Enhanced Resolution in Structured Media

  title={Enhanced Resolution in Structured Media},
  author={Habib M. Ammari and Eric Bonnetier and Yves Capdeboscq},
  journal={SIAM J. Appl. Math.},
The aim of this paper is to prove that we can achieve a resolution enhancement in detecting a target inclusion if it is surrounded by an appropriate structured medium. The physical notions of resolution and focal spot are revisited. Indeed, the resolution enhancement is estimated in terms of the material parameters of the structured medium. 

Figures from this paper

Super-resolution in high-contrast media
  • H. Ammari, Hai Zhang
  • Physics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2015
A mathematical theory is developed to explain the super-resolution and super-focusing in high-contrast media. The approach is based on the resonance expansion of the Green function associated with
Medium induced resolution enhancement for broadband imaging
A number of recent studies discuss the phenomenon of super resolution, that is, the fact that a target can be localized with higher resolution than half a wavelength as suggested by the classical
Acousto-electromagnetic Tomography
A new inversion formula for the permittivity distribution is provided from cross-correlations between the electromagnetic boundary measurements in the perturbed medium and those in the unperturbed one and it is shown that it is possible to achieve a significant resolution enhancement.
Fast electromagnetic imaging of thin inclusions in half-space affected by random scatterers
We consider an inverse scattering problem wherein penetrable thin electromagnetic inclusions completely embedded in a half-space are surrounded by randomly distributed scatterers. A non-iterative
Diagnostic within a dielectric micro-structure: time-reversal and sparsity-constrained imaging
Computational imaging of micro-structured systems as a grid-like set of a finite number of circular cylindrical dielectric rods is considered. How to achieve meaningful localization,
On the Modeling and Diagnosis of a Micro-Structured Wire Antenna System
Micro-structured systems of wire antennas the inter-element distance of which being much smaller than the electromagnetic wavelengths either in transmission or reception are studied by the authors
Determination of the unknown support of thin penetrable inclusions within a half-space from multi-frequency response matrix
Thin, penetrable electromagnetic inclusions buried within a half space are retrieved from Multi-Static Response (MSR) matrix data collected above this half space at several frequencies. A
Microwave Imaging by Elastic Deformation
By using microwave measurements at different frequencies and ultrasound localized perturbations to create local changes in the medium it is possible to extend the method developed by Ammari et al. to reliably reconstruct both the real-valued functions a and q from the internal energies.


Edge Illumination and Imaging of Extended Reflectors
The singular value decomposition of the array response matrix is used to image selectively the edges of extended reflectors in a homogeneous medium and indicates that the subspaces spanned by the transition singular vectors are robust with respect to additive noise when the array has a large number of elements.
An Introduction to Mathematics of Emerging Biomedical Imaging
This paper presents a meta-modelling procedure that automates the very labor-intensive and therefore time-heavy and expensive process of manually cataloging and cataloging the materials used in tomographic and hybrid imaging procedures.
A filtered backpropagation algorithm for diffraction tomography.
The scattering support
We discuss inverse problems for the Helmholtz equation at fixed energy, specifically the inverse source problem and the inverse scattering problem from a medium or an obstacle. We introduce the
Focusing and imaging using eigenfunctions of the scattering operator.
An inverse scattering method that uses eigenfunctions of the scattering operator is presented. This approach provides a unified framework that encompasses eigenfunction methods of focusing and
Reconstruction of Small Inhomogeneities from Boundary Measurements
Introduction.- Part I: Detection of Small Conductivity Inclusions Transmission Problem Generalized Polarization Tensors Derivation of the Full Asymptotic Formula Detection of Inclusions.- Part II:
Focusing Beyond the Diffraction Limit with Far-Field Time Reversal
We present an approach for subwavelength focusing of microwaves using both a time-reversal mirror placed in the far field and a random distribution of scatterers placed in the near field of the
Time reversal imaging of obscured targets from multistatic data
  • A. Devaney
  • Computer Science
    IEEE Transactions on Antennas and Propagation
  • 2005
It is shown that the singular vectors of the K matrix together with knowledge of the Green function of the background medium in which the targets are embedded lead directly to classical time-reversal based images of the target locations as well as super-resolution images based on a generalized Multiple-Signal-Classification algorithm recently developed for use with the K Matrix.
An asymptotic formula for the voltage potential in a perturbed ε-periodic composite medium containing misplaced inclusions of size ε
We consider composite media made of homogeneous inclusions with C1,α,boundaries. Our goal is to compare the potential uε in a perfectly periodic composite with the potential uε,d, of a perturbed