Local Tomographic Methods in Sonar

Louis, Alfred K.; Quinto, Eric Todd

doi:10.1007/978-3-7091-6296-5_8

Cited by 83 publications

(106 citation statements)

References 17 publications

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“…The question of what parts of the singularities ͑i.e., sharp details͒ of the image can be stably reconstructed depending on the scanning geometry is addressed for the planar radon transform, 24 and for the circular one in connection with sonar. 23 Local tomography reconstructions also address similar issues.…”

Section: Circular Radon Transformmentioning

confidence: 97%

“…22 Then results by Quinto and Louis developed for sonar are applied to determine the ''stably visible'' parts of the objects in TAT. 23 In particular, a piece of the boundary of an object ͑i.e., interfaces between objects͒ can be stably reconstructed as soon as at any point on the boundary at least one of its two normal directions passes through a detector position. On an intuitive level, this is because an arbitrary interface can be considered as a combination of small flat interface segments, and each segment transmits acoustic waves identically in the two opposite directions perpendicular to the interface segment.…”

Section: Introductionmentioning

confidence: 99%

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Reconstructions in limited‐view thermoacoustic tomography

et al. 2004

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The limited-view problem is studied for thermoacoustic tomography, which is also referred to as photoacoustic or optoacoustic tomography depending on the type of radiation for the induction of acoustic waves. We define a ''detection region,'' within which all points have sufficient detection views. It is explained analytically and shown numerically that the boundaries of any objects inside this region can be recovered stably. Otherwise some sharp details become blurred. One can identify in advance the parts of the boundaries that will be affected if the detection view is insufficient. If the detector scans along a circle in a two-dimensional case, acquiring a sufficient view might require covering more than a -, or less than a -arc of the trajectory depending on the position of the object. Similar results hold in a three-dimensional case. In order to support our theoretical conclusions, three types of reconstruction methods are utilized: a filtered backprojection ͑FBP͒ approximate inversion, which is shown to work well for limited-view data, a local-tomography-type reconstruction that emphasizes sharp details ͑e.g., the boundaries of inclusions͒, and an iterative algebraic truncated conjugate gradient algorithm used in conjunction with FBP. Computations are conducted for both numerically simulated and experimental data. The reconstructions confirm our theoretical predictions.

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Section: Circular Radon Transformmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Reconstructions in limited‐view thermoacoustic tomography

et al. 2004

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“…In the reconstructed images one notices some blurred boundaries which are limited data artifacts [20,24,29] arising from the finite height of the stack of circular integrating detectors. Moreover the images reconstructed with (4.4) are less sensitive to noise.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Exact series reconstruction in photoacoustic tomography with circular integrating detectors

Zangerl

Scherzer

Haltmeier

2009

Communications in Mathematical Sciences

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A method for photoacoustic tomography is presented that uses circular integrals of the acoustic wave for the reconstruction of a three-dimensional image. Image reconstruction is a two-step process: In the first step data from a stack of circular integrating detectors are used to reconstruct the circular projection of the source distribution. In the second step the inverse circular Radon transform is applied. In this article we establish inversion formulas for the first step, which involves an inverse problem for the axially symmetric wave equation. Numerical results are presented that show the validity and robustness of the resulting algorithm.

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“…Microlocal results of [7,86,122], as well as the PDE approach of [42] further applied in [8] provide also some other conditions. We assemble some of these in the following theorem:…”

Section: Uniqueness For Acoustically Homogeneous Mediamentioning

confidence: 94%

“…Some of the mathematical foundations of this imaging modality were originally developed starting in the 1990s for the purposes of the approximation theory [84,85] (see [7,78] for extensive reviews of the resulting developments), integral geometry ( [48,Chapter 5], [50]), and sonar and radar [27,86,93].…”

Section: Introductionmentioning

confidence: 99%

Mathematics of Photoacoustic and Thermoacoustic Tomography

Kuchment

Kunyansky²

SpringerReference

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This is the manuscript of the chapter for a planned Handbook of Mathematical Methods in Imaging that surveys the mathematical models, problems, and algorithms of the Thermoacoustic (TAT) and Photoacoustic (PAT) Tomography. TAT and PAT represent probably the most developed of the several novel "hybrid" methods of medical imaging. These new modalities combine different physical types of waves (electromagnetic and acoustic in case of TAT and PAT) in such a way that the resolution and contrast of the resulting method are much higher than those achievable using only acoustic or electromagnetic measurements.

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Local Tomographic Methods in Sonar

Abstract: Abstract. Tomographic methods are described that will reconstruct object boundaries in shallow water using sonar data. The basic ideas involve micro local analysis, and they are valid under weak assumptions even if the data do not correspond exactly to our model.

Cited by 83 publications

References 17 publications

Reconstructions in limited‐view thermoacoustic tomography

Reconstructions in limited‐view thermoacoustic tomography

Exact series reconstruction in photoacoustic tomography with circular integrating detectors

Mathematics of Photoacoustic and Thermoacoustic Tomography

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