Related papers: Novel framework for the three-dimensional NLTE inv…
Integral field spectroscopy of high-redshift galaxies has become a powerful tool for understanding their dynamics and evolutionary states. However, in the case of gravitationally lensed systems, it has proved difficult to model both lensing…
Context. The solar irradiance is known to change on time scales of minutes to decades, and it is suspected that its substantial fluctua- tions are partially responsible for climate variations. Aims. We are developing a solar atmosphere code…
An inverse problem in spectroscopy is considered. The objective is to restore the discrete spectrum from observed spectrum data, taking into account the spectrometer's line spread function. The problem is reduced to solution of a system of…
Microwave imaging is commonly based on the solution of linearized inverse scattering problems by matched filtering algorithms, i.e., by applying the adjoint of the forward scattering operator to the observation data. A more rigorous…
Current strategies for solving image-based inverse problems apply latent diffusion models to perform posterior sampling.However, almost all approaches make no explicit attempt to explore the solution space, instead drawing only a single…
We derive a fully discrete Inverse Scattering Transform as a method for solving the initial-value problem for the Q3$_\delta$ lattice (difference-difference) equation for real-valued solutions. The initial condition is given on an infinite…
Nonlinear parametric inverse problems appear in many applications and are typically very expensive to solve, especially if they involve many measurements. These problems pose huge computational challenges as evaluating the objective…
The goal of this paper is to reconstruct spatially distributed dielectric constants from complex-valued scattered wave field by solving a 3D coefficient inverse problem for the Helmholtz equation at multi-frequencies. The data are generated…
Programmable shape-shifting materials can take different physical forms to achieve multifunctionality in a dynamic and controllable manner. Although morphing a shape from 2D to 3D via programmed inhomogeneous local deformations has been…
Modeling outdoor scenes for the synthetic 3D environment requires the recovery of reflectance/albedo information from raw images, which is an ill-posed problem due to the complicated unmodeled physics in this process (e.g., indirect…
Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…
The chemical compositions of stars encode the history of the universe and are thus fundamental for advancing our knowledge of astrophysics and cosmology. However, measurements of elemental abundances ratios, and our interpretations of them,…
We consider the problem of determination of a magnetic field from three dimensional polarimetric neutron tomography data. We see that this is an example of a non-Abelian ray transform and that the problem has a globally unique solution for…
This is a review of the main ideas of the inverse scattering method (ISM) for solving nonlinear evolution equations (NLEE), known as soliton equations. As a basic tool we use the fundamental analytic solutions (FAS) of the Lax operator L.…
This paper presents a new joint inversion approach to shape-based inverse problems. Given two sets of data from distinct physical models, the main objective is to obtain a unified characterization of inclusions within the spatial domain of…
{We aim to demonstrate the effect of atmospheric inhomogeneities on the emergent specific intensity and radiation flux of a spectral line radiation.} {We self-consistently solve the NLTE problem for a two-level atom in a 3D atmosphere using…
We present an algorithm based on numerical techniques that have become standard for solving nonlinear integral equations: Newton's method, homotopy continuation, the multilevel method and random projection to solve the inversion problem…
Inverse scattering problems without the phase information arise in imaging of nanostructures whose sizes are hundreds of nanometers as well as in imaging of biological cells. The governing equation is the 3-d generalized Helmholtz equation…
Regularization methods improve the stability of ill-posed inverse problems by introducing some a priori characteristics for the solution such as smoothness or sharpness. In this contribution, we propose a multidimensional, scale-dependent…
A meshless method is presented to solve the radiative transfer equation in the even parity formulation of the discrete ordinates method in complex 2D and 3D geometries. Prediction results of radiative heat transfer problems obtained by the…