Related papers: Inversions in astronomy and the SOLA method
Helioseismology, the study of global solar oscillations, has proved to be an extremely powerful tool for the investigation of the internal structure and dynamics of the Sun. Studies of time changes in frequency observations of solar…
The stellar occultation technique provides competitive accuracy in determining the sizes, shapes, astrometry, etc., of the occulting body, comparable to in-situ observations by spacecraft. With the increase in the number of known Solar…
The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…
Inferring interior properties of the Sun from photospheric measurements of the seismic wavefield constitutes the helioseismic inverse problem. Deviations in seismic measurements (such as wave travel times) from their fiducial values…
Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…
Integral equations frequently arise in surface science, and in some cases, they must be treated as inverse problems. In our previous work on optical tweezers, atomic force microscopy, and surface force measurement apparatus, we performed…
The work develops further the theory of the following inversion problem, which plays the central role in the rapidly developing area of thermoacoustic tomography and has intimate connections with PDEs and integral geometry: {\it Reconstruct…
Hyperspectral imaging has become a significant source of valuable data for astronomers over the past decades. Current instrumental and observing time constraints allow direct acquisition of multispectral images, with high spatial but low…
We describe a method for determining the limb polarization and limb darkening of stars in eclipsing binary systems, by inverting photometric and polarimetric light curves. Because of the ill-conditioning of the problem, we use the…
Rotation information for spiral galaxies can be obtained through the observation of different spectral lines. While the Halpha(6563 A) line is often used for galaxies with low to moderate redshifts, it is redshifted into the near-infrared…
Supergranules create a peak in the spatial spectrum of photospheric velocity features. They have some properties of convection cells but their origin is still being debated in the literature. The time-distance helioseismology constitutes a…
Strong gravitational lensing provides a wealth of astrophysical information on the baryonic and dark matter content of galaxies. It also serves as a valuable cosmological probe by allowing us to measure the Hubble constant independently of…
Inverse Reinforcement Learning (RL) can be used to determine the behavior of Space Objects (SOs) by estimating the reward function that an SO is using for control. The approach discussed in this work can be used to analyze maneuvering of…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$…
Waveform inversion is concerned with estimating a heterogeneous medium, modeled by variable coefficients of wave equations, using sources that emit probing signals and receivers that record the generated waves. It is an old and intensively…
Radiative transfer coupled with highly realistic simulations of the solar atmosphere is routinely used to infer the physical properties underlying solar observations. Due to its computational efficiency, the method of short-characteristics…
We present combined Halpha+HI rotation curves for a sample of spiral galaxies. Most of the velocity profiles (spectra at single points) in these galaxies are asymmetric, preventing the use of standard methods like the first moment analysis…
Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…
We discuss current advances in forward and inverse modeling for local helioseismology. We report theoretical uniqueness results, in particular the Novikov-Agaltsov reconstruction algorithm, which is relevant to solving the non-linear…
In order to take full advantage of the long time series collected by the GONG and MDI helioseismic projects, we present here an adaptation of the rotation-corrected $m$-averaged spectrum technique in order to observe low radial-order solar…