Source Localization in Random Acoustic Waveguides

Borcea, Liliana; Issa, Leila; Tsogka, Chrysoula

doi:10.1137/100782711

Cited by 21 publications

(38 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, the functions Φ Dn in (71) are approximately proportional to Φ n , for n = −1, 0, and they give a similar contribution to the focus of the image for a full detector aperture or a smaller one. The focusing of (71) at points x in the support of the reflectivity r is primarily dictated by the coupling matrix S. The best focusing is for S jj = δ jj , corresponding to an incoherent source with θ defined in (14) and a full aperture A s = (0, X). The terms in j =j in the square brackets in (71) vanish in this case and, if in addition the detector has full aperture, the imaging function becomes…”

Section: Quantification Of Resolutionmentioning

confidence: 99%

A ghost imaging modality in a random waveguide

Borcea¹,

Garnier²

2018

Inverse Problems

Self Cite

View full text Add to dashboard Cite

We study the imaging of a penetrable scatterer, aka target, in a waveguide with randomly perturbed boundary. The target is located between a partially coherent source which transmits the wave, and a detector which measures the spatially integrated energy flux of the wave. The imaging is impeded by random boundary scattering effects that accumulate as the wave propagates. We consider a very large distance (range) between the target and the detector, where that cumulative scattering is so strong that it distributes the energy evenly among the components (modes) of the wave. Conventional imaging is impossible in this equipartition regime. Nevertheless, we show that the target can be located with a ghost imaging modality. This forms an image using the cross-correlation of the measured energy flux, integrated over the aperture of the detector, with the time and space resolved energy flux in a reference waveguide, at the search range. We consider two reference waveguides: The waveguide with unperturbed boundary, in which we can calculate the energy flux, and the actual random waveguide, before the presence of the target, in which the energy flux should be measured. We analyze the ghost imaging modality from first principles and show that it can be efficient in a random waveguide geometry in which there is both strong modal dispersion and mode coupling induced by scattering, provided that the standard ghost imaging function is modified and integrated over a suitable time offset window in order to compensate for dispersion and diffusion. The analysis quantifies the resolution of the image in terms of the source and detector aperture, the range offset between the source and the target, and the duration of the measurements.

show abstract

Section: Quantification Of Resolutionmentioning

confidence: 99%

A ghost imaging modality in a random waveguide

Borcea¹,

Garnier²

2018

Inverse Problems

Self Cite

View full text Add to dashboard Cite

show abstract

“…We refer to [2, 5-9, 19, 20, 23, 24] for mathematical studies of inverse scattering problems in acoustic and elastic waveguides with straight walls, and filled with homogeneous media. Random acoustic waveguides with finite cross-section are considered in [4,11], and with unbounded cross-section, as encountered in ocean acoustics, in [3,21]. Examples of inverse scattering problems in planar electromagnetic waveguides are in [13,17,22], where the problem is reduced to one for the scalar Helmholtz equation by considering a single type of waves, transverse electric or magnetic.…”

Section: 3)mentioning

confidence: 99%

Imaging with electromagnetic waves in terminating waveguides

Borcea¹,

Nguyen²

2016

IPI

Self Cite

View full text Add to dashboard Cite

We study an inverse scattering problem for Maxwell's equations in terminating waveguides, where localized reflectors are to be imaged using a remote array of sensors. The array probes the waveguide with waves and measures the scattered returns. The mathematical formulation of the inverse scattering problem is based on the electromagnetic Lippmann-Schwinger integral equation and an explicit calculation of the Green tensor. The image formation is carried with reverse time migration and with ℓ 1 optimization.

show abstract

“…The method there uses definition (3.29) of the Wigner transform for a search range Z s A , and estimates Z A as the minimizer of the misfit between the peak time of the theoretical model (4.9) and the calculated (C j (τ )) 1≤j≤N from the data. It is observed in [8] that the range estimation is not sensitive to knowing the source density and that the search for Z A can be done in conjunction with the estimation of the autocorrelation of the fluctuations, in case it is unknown. The method in [8] has been tested extensively with numerical simulations for both large and small arrays in waveguides with random wave speed.…”

Section: Arrival Time Analysismentioning

confidence: 99%

Source estimation with incoherent waves in random waveguides

2015

Self Cite

View full text Add to dashboard Cite

Abstract. We study an inverse source problem for the acoustic wave equation in a random waveguide. The goal is to estimate the source of waves from measurements of the acoustic pressure at a remote array of sensors. The waveguide effect is due to boundaries that trap the waves and guide them in a preferred (range) direction, the waveguide axis, along which the medium is unbounded. The random waveguide is a model of perturbed ideal waveguides which have flat boundaries and are filled with known media that do not change with range. The perturbation consists of fluctuations of the boundary and of the wave speed due to numerous small inhomogeneities in the medium. The fluctuations are uncertain in applications, which is why we model them with random processes, and they cause significant cumulative scattering at long ranges from the source. The scattering effect manifests mathematically as an exponential decay of the expectation of the acoustic pressure, the coherent part of the wave. The incoherent wave is modeled by the random fluctuations of the acoustic pressure, which dominate the expectation at long ranges from the source. We use the existing theory of wave propagation in random waveguides to analyze the inverse problem of estimating the source from incoherent wave recordings at remote arrays. We show how to obtain from the incoherent measurements high fidelity estimates of the time resolved energy carried by the waveguide modes, and study the invertibility of the system of transport equations that model energy propagation in order to estimate the source.Key words. Waveguides, random media, transport equations, Wigner transform. AMS subject classifications. 35Q61, 35R601. Introduction. We study an inverse problem for the scalar (acoustic) wave equation, where we wish to estimate the source of waves from measurements of the acoustic pressure field p(t, x) at a remote array of receiver sensors. The waves propagate in a waveguide, meaning that they are trapped by boundaries and are guided in the range direction, the waveguide axis, along which the medium is unbounded. Ideally the boundaries are straight and the medium does not change with range. We consider perturbed waveguides filled with heterogeneous media, where the boundary and the wave speed have small fluctuations on scales similar to the wavelength. These fluctuations have little effect in the vicinity of the source, but they are important at long ranges because they cause significant cumulative wave scattering. We suppose that the array of receivers is far from the source, as is typical in applications in underwater acoustics, sound propagation in corrugated pipes, in tunnels, etc., and study how cumulative scattering impedes the inversion.In most setups the fluctuations are uncertain, which is why we introduce a stochastic framework and model them with random processes. The inversion is carried in only one perturbed waveguide, meaning that the array measures one realization of the random pressure field, the solution of the wave equation in that waveguide...

show abstract

Source Localization in Random Acoustic Waveguides

Cited by 21 publications

References 19 publications

A ghost imaging modality in a random waveguide

A ghost imaging modality in a random waveguide

Imaging with electromagnetic waves in terminating waveguides

Source estimation with incoherent waves in random waveguides

Contact Info

Product

Resources

About