Related papers: Homometric Point Sets and Inverse Problems
Consider the problem of scattering of electromagnetic waves by a doubly periodic structure. The medium above the structure is assumed to be inhomogeneous characterized completely by an index of refraction. Below the structure is a perfect…
We study in this paper three natural notions of convergence of homogeneous manifolds, namely infinitesimal, local and pointed, and their relationship with a fourth one, which only takes into account the underlying algebraic structure of the…
The paper gives a thorough introduction to spectra of digraphs via its Hermitian adjacency matrix. This matrix is indexed by the vertices of the digraph, and the entry corresponding to an arc from $x$ to $y$ is equal to the complex unity…
In this paper we consider the inverse electromagnetic scattering for a cavity surrounded by an inhomogeneous medium in three dimensions. The measurements are scattered wave fields measured on some surface inside the cavity, where such…
When an inverse problem is solved by a gradient-based optimization algorithm, the corresponding forward and adjoint problems, which are introduced to compute the gradient, can be also solved iteratively. The idea of iterating at the same…
We show that real model sets with real internal spaces are determined, up to translation and changes of density zero by their two- and three-point correlations. We also show that there exist pairs of real (even one dimensional) aperiodic…
The problem to compute the vertices of a polytope given by affine inequalities is called vertex enumeration. The inverse problem, which is equivalent by polarity, is called the convex hull problem. We introduce `approximate vertex…
This paper is concerned with reconstructing an acoustic obstacle and its excitation sources from the phaseless near-field measurements. By supplementing some artificial sources to the inverse scattering system, this co-inversion problem can…
To properly solve the coincidence problem ($\Omega_\mathrm{DM} \simeq 5\Omega_\mathrm{VM}$) in a model of asymmetric dark matter, one cannot simply relate the number densities of visible and dark matter without also relating their particle…
In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it…
The linear code equivalence (LCE) problem is shown to be equivalent to the point set equivalence (PSE) problem, i.e., the problem to check whether two sets of points in a projective space over a finite field differ by a linear change of…
An obstruction theory for representing homotopy classes of surfaces in 4-manifolds by immersions with pairwise disjoint images is developed, using the theory of non-repeating Whitney towers. The accompanying higher-order intersection…
We study an inverse problem for the wave equation where localized wave sources in random scattering media are to be determined from time resolved measurements of the waves at an array of receivers. The sources are far from the array, so the…
We study fixed point sets for holomorphic automorphisms (and endomorphisms) on complex manifolds. The main object of our interest is to determine the number and configuration of fixed points that forces an automorphism (endomorphism) to be…
Many naturally-occuring models in the sciences are well-approximated by simplified models, using multiscale techniques. In such settings it is natural to ask about the relationship between inverse problems defined by the original problem…
Diffraction tomography is a widely used inverse scattering technique for quantitative imaging of weakly scattering media. In its conventional formulation, diffraction tomography assumes monochromatic plane wave illumination. This…
The photometric stereo (PS) problem consists in reconstructing the 3D-surface of an object, thanks to a set of photographs taken under different lighting directions. In this paper, we propose a multi-scale architecture for PS which,…
Obtaining meaningful solutions for inverse problems has been a major challenge with many applications in science and engineering. Recent machine learning techniques based on proximal and diffusion-based methods have shown promising results.…
In this announcement, we deal with the Orthogonal Procrustes Problem, in which two point configurations are compared in order to construct a map to optimally align the two sets. This extends this to $\varepsilon$-diffeomorphisms, introduced…
Holographic coherent X-ray imaging enables nanoscale imaging of biological cells and tissues, rendering both phase and absorption contrast, i.e. real and imaginary parts of the refractive index. Unlike the standard model, which assumes a…