Related papers: Harmonic inversion as a general method for periodi…
Full-waveform inversion (FWI) is known as a seismic data processing method that achieves high-resolution imaging. In the inversion part of the method that brings high resolution in finding a convergence point in the model space, a local…
In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…
We present the world-line quantisation of a system invariant under the symmetries of reciprocal relativity (pseudo-unitary transformations on ``phase space coordinates" $(x^\mu(\tau),p^\mu(\tau))$ which preserve the Minkowski metric and the…
In this paper, a reconstruction method for the spatially distributed dielectric constant of a medium from the back scattering wave field in the frequency domain is considered. Our approach is to propose a globally convergent algorithm,…
Motivated by applications to acoustic imaging, the present work establishes a framework to analyze scattering for the one-dimensional wave, Helmholtz, Schr\"odinger and Riccati equations that allows for coefficients which are more singular…
We propose a sparse regularization model for inversion of incomplete Fourier transforms and apply it to seismic wavefield modeling. The objective function of the proposed model employs the Moreau envelope of the $\ell_0$ norm under a tight…
A construction of integrable hamiltonian systems associated with different graded realizations of untwisted loop algebras is proposed. Such systems have the form of Euler - Arnold equations on orbits of loop algebras. The proof of…
A well-known method of transferring the population of a quantum system from an eigenspace of the free Hamiltonian to another is to use a periodic control law with an angular frequency equal to the difference of the eigenvalues. For finite…
This paper concerns the inverse source scattering problems of recovering random sources for acoustic and elastic waves. The underlying sources are assumed to be random functions driven by an additive white noise. The inversion process aims…
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…
In this paper we study direct and inverse problems for discrete and continuous time skew-selfadjoint Dirac systems with rectangular (possibly non-square) pseudo-exponential potentials. For such a system the Weyl function is a strictly…
We present a systematic study of the performance of numerical pseudo-atomic orbital basis sets in the calculation of dielectric matrices of extended systems using the self-consistent Sternheimer approach of [F. Giustino et al., Phys. Rev. B…
This paper investigates the inverse scattering problem of time-harmonic plane waves incident on a perfectly reflecting random periodic structure. To simulate random perturbations arising from manufacturing defects and surface wear in…
We present a new boundary integral formulation for time-harmonic wave diffraction from two-dimensional structures with many layers of arbitrary periodic shape, such as multilayer dielectric gratings in TM polarization. Our scheme is robust…
A quantum generalization of the semiclassical theory of Gutzwiller is given. The new formulation leads to systematic orbit-by-orbit inclusion of higher $\hbar$ contributions to the spectral determinant. We apply the theory to billiard…
Interferometric inversion involves recovery of a signal from cross-correlations of its linear transformations. A close relative of interferometric inversion is the generalized phase retrieval problem, which consists of recovering a signal…
We introduce an $O(M)$ algorithm for evaluating the azimuthal Fourier modes $G_{k,m}$, $m = 0, 1, ..., M$, of the three-dimensional Helmholtz Green's function with real wavenumber $k$, together with all their first- and second-order…
Hawking radiation has become experimentally testable thanks to the many analogue systems which mimic the effects of the event horizon on wave propagation. These systems are typically dominated by dispersion, and give rise to a numerically…
This work studies the semiclassical methods in multi-dimensional quantum systems bounded by finite potentials. By replacing the Maslov index by the scattering phase, the modified transfer operator method gives rather accurate corrections to…
Commuting integral and differential operators connect the topics of Signal Processing, Random Matrix Theory, and Integrable Systems. Previously, the construction of such pairs was based on direct calculation and concerned concrete special…