Related papers: Inversions in astronomy and the SOLA method
Asteroseismology allows us to probe the internal structure of stars through their global modes of oscillation. Thanks to missions such as the NASA Kepler space observatory, we now have high-quality asteroseismic data for nearly 100…
We study an inverse problem for the wave equation, concerned with estimating the wave speed, aka velocity, from data gathered by an array of sources and receivers that emit probing signals and measure the resulting waves. The typical…
Several methods have been recently proposed for estimating sparse Gaussian graphical models using $\ell_{1}$ regularization on the inverse covariance matrix. Despite recent advances, contemporary applications require methods that are even…
Supergranulation is one of the most visible length scales of solar convection and has been studied extensively by local helioseismology. We use synthetic data computed with the Seismic Propagation through Active Regions and Convection…
Ill-posed inverse problems are fundamental in many domains, ranging from astrophysics to medical imaging. Emerging diffusion models provide a powerful prior for solving these problems. Existing maximum-a-posteriori (MAP) or posterior…
We propose a general inverse formula for extracting inflationary parameters from the observed power spectrum of cosmological perturbations. Under the general slow-roll scheme, which helps to probe the properties of inflation in a model…
The paper surveys recent progress in establishing uniqueness and developing inversion formulas and algorithms for the thermoacoustic tomography. In mathematical terms, one deals with a rather special inverse problem for the wave equation.…
The Laser Interferometer Space Antenna (LISA) is a planned space-based gravitational wave telescope with the goal of measuring gravitational waves in the milli-Hertz frequency band, which is dominated by millions of Galactic binaries. While…
The following two inversion methods for Radon-like transforms are widely used in integral geometry and related harmonic analysis. The first method invokes mean value operators in accordance with the classical Funk-Radon-Helgason scheme. The…
Seismic waves are the most sensitive probe of the Earth's interior we have. With the dense data sets available in exploration, images of subsurface structures can be obtained through processes such as migration. Unfortunately, relating…
Despite the strong evidence that the peaks in the spectrum of solar oscillations are asymmetric, most determinations of mode frequencies have been based on fits of symmetric Lorentzian profiles to the Fourier or power spectra of oscillation…
We introduce a reduced order model (ROM) methodology for inverse electromagnetic wave scattering in layered lossy media, using data gathered by an antenna which generates a probing wave and measures the time resolved reflected wave. We…
Digital co-addition of astronomical images is a common technique for increasing signal-to-noise and image depth. A modification of this simple technique has been applied to the detection of minor bodies in the Solar System: first stationary…
An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are explicitly constructed in terms of the scattering data. The main…
Symplectic integrators are widely used for the study of planetary dynamics and other $N$-body problems. In a study of the outer Solar system, we demonstrate that individual symplectic integrations can yield biased errors in the semi-major…
Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical…
We have compiled a new sample of galaxies with published catalogs of HII region coordinates. This sample, together with the former catalog of Garcia-Gomez and Athanassoula (1991) will form the basis for subsequent studies of the spiral…
Most problems in gravitational lensing require numerical solutions. The most frequent types of problems are (1) finding multiple images of a single source and classifying the images according to their properties like magnification or…
Strong gravitational lensing offers a wealth of astrophysical information on the background source it affects, provided the lensed source can be reconstructed as if it was seen in the absence of lensing. In the present work, we illustrate…
A major goal of helioseismology is the three-dimensional reconstruction of the three velocity components of convective flows in the solar interior from sets of wave travel-time measurements. For small amplitude flows, the forward problem is…