Related papers: Perturbative numeric approach in microwave imaging
The purpose of this paper is to propose a non-iterative method for the inverse conductivity problem of recovering multiple small anomalies from the boundary measurements. When small anomalies are buried in a conducting object, the electric…
We propose an efficient method for demodulation of phase modulated signals via iterated Hilbert transform embeddings. We show that while a usual approach based on one application of the Hilbert transform provides only an approximation to a…
A long-standing open problem in harmonic analysis is: given a non-negative measure $\mu$ on $\mathbb R$, find the infimal width of frequencies needed to approximate any function in $L^2(\mu)$. We consider this problem in the "perturbative…
In this paper, we extend our research concerning the standard and linearized monotonicity methods for the inverse problem of the time harmonic elastic wave equation and introduce the modification of these methods for noisy data. In more…
The electrical generation and detection of elastic waves are the foundation for acousto-electronic and acousto-optic systems. For surface-acoustic-wave devices, micro-/nano-electromechanical systems, and phononic crystals, tailoring the…
We consider an undetermined coefficient inverse problem for a nonlinear partial differential equation describing high intensity ultrasound propagation as widely used in medical imaging and therapy. The usual nonlinear term in the standard…
This paper proposes a novel approach to reconstruct changes in a target conductivity from electrical impedance tomography measurements. As in the conventional difference imaging, the reconstruction of the conductivity change is based on…
We provide a mathematical analysis and a numerical framework for Lorentz force electrical conductivity imaging. Ultrasonic vibration of a tissue in the presence of a static magnetic field induces an electrical current by the Lorentz force.…
The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and non-diagonal elements of the Fock state. The diagonal elements of the Fock state are solvable but can contain the information about coupling constants.…
In this paper, we consider the scattering of a plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in three dimensions. Based on the Helmholtz decomposition, the elastic scattering problem is reduced to a…
We employ ptychography, a phase-retrieval imaging technique, to show experimentally for the first time that a partially coherent high-energy matter (electron) wave emanating from an extended source can be decomposed into a set of mutually…
We present a method that formally calculates \emph{exact} frequency shifts of an electromagnetic field for arbitrary changes in the refractive index. The possible refractive index changes include both anisotropic changes and boundary…
We perturb with an additive Gaussian white noise the Hamiltonian system associated to a cubic anharmonic oscillator. The stochastic system is assumed to start from initial conditions that guarantee the existence of a periodic solution for…
In this paper, we investigate two types of time-harmonic elastic wave scattering problems. The first one involves the scattered wave generated by an active elastic source with compact support. The second one concerns elastic wave scattering…
Electrical impedance tomography aims at reconstructing the conductivity inside a physical body from boundary measurements of current and voltage at a finite number of contact electrodes. In many practical applications, the shape of the…
We provide a rigorous derivation of an asymptotic formula for perturbations in the resonance values caused by the presence of finite number of anisotropic imperfections of small shapes with constitutive parameters different from the…
Multi-wave inverse problems are indirect imaging methods using the interaction of two different imaging modalities. One brings spatial accuracy, and the other contrast sensitivity. The inversion method typically involve two steps. The first…
We pursue the investigations initiated in [Aur{\'e}lien Deya: A non-linear wave equation with fractional perturbation (2017)] about a wave-equation model with quadratic perturbation and stochastic forcing given by a space-time fractional…
We survey functional analytic methods for studying subwavelength resonator systems. In particular, rigorous discrete approximations of Helmholtz scattering problems are derived in an asymptotic subwavelength regime. This is achieved by…
This paper discusses the modeling of acoustic wave fields in microstructured elastic solids within the framework of Riemann-Cartan geometry. We consider a scenario in which microstructural deformations occur significantly faster than those…