel of the integral transform are stated.…
The problem of reconstruction a function from spherical means is at the heart of several modern imaging modalities and other applications. In this paper we derive universal back-projection type reconstruction formulas for recovering a…
The time reversal method in thermoacoustic tomography is used for approximating the initial pressure inside a biological object using measurements of the pressure wave made on a surface surrounding the object. This article presents error…
Tomographic image reconstruction is generally an ill-posed linear inverse problem. Such ill-posed inverse problems are typically regularized using prior knowledge of the sought-after object property. Recently, deep neural networks have been…
In this paper, we derive explicit reconstruction formulas for two common measurement geometries: a plane and a sphere. The problem is formulated as inverting the forward operator $R^a$, which maps the initial source to the measured wave…
Since the early 1970s, inversion techniques have become the most useful tool for inferring the magnetic, dynamic, and thermodynamic properties of the solar atmosphere. The intrinsic model dependence makes it necessary to formulate specific…
In parallel beam computed tomography (CT), an object is reconstructed from a series of projections taken at different angles. However, in some industrial and biomedical imaging applications, the projection geometry is unknown, completely or…
Traditional sampling schemes often assume that the sampling locations are known. Motivated by the recent bioimaging technique known as cryogenic electron microscopy (cryoEM), we consider the problem of reconstructing an unknown 3D structure…
To obtain the initial pressure from the collected data on a planar sensor arrangement in Photoacoustic tomography, there exists an exact analytic frequency domain reconstruction formula. An efficient realization of this formula needs to…
Here we present practical methods for simulation and reconstruction of in-line digital holograms recorded with plane and spherical waves. The algorithms described here are applicable to holographic imaging of an object exhibiting absorption…
We analyze multi-bounce propagation of light in an unknown hidden volume and demonstrate that the reflected light contains sufficient information to recover the 3D structure of the hidden scene. We formulate the forward and inverse theory…
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…
This paper is concerned with a practical inverse problem of simultaneously reconstructing the surface heat flux and the thickness of a solid structure from the associated ultrasonic measurements. In a thermoacoustic coupling model, the…
We propose a framework to jointly determine the deformation parameters and reconstruct the unknown volume in electron cryotomography (CryoET). CryoET aims to reconstruct three-dimensional biological samples from two-dimensional projections.…
Filtered backprojection (FBP) is an efficient and popular class of tomographic image reconstruction methods. In photoacoustic tomography, these algorithms are based on theoretically exact analytic inversion formulas which results in…