# Resolution and denoising in near-field imaging

@article{Derveaux2006ResolutionAD, title={Resolution and denoising in near-field imaging}, author={Gr{\'e}goire Derveaux and George C Papanicolaou and Chrysoula Tsogka}, journal={Inverse Problems}, year={2006}, volume={22}, pages={1437-1456} }

We consider the inverse problem of reconstructing surface displacements from noisy acoustic measurements collected at a distance from the surface that is comparable to the wavelength. As the detectors move closer to the surface and information from evanescent waves is recorded, the resolution of the image improves up to a level that is limited by the signal-to-noise ratio (SNR). We review this basic trade-off in near-field imaging with narrowband signals and then extend it to broadband signals…

## Figures and Tables from this paper

## 17 Citations

Near-field imaging of the surface displacement on an infinite ground plane

- Mathematics
- 2013

This paper is concerned with the
inverse diffraction problem for an unbounded obstacle which is a
ground plane with some local disturbance. The data is collected in
the near-field regime with a…

Imaging of locally rough surfaces from intensity-only far-field or near-field data

- Mathematics
- 2016

This paper is concerned with a nonlinear imaging problem, which aims to reconstruct a locally perturbed, perfectly reflecting, infinite plane from intensity-only (or phaseless) far-field or…

Imaging of reflective surfaces by near-field optics.

- Physics, MedicineOptics letters
- 2012

An imaging problem that aims to identify the profile of a reflective surface by the scattered wave measured in the near field is considered and a novel multiple frequency approach is presented that captures both the main features as well as the fine details of the structure.

Resolution and stability analysis in full-aperture, linearized conductivity and wave imaging

- Chemistry
- 2013

In this paper we consider resolution estimates in both the linearized conductivity problem and the wave imaging problem. Our purpose is to provide explicit formulas for the resolving power of the…

. RESOLUTION AND STABILITY ANALYSIS IN LINEARIZED CONDUCTIVITY AND WAVE IMAGING. PART I: FULL APERTURE CASE

- 2011

In this paper we consider resolution estimates in both the linearized conductivity problem and the wave imaging problem. Our purpose is to provide explicit formulas for the resolving power of the…

Near-Field Imaging of Infinite Rough Surfaces in Dielectric Media

- Mathematics, Computer ScienceSIAM J. Imaging Sci.
- 2014

This paper is concerned with an inverse surface scattering problem in near-field optical imaging, which is to reconstruct the scattering surface of a dielectric medium with a resolution beyond the…

Compressive imaging of subwavelength structures: periodic rough surfaces.

- Physics, MedicineJournal of the Optical Society of America. A, Optics, image science, and vision
- 2012

Surprisingly, it can be shown heuristically and numerically that under the Rayleigh hypothesis the angular spectrum is compressible and amenable to compressed sensing techniques.

Imaging of Local Surface Displacement on an Infinite Ground Plane: The Multiple Frequency Case

- Mathematics, Computer ScienceSIAM J. Appl. Math.
- 2011

By using multiple frequency data to image the profile of the surface displacement, a stable and accurate reconstruction method is presented and an integral equation approach is introduced for the solution of the forward scattering problem.

Near-Field Imaging of Interior Cavities

- Physics
- 2015

A novel method is developed for solving the inverse problem of reconstructing the shape of an interior cavity. The boundary of the cavity is assumed to be a small and smooth perturbation of a circle.…

Numerical solution of an inverse obstacle scattering problem with near-field data

- Mathematics, Computer ScienceJ. Comput. Phys.
- 2015

A novel method is presented for solving the inverse obstacle scattering problem of the two-dimensional Helmholtz equation, which is to reconstruct the obstacle surface by using the near-field data.

## References

SHOWING 1-10 OF 25 REFERENCES

Resolution and super-resolution in inverse diffraction

- Physics
- 1997

In this tutorial paper we discuss the concept of resolution in problems of inverse diffraction. These problems have direct applications in areas such as acoustic holography and can also be considered…

Theory and applications of time reversal and interferometric imaging

- Mathematics
- 2003

In time reversal, an array of transducers receives the signal emitted by a localized source, time reverses it and re-emits it into the medium. The emitted waves back-propagate to the source and tend…

Coherent Interferometry in Finely Layered Random Media

- Physics, Computer ScienceMultiscale Model. Simul.
- 2006

It is shown that coherent interferometry exploits the time coherence in the data, leading to stable images, and it is proved that in this regime only the ODA behavior plays a role in the imaging, and the resolution of CINT is quantified explicitly in terms of this time coherent and the array aperture.

Conformal generalized near‐field acoustic holography for axisymmetric geometries

- Physics
- 1990

The normal velocity field on the boundary σ of a radiating source is reconstructed with high resolution by using pressure data, measured in the very near field to include evanescent components, fast…

Near-field optics theories

- Physics
- 1996

The development of near-field optics theory is reviewed. We first recall that near-field optics is not limited to near-field microscopy. Broadly speaking, it concerns phenomena involving evanescent…

Generalized nearfield acoustical holography for cylindrical geometry : theory and experiment

- Physics
- 1987

From the measurement of the acoustic pressure on a cylindrical, two‐dimensional contour located close to the surface of an underwater, vibrating cylinder, the complete three‐dimensional sound field…

Nearfield acoustical holography using an underwater, automated scanner

- Physics
- 1985

A computer‐controlled, three‐axis Cartesian scanning facility has been constructed in a large water tank to provide accurate preprogrammed contouring with hydrophone probes. As the scanner moves on…

Sound source reconstructions using a microphone array

- Physics
- 1980

A square microphone array with 256 elements has been constructed along with interfacing electronics to study low‐frequency (1–5 kHz) sound sources in air using the principles of acoustical…

Interferometric array imaging in clutter

- Mathematics
- 2005

We introduce a space-time interferometric array imaging functional that provides statistically stable images in cluttered environments. We also present a resolution theory for this imaging functional…

Near Field Microscopy and Near Field Optics

- Physics
- 2003

The early eighties have experienced a revolution in the perception of physical phenomena. This revolution is the birth of a new generation of imaging systems based on the detection of non-radiating…