Green’s function estimation in speckle using the decomposition of the time reversal operator: Application to aberration correction in medical imaging

2008 ◽  
Vol 123 (2) ◽  
pp. 866-877 ◽  
Author(s):  
Jean-Luc Robert ◽  
Mathias Fink
Keyword(s):  
Medical Imaging ◽  
Green’S Function ◽  
Green's Function ◽  
Time Reversal ◽  
Aberration Correction ◽  
Function Estimation

scholarly journals Unified double- and single-sided homogeneous Green’s function representations

2016 ◽  
Vol 472 (2190) ◽  
pp. 20160162 ◽  
Author(s):  
Kees Wapenaar ◽  
Joost van der Neut ◽  
Evert Slob
Keyword(s):  
Green’S Function ◽  
Multiple Scattering ◽  
Green's Function ◽  
Time Reversal ◽  
Wave Theory ◽  
Boundary Integral ◽  
Open Boundary ◽  
Quantum Mechanical ◽  
Holographic Imaging ◽  
Scattering Time

In wave theory, the homogeneous Green’s function consists of the impulse response to a point source, minus its time-reversal. It can be represented by a closed boundary integral. In many practical situations, the closed boundary integral needs to be approximated by an open boundary integral because the medium of interest is often accessible from one side only. The inherent approximations are acceptable as long as the effects of multiple scattering are negligible. However, in case of strongly inhomogeneous media, the effects of multiple scattering can be severe. We derive double- and single-sided homogeneous Green’s function representations. The single-sided representation applies to situations where the medium can be accessed from one side only. It correctly handles multiple scattering. It employs a focusing function instead of the backward propagating Green’s function in the classical (double-sided) representation. When reflection measurements are available at the accessible boundary of the medium, the focusing function can be retrieved from these measurements. Throughout the paper, we use a unified notation which applies to acoustic, quantum-mechanical, electromagnetic and elastodynamic waves. We foresee many interesting applications of the unified single-sided homogeneous Green’s function representation in holographic imaging and inverse scattering, time-reversed wave field propagation and interferometric Green’s function retrieval.

Accuracy of Green's function estimation from correlation of diffuse elastic waves on thin plates

2019 ◽  
Vol 146 (5) ◽  
pp. 3505-3511
Author(s):  
Lynda Chehami ◽  
Emmanuel Moulin ◽  
Julien de Rosny ◽  
Claire Prada
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Elastic Waves ◽  
Thin Plates ◽  
Function Estimation

scholarly journals A single-sided homogeneous Green's function representation for holographic imaging, inverse scattering, time-reversal acoustics and interferometric Green's function retrieval

2016 ◽  
Vol 205 (1) ◽  
pp. 531-535 ◽  
Author(s):  
Kees Wapenaar ◽  
Jan Thorbecke ◽  
Joost van der Neut
Keyword(s):  
Green’S Function ◽  
Inverse Scattering ◽  
Green's Function ◽  
Time Reversal ◽  
Boundary Integral ◽  
Open Surface ◽  
Function Representation ◽  
Holographic Imaging ◽  
Scattering Time ◽  
Time Reversal Acoustics

Abstract Green's theorem plays a fundamental role in a diverse range of wavefield imaging applications, such as holographic imaging, inverse scattering, time-reversal acoustics and interferometric Green's function retrieval. In many of those applications, the homogeneous Green's function (i.e. the Green's function of the wave equation without a singularity on the right-hand side) is represented by a closed boundary integral. In practical applications, sources and/or receivers are usually present only on an open surface, which implies that a significant part of the closed boundary integral is by necessity ignored. Here we derive a homogeneous Green's function representation for the common situation that sources and/or receivers are present on an open surface only. We modify the integrand in such a way that it vanishes on the part of the boundary where no sources and receivers are present. As a consequence, the remaining integral along the open surface is an accurate single-sided representation of the homogeneous Green's function. This single-sided representation accounts for all orders of multiple scattering. The new representation significantly improves the aforementioned wavefield imaging applications, particularly in situations where the first-order scattering approximation breaks down.

Localization of acoustic sensors from passive Green's function estimation

2015 ◽  
Vol 138 (5) ◽  
pp. 3010-3018 ◽  
Author(s):  
Thibault Nowakowski ◽  
Laurent Daudet ◽  
Julien de Rosny
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Acoustic Sensors ◽  
Function Estimation
Sign in / Sign up

Export Citation Format

Share Document