Passive Synthetic Aperture Imaging

Garnier, Josselin; Papanicolaou, George

doi:10.1137/15m1019696

Cited by 8 publications

(23 citation statements)

References 25 publications

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“…The goal is to estimate this ensemble of impulse responses, which in many applications reveals the structure of the environment being sensed. Problems of this type arise in a wide variety of applications including as opportunistic channel estimation in underwater acoustics [4,[41][42][43], seismic interferometry [8], and passive synthetic aperture imaging [13].…”

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confidence: 99%

Spectral Methods for Passive Imaging: Nonasymptotic Performance and Robustness

Lee¹,

Krahmer²,

Romberg³

2018

SIAM J. Imaging Sci.

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We study the problem of passive imaging through convolutive channels. A scene is illuminated with an unknown, unstructured source, and the measured response is the convolution of this source with multiple channel responses, each of which is time-limited. Spectral methods based on the commutativity of convolution, first proposed and analyzed in the 1990s, provide an elegant mathematical framework for attacking this problem. However, these now classical methods are very sensitive to noise, especially when working from relatively small sample sizes.In this paper, we show that a linear subspace model on the coefficients of the impulse responses of the channels can make this problem well-posed. We derive non-asymptotic error bounds for the generic subspace model by analyzing the spectral gap of the cross-correlation matrix of the channels relative to the perturbation introduced by noise. Numerical results show that this modified spectral method offers significant improvements over the classical method and outperforms other competing methods for multichannel blind deconvolution.

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confidence: 99%

Spectral Methods for Passive Imaging: Nonasymptotic Performance and Robustness

Lee¹,

Krahmer²,

Romberg³

2018

SIAM J. Imaging Sci.

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“…In practice the spectrum may not be equal to (13) but of the formF (ω) = f o |ω| exp(− |ω|) for some > 0 for instance. This situation is analyzed in B.3.…”

Section: Remarkmentioning

confidence: 99%

“…The situation is different when the observer is moving, because the observer may then be able to exploit the synthetic aperture generated by its trajectory. For instance, active synthetic aperture radar (when the moving antenna transmits and receives) has proved to be a very efficient imaging modality [5,7] and bistatic or passive versions (when the moving antenna only records and uses signals transmitted by controlled or opportunistic sources) are now the subject of intense research [2,11,13,20]. When the observer is moving, the autocorrelation function of the recorded signal depends in a complicated and interesting way of the environment.…”

Section: Introductionmentioning

confidence: 99%

How a moving passive observer can perceive its environment ? The Unruh effect revisited

Fink

Garnier

2020

Wave Motion

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We consider a point-like observer that moves in a medium illuminated by noise sources with Lorentz-invariant spectrum. We show that the autocorrelation function of the signal recorded by the observer allows it to perceive its environment. More precisely, we consider an observer with constant acceleration (along a Rindler trajectory) and we exploit the recent work on the emergence of the Green's function from the cross correlation of signals transmitted by noise sources. First we recover the result that the signal recorded by the observer has a constant Wigner transform, i.e. a constant local spectrum, when the medium is homogeneous (this is the classical analogue of the Unruh effect). We complete that result by showing that the Rindler trajectory is the only straight-line trajectory that satisfies this property. We also show that, in the presence of an obstacle in the form of an infinite perfect mirror, the Wigner transform is perturbed when the observer comes into the neighborhood of the obstacle. The perturbation makes it possible for the observer to determine its position relative to the obstacle once the entire trajectory has been traversed.

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“…In [13], the stop-go approximation was made. The receiver was supposed to be at the stationary position x j during the time interval [T j , T j +∆T ] for the N successive positions x j , j = 1, .…”

Section: Passive Synthetic Aperture Imaging Set Upmentioning

confidence: 99%

“…When there is one opportunistic source emitting repeatedly the same pulse, it has been shown that correlation-based techniques could be used to image reflectors [23,24,26,27]. When there are many noise sources and the illumination is diversified enough, that is to say, when the noise sources are dense enough and are distributed in an extended region, it was shown in [13] that the reflectors can be imaged by migrating the autocorrelation functions of the received signals over successive time windows. The imaging method proposed in [13] follows the principle of seismic interferometry, in which a passive receiver array is used to perform travel-time tomography and reflector imaging using only ambient noise illumination [3,10,20,25,11,12,14].…”

Section: Introductionmentioning

confidence: 99%

Passive synthetic aperture imaging with limited noise sources

Garnier¹

2016

Inverse Problems

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We consider a passive synthetic aperture imaging problem. A single moving receiver antenna records random signals generated by one or several distant noise sources and backscattered by one or several reflectors. The sources emit noise signals modeled by stationary random processes. The reflectors can be imaged by summing the autocorrelation functions of the received signals computed over successive time windows, corrected for Doppler factors and migrated by appropriate travel times. In particular the Doppler effect plays an important role and it can be used for resolution enhancement. When the noise source positions are not known, the reflector can be localized with an accuracy proportional to the reciprocal of the noise bandwidth, even when only a very small number of sources are available. When the noise source positions are known, the reflector can be localized with a cross range resolution proportional to the carrier wavelength and inversely proportional to the length of the receiver trajectory (i.e., the synthetic aperture), and with a range resolution proportional to the reciprocal of the bandwidth, even with only one noise source.

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Passive Synthetic Aperture Imaging

Cited by 8 publications

References 25 publications

Spectral Methods for Passive Imaging: Nonasymptotic Performance and Robustness

Spectral Methods for Passive Imaging: Nonasymptotic Performance and Robustness

How a moving passive observer can perceive its environment ? The Unruh effect revisited

Passive synthetic aperture imaging with limited noise sources

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