Related papers: V-line tensor tomography: numerical results

In this note, we solve an inverse spectral problem for a class of finite band symmetric matrices. We provide necessary and sufficient conditions for a matrix valued function to be a spectral function of the operator corresponding to a…

This paper presents a neural network approach for solving two-dimensional optical tomography (OT) problems based on the radiative transfer equation. The mathematical problem of OT is to recover the optical properties of an object based on…

Vision Transformer (ViT) architectures represent images as collections of high-dimensional vectorized tokens, each corresponding to a rectangular non-overlapping patch. This representation trades spatial granularity for embedding…

Within the field of numerical multilinear algebra, block tensors are increasingly important. Accordingly, it is appropriate to develop an infrastructure that supports reasoning about block tensor computation. In this paper we establish…

Recovering the digital input of a time-discrete linear system from its (noisy) output is a significant challenge in the fields of data transmission, deconvolution, channel equalization, and inverse modeling. A variety of algorithms have…

This study presents a technique for 2D tomography under unknown viewing angles when the distribution of the viewing angles is also unknown. Unknown view tomography (UVT) is a problem encountered in cryo-electron microscopy and in the…

Exterior inverse problem for the circular means transform (CMT) arises in the intravascular photoacoustic imaging (IVPA), in the intravascular ultrasound imaging (IVUS), as well as in radar and sonar. The reduction of the IPVA to the CMT is…

In this paper, we consider a special V-line transform. It integrates a given function f over the V-lines whose centers are on a circle centered at the origin and the symmetric axes pass through the origin. We derive two sampling scheme of…

Atmospheric aerosols have a major influence on the earths climate and public health. Hence, studying their properties and recovering them from light scattering measurements is of great importance. State of the art retrieval methods such as…

The inversion of linear systems is a fundamental step in many inverse problems. Computational challenges exist when trying to invert large linear systems, where limited computing resources mean that only part of the system can be kept in…

We provide a new algorithm for the treatment of the deconvolution problem on the sphere which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. We establish upper bounds for the…

We show that on simple surfaces the geodesic ray transform acting on solenoidal symmetric tensor fields of arbitrary order is injective. This solves a long standing inverse problem in the two-dimensional case.

The inverse quantum scattering problem for the perturbed Bessel equation is considered. A direct and practical method for solving the problem is proposed. It allows one to reduce the inverse problem to a system of linear algebraic…

In their study of inverse Doppler shift and superluminal light [Phys. Rev. A 91, 053807 (2015)], Ghafoor et al. consider a three-level atomic arrangement with transitions in the optical domain. In fact, the values they give to the…

We study the efficient numerical solution of linear inverse problems with operator valued data which arise, e.g., in seismic exploration, inverse scattering, or tomographic imaging. The high-dimensionality of the data space implies…

The Rytov approximation has been commonly used to obtain reconstructed images for optical tomography. However, the method requires linearization of the nonlinear inverse problem. Here, we demonstrate nonlinear Rytov approximations by…

In numerical simulations of classical and quantum lattice systems, 2d corner transfer matrices (CTMs) and 3d corner tensors (CTs) are a useful tool to compute approximate contractions of infinite-size tensor networks. In this paper we show…

This work introduces a general numerical technique to invert one dimensional analytic or tabulated nonlinear functions in assigned ranges of interest. The proposed approach is based on an optimal version of the k-vector range searching, an…

Higher order tensor inversion is possible for even order. We have shown that a tensor group endowed with the Einstein (contracted) product is isomorphic to the general linear group of degree $n$. With the isomorphic group structures, we…

We derive explicit reconstruction formulas for the attenuated geodesic X-ray transform over functions and, in the case of non-vanishing attenuation, vector fields, on a class of simple Riemannian surfaces with boundary. These formulas…