Robust multifrequency imaging with MUSIC

Moscoso, Miguel; Novikov, Alexei; Papanicolaou, George; Tsogka, Chrysoula

doi:10.1088/1361-6420/aaede6

Cited by 11 publications

(15 citation statements)

References 33 publications

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“…The resolution in depth is determined by the bandwidth B used to form the images, and it is of the order of c/B (in [22], numerical results suggest a 0.1 c/B range resolution for MUSIC). For a 2 GHz bandwidth, this means a poor c/B = 15 cm depth resolution.…”

Section: Resultsmentioning

confidence: 99%

“…We explain how to apply MUSIC to find the depth or range of the unknown inhomogeneities. The method is similar to the one given in [22] for the one-dimensional reflectivity imaging problem for the wave equation. The cross-range dependence of the inhomogeneities is recovered by moving the source-detector pair across the sample.…”

Section: Image Reconstruction Methodsmentioning

confidence: 99%

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Quantitative subsurface imaging in strongly scattering media

González-Rodríguez¹,

Kim²,

Moscoso³

et al. 2018

Opt. Express

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We present a method to obtain quantitatively accurate images of small obstacles or inhomogeneities situated near the surface of a strongly scattering medium. The method uses time-resolved measurements of backscattered light to form the images. Using the asymptotic solution of the radiative transfer equation for this problem, we determine that the key information content in measurements is modeled by a diffusion approximation that is valid for small sourcedetector distances, and shallow penetration depths. We simplify this model further by linearizing the effect of the inhomogeneities about the known background optical properties using the Born approximation. The resulting model is used in a two-stage imaging algorithm. First, the spatial location of the inhomogeneities are determined using a modification of the multiple signal classification (MUSIC) method. Using those results, we then determine the quantitative values of the inhomogeneities through a least-squares approximation. We find that this two-stage method is most effective for reconstructing a sequence of one-dimensional images along the penetration depth corresponding to null source-detector separations rather than simultaneously using measurements over several source-detector distances. This method is limited to penetration depths and distances between boundary measurements on the order of the scattering mean-free path.

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Section: Resultsmentioning

confidence: 99%

Section: Image Reconstruction Methodsmentioning

confidence: 99%

Quantitative subsurface imaging in strongly scattering media

González-Rodríguez¹,

Kim²,

Moscoso³

et al. 2018

Opt. Express

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show abstract

“…x is a K-vector whose entries are the unknowns X k for k = 1, • • • , K. Linear system (10) falls into the framework of the multiple measurement vector problem analyzed by Moscoso et al [22]. They show that MUSIC provides the exact support of x for Eq.…”

Section: Multiple Signal Classification (Music) Methodsmentioning

confidence: 99%

“…MUSIC is a direct sampling method that recovers the location and shape of the scattering objects. Moscoso et al [22] give a rigorous mathematical analysis of the MUSIC algorithm. Ammari et al [23] have extended MUSIC to study subsurface imaging problems.…”

Section: Introductionmentioning

confidence: 99%

Intensity-only inverse scattering with MUSIC

Kim¹,

Tsogka²

2019

J. Opt. Soc. Am. A

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We present a method for inverse scattering that relies on intensity-only measurements of the scattered field on a single measurement plane. By collecting measurements from a suite of experiments in which the sample is illuminated using different incident fields, we create sufficient data diversity to overcome the limitations of the intensity-only measurements. We give an explicit procedure which uses an algebraic relation called the polarization identity to convert intensity measurements of scattered fields to interferometric measurements in which one of the scattered fields serves as the reference. By adjusting the multiple signal classification (MUSIC) method for these interferometric data, we effectively recover the location and shapes of multiple objects contained in the imaging region. This method is effective and robust to noise as long as there is sufficiently high data diversity and the fractional volume of the scattering objects is not too high. We present image reconstructions for several three-dimensional examples with simulated data computed using the Method of Fundamental Solutions that demonstrate the effectiveness of this imaging method.

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“…MUSIC (multiple signal classication) is another sampling method that has been widely used in several imaging applications [8,9,12,16]. To explain the main idea of MUSIC, let us consider the single-frequency array imaging problem.…”

Section: Introductionmentioning

confidence: 99%

High-resolution, quantitative signal subspace imaging for synthetic aperture radar

Kim¹,

Tsogka²

2021

Preprint

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We consider synthetic aperture radar imaging of a region containing point-like targets. Measurements are the set of frequency responses to scattering by the targets taken over a collection of individual spatial locations along the flight path making up the synthetic aperture. Because signal subspace imaging methods do not work on these measurements directly, we rearrange the frequency response at each spatial location using the Prony method and obtain a matrix that is suitable for these methods. We arrange the set of these Prony matrices as one block-diagonal matrix and introduce a signal subspace imaging method for it. We show that this signal subspace method yields high-resolution and quantitative images provided that the signal-to-noise ratio is sufficiently high. We give a resolution analysis for this imaging method and validate this theory using numerical simulations. Additionally, we show that this imaging method is stable to random perturbations to the travel times and validate this theory with numerical simulations using the random travel time model for random media.

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Robust multifrequency imaging with MUSIC

Cited by 11 publications

References 33 publications

Quantitative subsurface imaging in strongly scattering media

Quantitative subsurface imaging in strongly scattering media

Intensity-only inverse scattering with MUSIC

High-resolution, quantitative signal subspace imaging for synthetic aperture radar

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