Related papers: Problems in computational helioseismology
In passive imaging, one attempts to reconstruct some coefficients in a wave equation from correlations of observed randomly excited solutions to this wave equation. Many methods proposed for this class of inverse problem so far are only…
Since the first observations of solar oscillations, helioseismology has been one of the most successful fields of astrophysics. Data of high quality were obtained through the implementation of networks of ground-based observatories such as…
Many practical imaging systems suffer from uncertainty in acquisition geometry -- such as projection angles in computed tomography or sensor positions in photoacoustic tomography -- leading to nonlinear inverse problems that require joint…
Consider the geometric inverse problem: There is a set of delta-sources in spacetime that emit waves travelling at unit speed. If we know all the arrival times at the boundary cylinder of the spacetime, can we reconstruct the space, a…
A new algorithm is proposed for solving the three-dimensional scalar inverse problem of acoustic sounding in an inhomogeneous medium. The data for the algorithm are the complex amplitudes of the wave field measured outside the inhomogeneity…
Several problems in machine learning, statistics, and other fields rely on computing eigenvectors. For large scale problems, the computation of these eigenvectors is typically performed via iterative schemes such as subspace iteration or…
We consider a heat equation and a wave equation in a spatial interval over a time interval. This article deals with inverse problems of determining sizes of spatial intervals by extra boundary data of solutions of the governing equations.…
Helioseismology provides a powerful tool to explore the deep interior of the Sun: for example, the adiabatic sound speed can be inferred with an accuracy of a few parts in 10,000. This has become a serious challenge to theoretical models of…
Time-distance helioseismology is the method of the study of the propagation of waves through the solar interior via the travel times of those waves. The travel times of wave packets contain information about the conditions in the interior…
Linear time-distance helioseismic inversions are carried out for vector flow velocities using travel times measured from two $\sim 100^2\,{\rm Mm^2}\times 20\,{\rm Mm}$ realistic magnetohydrodynamic quiet-Sun simulations of about 20 hr. The…
In this article, we are concerned with the analysis on the numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation. This ill-posed problem is solved through a stabilized nonlinear…
This paper introduces a method for computing eigenvalues and eigenvectors of a generalized Hermitian, matrix eigenvalue problem. The work is focused on large scale eigenvalue problems, where the application of a direct inverse is out of…
We address the inverse problem of cosmic large-scale structure reconstruction from a Bayesian perspective. For a linear data model, a number of known and novel reconstruction schemes, which differ in terms of the underlying signal prior,…
The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…
We develop a novel wave imaging scheme for reconstructing the shape of an inhomogeneous scatterer and we consider the inverse acoustic obstacle scattering problem as a prototype model for our study. There exists a wealth of reconstruction…
Global hydrodynamic simulations of internal solar dynamics have focused on replicating the conditions for solar-like differential rotation and meridional circulation using the results of helioseismic inversions as a constraint. Inferences…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
In this work the numerical solution of acoustic tomography problem based on the iterative and functional-analytical algorithms is considered. The mathematical properties of these algorithms were previously described in works of R.G.Novikov…
Measurement of the differential rotation of the Sun's interior is one of the great achievements of helioseismology, providing important constraints for stellar physics. The technique relies on observing and analyzing rotationally-induced…
Thermo- and photo- acoustic tomography require reconstructing initial acoustic pressure in a body from time series of pressure measured on a surface surrounding the body. For the classical case of free space wave propagation, various…