Robustness of time reversal for waves in time-dependent random media

Vigo, Daniel G. Alfaro; Fouque, Jean‐Pierre; Garnier, Josselin; Nachbin, André

doi:10.1016/j.spa.2004.04.002

Cited by 16 publications

(6 citation statements)

References 23 publications

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“…However, the accuracy to which we need to know the Green function is quite high. In a series of recent papers [1,12,13], it was shown that even quite small errors in the estimate of the Green function could very much perturb the refocusing properties of the time reversed signal. Sufficiently accurate knowledge of the media at the microscopic level is therefore out of reach in many interesting applications.…”

Section: Introductionmentioning

confidence: 99%

Time-reversal-based detection in random media

Bal¹,

Pinaud²

2005

Inverse Problems

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We consider the detection and imaging of inclusions buried in highly heterogeneous media. We assume that only the statistical properties of the heterogeneous media can be observed and that the wave energy density may be modelled by macroscopic equations. The detection and imaging capabilities hinge on ensuring that the measured data are statistically stable, which means that they depend only on the macroscopic statistical parameters of the random media and not on the microscopic statistical realization. In this paper, the macroscopic model is a diffusion equation. In this context, we construct statistical tests to detect inclusions based on macroscopic diffusion measurements and perform asymptotic expansions to image their location and volume. We show that time-reversal measurements enjoy a much larger signal-to-noise ratio in the presence of background noise than do direct wave energy measurements. This is a direct consequence of the enhanced refocusing properties that characterize time reversed waves propagating in heterogeneous media. Finally, we present numerical simulations of acoustic waves propagating in heterogeneous two-dimensional media. The numerical simulations illustrate which factors contribute to 'noise' in the measured data and how they affect the detection and imaging capabilities.

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Section: Introductionmentioning

confidence: 99%

Time-reversal-based detection in random media

Bal¹,

Pinaud²

2005

Inverse Problems

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“…However, the computational cost of 3D back propagation in the model domain is much higher than the 2D case. Statistical analysis (Alfaro Vigo et al 2004) and a broader frequency bandwidth should also be considered in future studies. However, the degree of applicability of the time-reversal method at higher frequencies in outdoor environment remains a challenging question to be answered.…”

Section: Resultsmentioning

confidence: 99%

The effect of changing scatterer positions on acoustic time-reversal refocusing in a 2D urban environment at low frequencies

2007

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In a previous work, we considered time-reversal refocusing for localizing a sound source in a highly reverberant urban environment with non-line-of-sight (NLOS) receivers. The approach involved a virtual (computer-based) time-reversal propagation calculation using a priori knowledge of the receiver and scatterer positions. Among the errors that affect the quality of refocusing is the imperfect accuracy of the assumed scatterer locations. Some practical analogues of changing scatterer positions are (a) the building coordinate errors (or mistakes) and (b) the random movement of vehicles on the street of an urban setting. We address these issues by conducting a time-reversal analysis of a set of numerically generated synthetic acoustic pressure recordings after intentionally introducing errors by altering the position of the scatterers. The numerical experiment results indicate that, for a realistically complicated urban setting, coordinate errors in the position of only a few scatterers have little detrimental effect. The effect of coordinate errors in one or a few scatterers is suppressed by the constraints imposed by correct propagation features (both kinematic and dynamic) generated by multiple reflections and diffractions from other precisely located scatterers. The dependence of source localization accuracy on the relative error in scatterer coordinates, the relative number of scatterers with coordinate errors and the number of receivers is quantitatively assessed in this paper. In general, time-reversal refocusing with a large number of receivers can compensate for more severe errors. Even for only three non-line-of-sight receivers, building location errors in the order of 3 m still give good results. Adding small scatterers (like vehicles) close to a receiver is more critical than adding scatterers relatively far from the receivers.

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“…The ansatz (15) corresponds to a plane wave propagating along the z-axis with a slowly varying transverse envelope. In the regime ε 1, it has been shown in [12] that the forward-scattering approximation in the negative z-direction and the white-noise approximation are valid, which means that the second-order derivative in z in (16) can be neglected and the random potential 1 ε µ x, z ε 2 can be replaced by a white noise. The mathematical statement is that the functionφ ε (ω, x, z) weakly converges to the solutionφ(ω, x, z) of the Itô-Schrödinger equation 172i…”

Section: 2mentioning

confidence: 99%

“…In the time-reversal interpretation, this means that the wave backpropagates in a different realization of the random medium. We know that time-reversal refocusing is sensitive to any change in the medium [1,2], so we can anticipate that random scattering is not good for ghost imaging.…”

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confidence: 99%

Ghost imaging in the random paraxial regime

Garnier¹

2016

IPI

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In this paper we analyze a wave-based imaging modality called ghost imaging that can produce an image of an object illuminated by a partially coherent source. The image of the object is obtained by correlating the intensities measured by two detectors, one that does not view the object and another one that does view the object. More exactly, a high-resolution detector measures the intensity of a wave field emitted by a partially coherent source which has not interacted with the object to be imaged. A bucket (or singlepixel) detector collects the total (spatially-integrated) intensity of the wave field emitted by the same source that has interacted with the object. The correlation of the intensity measured at the high-resolution detector with the intensity measured by the bucket detector gives an image of the object. In this paper we analyze this imaging modality when the medium through which the waves propagate is random. We discuss the relation with time reversal focusing and with correlation-based imaging using ambient noise sources. We clarify the role of the partial coherence of the source and we study how scattering affects the resolution properties of the ghost imaging function in the paraxial regime: the image resolution is all the better as the source is less coherent, and all the worse as the medium is more scattering.

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Robustness of time reversal for waves in time-dependent random media

Cited by 16 publications

References 23 publications

Time-reversal-based detection in random media

Time-reversal-based detection in random media

The effect of changing scatterer positions on acoustic time-reversal refocusing in a 2D urban environment at low frequencies

Ghost imaging in the random paraxial regime

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