Related papers: Novel framework for the three-dimensional NLTE inv…
A review of the author's results is given. Inversion formulas and stability estimates for the solutions to 3D inverse scattering problems with fixed-energy data are obtained. Inversions of exact and noisy data are stidied. The inverse…
This is a continuation of two recent publications of the authors about reconstruction procedures for 3-d phaseless inverse scattering problems. The main novelty of this paper is that the Born approximation for the case of the wave-like…
The Helmholtz equation is related to seismic exploration, sonar, antennas, and medical imaging applications. It is one of the most challenging problems to solve in terms of accuracy and convergence due to the scalability issues of the…
This paper concerns electromagnetic 3D subsurface imaging in connection with sparsity of signal sources. We explored an imaging approach that can be implemented in situations that allow obtaining a large amount of data over a surface or a…
This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for inverse elastic scattering problems with phaseless far field data. Systematically, we study two basic models, i.e., inverse scattering of plane…
We introduce a time-dimensional reduction method for the inverse source problem in linear elasticity, where the goal is to reconstruct the initial displacement and velocity fields from partial boundary measurements of elastic wave…
We introduce a new system of surface integral equations for Maxwell's transmission problem in three dimensions. This system has two remarkable features, both of which we prove. First, it is well-posed at all frequencies. Second, the…
We propose a scheme for imaging periodic surfaces using a superlens. By employing an inverse scattering model and the transformed field expansion method, we derive an approximate reconstruction formula for the surface profile, assuming…
Context - Exoplanetary upper atmospheres are low density environments where radiative processes can compete with collisional ones and introduce non-local thermodynamic equilibrium (NLTE) effects into transmission spectra. Aims - We develop…
Robust 3D registration is a fundamental problem in computer vision and robotics, where the goal is to estimate the geometric transformation between two sets of measurements in the presence of noise, mismatches, and extreme outlier…
We present a new method to invert variable stress changes of fractures from InSAR ground displacements. Fractures can be either faults or magma intrusions, embeded in a 3D heterogeneous crust with prominent topographies. The method is based…
The Newton-Sabatier method for solving inverse scattering problem with fixed-energy phase shifts for a sperically symmetric potential is discussed. It is shown that this method is fundamentally wrong: in general it cannot be carried…
Land surface temperature (LST) retrieval from remote sensing data is pivotal for analyzing climate processes and surface energy budgets. However, LST retrieval is an ill-posed inverse problem, which becomes particularly severe when only a…
Remarkable mathematical properties of the integrable nonlinear Schr\"odinger equation (NLSE) can offer advanced solutions for the mitigation of nonlinear signal distortions in optical fibre links. Fundamental optical soliton, continuous and…
Vision-Language Latent Diffusion Models (LDMs) (Rombach et al., 2022) provide powerful generative priors for inverse problems. However, existing LDM-based inverse solvers typically require a large number of neural function evaluations…
Multi-view mesh reconstruction remains a core challenge in computer graphics and vision, especially for recovering high-frequency geometry from sparse observations. Recent methods such as 3D Gaussian Splatting (3DGS) and Neural Radiance…
3-D astrophysical atmospheres will have random velocity fields. We seek to combine the methods we have developed for solving the 1-D problem with arbitrary flows to those that we have developed for solving the fully 3-D relativistic…
We propose a method for optical nano-imaging in which the structure of a three-dimensional inhomogeneous medium may be recovered from far-field power measurements. Neither phase control of the illuminating field nor phase measurements of…
This paper presents reconstructions of homogeneous targets from the 2D and 3D Fresnel databases by one-step imaging methods based on the computation of topological derivative and topological energy fields. The electromagnetic inverse…
The spectral numerical mode-matching (SNMM) method is developed to simulate the 3D layered multi-region structures. The SNMM method is a semi-analytical solver having the properties of dimensionality reduction to reduce computational costs;…