Instability of the linearized problem in  multiwave tomography  of  recovery both the source and the speed

Stefanov, Plamen; Uhlmann, Günther

doi:10.3934/ipi.2013.7.1367

Cited by 43 publications

(51 citation statements)

References 31 publications

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“…12(a) and (c) was assumed, respectively. These results demonstrate that the problem of reconstructing c for a given A is ill-conditioned in the sense that small changes in A can produce significant changes in the reconstructed estimate of c. This observation is consistent with the theoretical results in [30].…”

Section: ) Effect Of Perturbations Of A(r)supporting

confidence: 90%

Joint Reconstruction of Absorbed Optical Energy Density and Sound Speed Distributions in Photoacoustic Computed Tomography: A Numerical Investigation

Huang

Wang

Schoonover

et al. 2016

IEEE Trans. Comput. Imaging

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Photoacoustic computed tomography (PACT) is a rapidly emerging bioimaging modality that seeks to reconstruct an estimate of the absorbed optical energy density within an object. Conventional PACT image reconstruction methods assume a constant speed-of-sound (SOS), which can result in image artifacts when acoustic aberrations are significant. It has been demonstrated that incorporating knowledge of an object’s SOS distribution into a PACT image reconstruction method can improve image quality. However, in many cases, the SOS distribution cannot be accurately and/or conveniently estimated prior to the PACT experiment. Because variations in the SOS distribution induce aberrations in the measured photoacoustic wavefields, certain information regarding an object’s SOS distribution is encoded in the PACT measurement data. Based on this observation, a joint reconstruction (JR) problem has been proposed in which the SOS distribution is concurrently estimated along with the sought-after absorbed optical energy density from the photoacoustic measurement data. A broad understanding of the extent to which the JR problem can be accurately and reliably solved has not been reported. In this work, a series of numerical experiments is described that elucidate some important properties of the JR problem that pertain to its practical feasibility. To accomplish this, an optimization-based formulation of the JR problem is developed that yields a non-linear iterative algorithm that alternatively updates the two image estimates. Heuristic analytic insights into the reconstruction problem are also provided. These results confirm the ill-conditioned nature of the joint reconstruction problem that will present significant challenges for practical applications.

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Section: ) Effect Of Perturbations Of A(r)supporting

confidence: 90%

Joint Reconstruction of Absorbed Optical Energy Density and Sound Speed Distributions in Photoacoustic Computed Tomography: A Numerical Investigation

Huang

Wang

Schoonover

et al. 2016

IEEE Trans. Comput. Imaging

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“…However, as mentioned earlier, the SOS and initial pressure distributions cannot both be stably recovered from PACT measurements alone. This was previously demonstrated theoretically [21] and through computer-simulation studies [22]. To investigate the feasibility of extracting useful information about the SOS distribution from PACT measurements, the SOS distribution was reconstructed assuming two different, fixed initial pressure distributions: (1) the true initial pressure distribution and (2) the true initial pressure distribution shifted by 1 mm along the x-direction.…”

Section: Description Of Computer-simulation Studiesmentioning

confidence: 99%

“…In practice, the SOS distribution is typically unknown. Further, it has been shown that, in general, the SOS and initial pressure distributions cannot both be stably recovered from PACT measurements alone [21, 22]. …”

Section: Introductionmentioning

confidence: 99%

Joint reconstruction of the initial pressure and speed of sound distributions from combined photoacoustic and ultrasound tomography measurements

Matthews

Anastasio

2017

Inverse Problems

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The initial pressure and speed of sound (SOS) distributions cannot both be stably recovered from photoacoustic computed tomography (PACT) measurements alone. Adjunct ultrasound computed tomography (USCT) measurements can be employed to estimate the SOS distribution. Under the conventional image reconstruction approach for combined PACT/USCT systems, the SOS is estimated from the USCT measurements alone and the initial pressure is estimated from the PACT measurements by use of the previously estimated SOS. This approach ignores the acoustic information in the PACT measurements and may require many USCT measurements to accurately reconstruct the SOS. In this work, a joint reconstruction method where the SOS and initial pressure distributions are simultaneously estimated from combined PACT/USCT measurements is proposed. This approach allows accurate estimation of both the initial pressure distribution and the SOS distribution while requiring few USCT measurements.

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“…The inverse initial source problem has been studied widely in the context of thermoacoustic and photoacoustic tomography: see [9], [20], [21] for the problem with partial data, see [22] for a speed with discontinuities, see [23] for numerical discussion, see [24], [25] and [26] for the problem in elastic and attenuating media respectively, and finally, one may find the surveys [27], [28], [29] of interest. There has also been recent work on the problem of jointly recovering the speed and source [30], and the problem of recovery with an approximate speed [31].…”

Section: Previous Literaturementioning

confidence: 99%

Uniqueness for a seismic inverse source problem modeling a subsonic rupture

Hoop

Oksanen

Tittelfitz

2016

Communications in Partial Differential Equations

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We consider an inverse problem for an inhomogeneous wave equation with discretein-time sources, modeling a seismic rupture. We assume that the sources occur along a path with subsonic velocity, and that data are collected over time on some detection surface. We explore the question of uniqueness for these problems, show how to recover the times and locations of sources microlocally, and then reconstruct the smooth part of the source assuming that it is the same at each source location.

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Instability of the linearized problem in multiwave tomography of recovery both the source and the speed

Abstract: In this paper we consider the linearized problem of recovering both the sound speed and the thermal absorption arising in thermoacoustic and photoacoustic tomography. We show that the problem is unstable in any scale of Sobolev spaces.

Cited by 43 publications

References 31 publications

Joint Reconstruction of Absorbed Optical Energy Density and Sound Speed Distributions in Photoacoustic Computed Tomography: A Numerical Investigation

Joint Reconstruction of Absorbed Optical Energy Density and Sound Speed Distributions in Photoacoustic Computed Tomography: A Numerical Investigation

Joint reconstruction of the initial pressure and speed of sound distributions from combined photoacoustic and ultrasound tomography measurements

Uniqueness for a seismic inverse source problem modeling a subsonic rupture

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