Synthetic Aperture Imaging of Direction- and Frequency-Dependent Reflectivities

Borcea, Liliana; Moscoso, Miguel; Papanicolaou, George; Tsogka, Chrysoula

doi:10.1137/15m1036063

Cited by 11 publications

(19 citation statements)

References 18 publications

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“…Let us change variables w = ω − ω o and use the notation 8) and integrate next over ω. We obtain after rearranging the terms that κ( y, z, z ) ≈ πN with notation We also have from ∆ = O(1) and definition (D.11) that both |ζ| and | ζ| are O(1).…”

Section: 32mentioning

confidence: 99%

Imaging in Random Media with Convex Optimization

Borcea¹,

Kocyigit

2017

SIAM J. Imaging Sci.

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Abstract. We study an inverse problem for the wave equation where localized wave sources in random scattering media are to be determined from time resolved measurements of the waves at an array of receivers. The sources are far from the array, so the measurements are affected by cumulative scattering in the medium, but they are not further than a transport mean free path, which is the length scale characteristic of the onset of wave diffusion that prohibits coherent imaging. The inversion is based on the Coherent Interferometric (CINT) imaging method which mitigates the scattering effects by introducing an appropriate smoothing operation in the image formation. This smoothing stabilizes statistically the images, at the expense of their resolution. We complement the CINT method with a convex (l 1 ) optimization in order to improve the source localization and obtain quantitative estimates of the source intensities. We analyze the method in a regime where scattering can be modeled by large random wavefront distortions, and quantify the accuracy of the inversion in terms of the spatial separation of individual sources or clusters of sources. The theoretical predictions are demonstrated with numerical simulations.Key words. waves in random media, coherent interferometric imaging, l 1 optimization, mutual coherence.1. Introduction. Waves measured by a collection of nearby sensors, called an array of receivers, carry information about their source and the medium through which they travel. We consider a typical remote sensing regime with sources of small (point-like) support, and study the inverse problem of determining them from the array measurements.When the waves travel in a known and non-scattering (e.g. homogeneous) medium, the sources can be localized with reverse time migration [4,5] also known as backprojection [20]. This estimates the source locations as the peaks of the image formed by superposing the array recordings delayed by travel times from the receivers to the imaging points. The accuracy of the estimates depends on the array aperture, the distance of the sources from the array, and the temporal support of the signals emitted by the sources. It may be improved under certain conditions by using l 1 optimization, which seeks to invert the linear mapping from supposedly sparse vectors of the discretized source amplitude on some mesh, to the array measurements. The fast growing literature of imaging with l 1 optimization in homogeneous media includes compressed sensing studies such as [19,18], synthetic radar imaging studies like [1,8], array imaging studies like [14], and the resolution study [7].In this paper we assume that the waves travel in heterogeneous media with fluctuations of the wave speed caused by numerous inhomogeneities. The amplitude of the fluctuations is small, meaning that a single inhomogeneity is a weak scatterer. However, there are many inhomogeneities that interact with the waves on their way from the sources to the receivers, and their scattering effect accumulates. Because in appli...

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Section: 32mentioning

confidence: 99%

Imaging in Random Media with Convex Optimization

Borcea¹,

Kocyigit

2017

SIAM J. Imaging Sci.

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“…The second goal of the paper is to explain how the theory applies to SAR imaging. The study [8] is proof of concept that MMV can be used to image direction dependent reflectivities from data gathered over multiple sub-apertures. However, it does not provide a resolution analysis and it does not demonstrate the advantage of using MMV over imaging with a single sub-aperture at a time.…”

mentioning

confidence: 78%

A Multiple Measurement Vector Approach to Synthetic Aperture Radar Imaging

Borcea¹,

Kocyigit²

2018

SIAM J. Imaging Sci.

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We study a multiple measurement vector (MMV) approach to synthetic aperture radar (SAR) imaging of scenes with direction dependent reflectivity and with polarization diverse measurements. The unknown reflectivity is represented by a matrix with row support corresponding to the location of the scatterers in the scene, and columns corresponding to measurements gathered from different sub-apertures, or different polarization of the waves. The MMV methodology is used to estimate the reflectivity matrix by inverting in an appropriate sense the linear system of equations that models the SAR data. We introduce a resolution analysis of imaging with MMV, which takes into account the sparsity of the imaging scene, the separation of the scatterers and the diversity of the measurements. The results of the analysis are illustrated with some numerical simulations.

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“…However, there are other configurations such as multiple frequency imaging with several transmitters and receivers for which this factorization is not feasible. Still, we show that factorization (2) approximately holds under the paraxial approximation, i.e., when the image region is far from the array and is small.…”

Section: Introductionmentioning

confidence: 85%

“…, K, be the fields at the grid positions y k in the IW, with g( y k ; ω) given by (5). Then, the data depend on the vector l = [g (1) f (ω) , g (2) f (ω) , . .…”

Section: Single Frequency Signals and Multiple Receiversmentioning

confidence: 99%

“…All these problems can be formulated as (1) in which multiple measurement vectors are recorded. We show that some array imaging problems admit the factorization (2) and, thus, the support of the unknown can be recovered exactly by MUSIC. However, there are other configurations such as multiple frequency imaging with several transmitters and receivers for which this factorization is not feasible.…”

Section: Introductionmentioning

confidence: 97%

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Robust multifrequency imaging with MUSIC

et al. 2018

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In this paper, we study the MUltiple SIgnal Classification (MUSIC) algorithm often used to image small targets when multiple measurement vectors are available. We show that this algorithm may be used when the imaging problem can be cast as a linear system that admits a special factorization. We discuss several active array imaging configurations where this factorization is exact, as well as other configurations where the factorization only holds approximately and, hence, the results provided by MUSIC deteriorate. We give special attention to the most general setting where an active array with an arbitrary number of transmitters and receivers uses signals of multiple frequencies to image the targets. This setting provides all the possible diversity of information that can be obtained from the illuminations. We give a theorem that shows that MU-SIC is robust with respect to additive noise provided that the targets are well separated. The theorem also shows the relevance of using appropriate sets of controlled parameters, such as excitations, to form the images with MUSIC robustly. We present numerical experiments that support our theoretical results.

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Synthetic Aperture Imaging of Direction- and Frequency-Dependent Reflectivities

Cited by 11 publications

References 18 publications

Imaging in Random Media with Convex Optimization

Imaging in Random Media with Convex Optimization

A Multiple Measurement Vector Approach to Synthetic Aperture Radar Imaging

Robust multifrequency imaging with MUSIC

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