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3D Wave-Equation-Based Finite-Frequency Tomography for Ultrasound Computed Tomography

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Pith's one-line read This paper introduces finite-frequency traveltime tomography to medical ultrasound, showing that volumetric, wave-equation-based sensitivity kernels make 3D sound-speed imaging from slice-by-slice 2D acquisition systems possible.

desk verdict A clean transfer of seismic banana-doughnut tomography to USCT with a useful matrix-free trick; the load-bearing water-calibration waveform similarity assumption is asserted, not tested. read the letter →

arxiv 1908.03302 v1 pith:O34AHCVH submitted 2019-08-09 physics.med-ph eess.IV

N. Korta Martiartu (1) , C. Boehm (1) , A. Fichtner (1) ((1) Institute of Geophysics , ETH Zurich , Zurich , Switzerland) This is my paper · ORCID
classification physics.med-pheess.IV MSC 92C5535R3086A22
keywords ultrasoundcomputedtomographyfinite-frequencytraveltimeBornapproximationFresnelsensitivitykernelsadjointmethodbreasttissueimagingslice-by-slice3Dacquisitionresolutionanalysis
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper brings finite-frequency traveltime tomography—a technique born in seismology—to medical ultrasound, with the goal of reconstructing three-dimensional sound-speed images of breast tissue from transmission measurements. Where classical ray tomography concentrates sensitivity on an infinitely thin path, the method derives volumetric sensitivity kernels from the wave equation, so measured traveltimes correctly reflect scattering and diffraction off the ray path. The paper linearizes the problem around a homogeneous water background using calibration data, which makes the sensitivity kernels analytic and independent of the unknown tissue model, turning the inverse problem into a large but linear least-squares system. A one-dimensional parameterization of the Jacobian avoids storing the dense forward matrix, making the approach computationally tractable at clinical megahertz frequencies. Validation on lab data and a simulated slice-by-slice 3D acquisition suggests the method can assemble true volumetric images from planar transducer rings, with vertical resolution set by overlapping Fresnel sensitivity across slices.

What carries the argument

The load-bearing object is the cross-correlation traveltime sensitivity kernel $K_0(\mathbf{x};\mathbf{x}_s,\mathbf{x}_r)$, derived from the Born approximation and the adjoint wavefield. Under the linearization $p_{\mathrm{obs}}(\mathbf{x}_r,t+\Delta T)\approx p_0(\mathbf{x}_r,t)$ and a homogeneous-water Green's function, the kernel becomes analytic: $K_0 = A \int_0^\infty \omega^3 |f(\omega)|^2 \sin\!\big(\tfrac{\omega}{c_0}(R_{xs}+R_{xr}-R_{sr})\big)\,d\omega \;\big/\; \int_0^\infty \omega^2 |f(\omega)|^2\,d\omega$, where $A$ accounts for geometrical spreading. Since the kernel depends only on $R=R_{xs}+R_{xr}-R_{sr}$, not on absolute positions, the full forward operator $F$ can be represented by a 1D analytic function and evaluated on the fly during matrix–vector products, which makes the otherwise dense Jacobian memory-efficient and GPU-friendly for large 3D inversions.

What would settle it

Feed full-waveform synthetic data from a numerical breast phantom with realistic dense-tissue sound-speed contrasts into the paper's linearized inversion, using only water-calibration traces; the claim fails if the recovered sound-speed map deviates from the true model beyond the stated resolution or if traveltime residuals stay systematically large.

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Extended reading notes

Core claim

The central claim is that cross-correlation traveltime shifts measured in ultrasound computed tomography can be modeled as a linear function of sound-speed perturbations, with sensitivity distributed over finite Fresnel volumes rather than confined to rays. In a homogeneous water background, the sensitivity kernel for any emitter–receiver pair reduces to an analytic function of the sum of the source-to-point and receiver-to-point distances minus the direct source–receiver distance, $R = R_{xs}+R_{xr}-R_{sr}$. Because this function is independent of the emitter–receiver geometry, the entire Jacobian operator can be encoded by a one-dimensional parameterization and applied matrix-free. The paper shows on lab data that this linearized finite-frequency inversion recovers a tissue-mimicking phantom, and it demonstrates that combining measurements from several elevations markedly improves vertical resolution, supporting the claim that true 3D images can be built from slice-by-slice acquisitions.

Load-bearing premise

The whole inversion rests on treating each observed ultrasonic signal as a time-shifted copy of the water calibration signal, so the method breaks if real tissue produces refracted, dispersed, attenuated, or multiply scattered arrivals that are not simply delayed versions of the calibration pulse.

Editorial extensions

If this is right

  • Traveltime measurements in separate frequency bands can be treated as independent data, enlarging the dataset and improving tomographic resolution.
  • Slice-by-slice acquisition systems, currently limited to stacked 2D images, can produce true 3D reconstructions because sensitivity extends out of the acquisition plane.
  • Because the Jacobian no longer depends on the unknown model once water calibration data are available, forward-operator properties can be computed before any patient measurement, shortening time to solution in clinical use.
  • The nonzero width of finite-frequency kernels prevents the over-optimistic resolution that thin-ray assumptions can suggest, tying resolution to what the wavefield's frequency content actually allows.
  • Overlapping sensitivity from adjacent elevations, as in the 3 mm spacing experiment, sharpens vertical resolution beyond simply avoiding gaps between slices.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural stress test not performed here is to image phantoms with velocity contrasts above the cited 10% or with strongly refractive inclusions; the linearized water-background kernels would be expected to show growing bias, pointing to where a nonlinear update or a ray-bending-corrected background becomes necessary.
  • Because the sensitivity kernel is an analytic function of $R = R_{xs}+R_{xr}-R_{sr}$, the same encoding could be extended to attenuation or density tomography by measuring amplitude or spectral changes rather than traveltime shifts.
  • The matrix-free 1D parameterization implies the full Jacobian can be stored as a short lookup table, so real-time 3D reconstruction on clinical hardware is a plausible engineering step beyond the paper.
  • If the linearization holds in vivo, multi-frequency traveltime tomography could exploit the dispersive character of breast tissue, though the paper only notes this possibility rather than testing it.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The manuscript introduces finite-frequency traveltime tomography to ultrasound computed tomography. Starting from the acoustic wave equation and a Born approximation, the authors derive a cross-correlation traveltime sensitivity kernel for a homogeneous water background, and then develop a 1D parameterization of this kernel that encodes the full Jacobian implicitly, avoiding the explicit construction of a dense forward matrix. The method is demonstrated on an open 2D USCT phantom dataset: first with a 2D inversion, then with a volumetric reconstruction using 3D sensitivity kernels from the same 2D data, and finally with a simulated slice-by-slice acquisition in which the same 2D dataset is replicated at different elevations under cylindrical symmetry. The paper also presents a resolution analysis based on point-spread functions and low-rank approximations of the resolution and posterior covariance matrices.

Significance. If the linearization assumptions hold, the paper offers a computationally attractive middle ground between ray-based USCT and full waveform inversion: analytic finite-frequency kernels capture volumetric sensitivity and out-of-plane effects at far lower cost than numerical wave-propagation inversion. The 1D parameterization of the Jacobian is a useful implementation contribution, and the resolution analysis is a sensible way to compare acquisition geometries. The mathematical derivation from the Born approximation to the analytical kernel is standard and appears sound, and the forward operator is not fitted to the target data, so circularity is not a concern. The principal weaknesses are empirical: the validation is qualitative, the waveform-similarity assumption that underpins the linearization is asserted rather than tested, and the 3D slice-by-slice demonstration uses a cylindrically symmetric phantom with replicated data, so it cannot substantiate the claim of truly 3D imaging in the presence of vertical heterogeneity.

major comments (3)
  1. [§II-A and §VI] The linearization in Eq. (12) assumes that the observed transmission signal is a time-shifted copy of the water-calibration signal, i.e., pobs(xr, t + ΔT) ≈ p0(xr, t). This assumption is load-bearing because it makes the sensitivity kernel K0 in Eqs. (15) and (22) independent of the unknown medium and allows F to be evaluated analytically. The paper states in §VI that 'sufficient waveform similarity' is satisfied in breast USCT, but no measurement or simulation is presented that checks this. In attenuating, heterogeneous breast tissue at MHz frequencies, frequency-dependent attenuation, dispersion, and multipathing can alter the pulse shape, so the cross-correlation maximum need not equal the Born traveltime of Eq. (9). The 10% contrast bound from [33] concerns linearity of delay times in a nondissipative setting and does not by itself establish waveform similarity in lossy tissue. I ask the authors to quantify waveform similarity on the lab data or in a realistic simulation (e.g., normalized correlation coefficients between observed and time-shifted calibration pulses), or to substantially temper the breast-imaging claims.
  2. [§III, Fig. 4] The validation in Section III is qualitative. The paper explicitly states that empirical velocity measurements of the true phantom are not available and that agreement with other groups' reconstructions [46] is not quantified. Consequently, the reconstruction accuracy of the proposed method is not established, and one cannot tell whether the finite-frequency forward operator improves accuracy relative to ray-based tomography or whether the linearization introduces a detectable bias. I recommend adding at least one quantitative test: a phantom with a known sound-speed map, or a synthetic test with realistically heterogeneous and attenuating tissue-mimicking media, reporting velocity errors and, ideally, a direct comparison with ray-based inversion on the same data.
  3. [§V, Figs. 8–9] The simulated slice-by-slice experiment does not constitute an independent 3D validation. Because the phantom is cylindrically symmetric, the same 2D dataset is assumed to be recorded at every elevation, so the data are exactly consistent with the z-invariance that the 2D approximation assumes. This experiment cannot expose errors in the out-of-plane sensitivity of the 3D kernels or in cross-slice coupling, and it therefore cannot support the strong claim in §VI that the method 'provides truly 3D reconstructions using slice-by-slice devices.' Please either present a simulation with genuine 3D structure (e.g., inclusions whose size or position varies with z) or rephrase the claim as a feasibility demonstration under cylindrical symmetry.
minor comments (4)
  1. [§II-D, Eq. (23) and Fig. 5] The text 'Γnoise = σ−2p I' is inconsistent with the definition of Γnoise as a covariance matrix in Eq. (23). It should presumably be Γnoise = σp² I (or Γnoise−1 = σp−2 I). The distinction matters because this parameter sets the scale of the data misfit term and hence the posterior variances shown in Fig. 5.
  2. [§II-C, Eq. (22)] The integration limits in Eq. (22) are ambiguous as typeset ('∫ω0'); please clarify that the integrals run over the full positive-frequency band and state the constants absorbed into A(x) so that the kernel normalization is reproducible.
  3. [§I and §VI] The claim that the 10% contrast condition is 'guaranteed in breast tissue' overstates what [33] establishes. Some breast-tissue-to-water sound-speed contrasts can approach or exceed 10%, and the cited study is a seismological analysis. I suggest replacing 'guaranteed' with a more cautious formulation such as 'typically satisfied' and noting that the actual range should be verified for the intended patient population.
  4. [§IV, Fig. 7] The PSFs in Fig. 7(b) are shown with horizontal and vertical cross sections in the same panel; please state in the caption how the displayed normalization is applied, since the different cross sections otherwise appear to have different scales.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the finite-frequency kernel is an analytical forward model, not a fit to the target data.

full rationale

The derivation chain is self-contained against external benchmarks. The linearized forward operator δT=Fδc (Eq. 17) is obtained analytically from the cross-correlation traveltime definition (Eq. 2), the Born approximation (Eq. 6), and the homogeneous-water Green's function (Eq. 13); the resulting kernel K0 (Eq. 22) is stated by the authors to 'not depend on the unknown model parameters nor on the observed data' (Section II-A). No parameter is fitted to the USCT data and then renamed a prediction. The 1D parameterization in Section II-C is a pure change of variables (R = Rxs+Rxr−Rsr) with a stored analytical function; it is a computational encoding of the same kernel, not a new empirical input. The calibration data in water serve as an external benchmark for the source wavelet, not as the target quantity. Self-citations [15], [45], [50], [51] cover adjoint methods, resolution analysis, and transducer placement; these are methodological tools and do not carry the central claim, which rests on the Born/cross-correlation theory and on external benchmarks such as the USCT Data Challenge 2017 dataset [46] and external linearity tests [33]. The assumption of waveform similarity (Eq. 12) and the unverified extension of the 10% contrast condition to attenuating breast tissue are correctness risks and are acknowledged in Section VI ('A prerequisite of our method is access to calibration data that ensure sufficient waveform similarity'); but an untested assumption is not circularity under the definitions used here. The 3D slice-by-slice demonstration reuses the same 2D data under cylindrical symmetry, so it is a self-consistency demonstration rather than independent 3D validation, yet it does not amount to the prediction being equivalent to its input by construction.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central derivation is a linearized Born forward model around homogeneous water; it introduces no new physical entities. The free parameters are regularization, noise, and truncation choices, while the main axioms are waveform similarity, small velocity contrasts, and lossless propagation. The cylindrical symmetry assumption for the slice-by-slice simulation is an ad hoc enabler of the 3D demonstration.

free parameters (3)
  • TV regularization weight α
    Controls the trade-off between data misfit and total variation regularization in Eq. (23). No value is reported, and the reconstruction depends on it.
  • noise standard deviation σp = 2.5e-8 s
    Assumed minimum measurable cross-correlation time shift, used for Γnoise in the resolution analysis (Section III-D).
  • SVD low-rank cutoff = 3000 singular values, 3 orders of magnitude decay
    Used to truncate the singular value spectrum and compute low-rank approximations of resolution and posterior covariance matrices (Section III-D).
assumptions (6)
  • standard math Born approximation is valid and wavefield perturbations are linear in δc
    Needed to derive Eq. (6) from the acoustic wave equation; a standard first-order scattering assumption.
  • domain assumption Velocity model is c0 + δc with |δc| << c0 and observed waveform is a time-shifted water calibration signal (Eq. 12)
    Central assumption that permits analytical homogeneous-background kernels and a linear forward problem; if waveform similarity fails, the kernels are invalid.
  • domain assumption Velocity contrasts in breast tissue are below roughly 10%
    Invoked after Eq. (9) with citation [33] to justify linearization; a key quantitative bound that may not hold for all breast tissue types.
  • domain assumption Propagation is lossless and density is constant
    Equation (1) is the lossless acoustic wave equation with constant density; attenuation and dispersion are not modeled.
  • ad hoc to paper For the 3D slice-by-slice demonstration, the phantom is cylindrically symmetric so identical 2D data can be assumed at different elevations
    Section V states: 'Because the phantom has cylindrical symmetry, we simulate a slice-by-slice acquisition, and we assume that the same data have been recorded at different elevations.' This makes the 3D demonstration synthetic.
  • domain assumption Breast tissue has sufficiently smooth z-variation for the 2D approximation of Eq. (16)
    Invoked in Section II-B for the 2D data application; accuracy depends on tissue structure and frequency, and the authors acknowledge it may fail at lower frequencies.

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Cite this review

Pith. "Pith review of 3D Wave-Equation-Based Finite-Frequency Tomography for Ultrasound Computed Tomography." pith.science (2026). https://pith.science/paper/O34AHCVH

@misc{pith2026190803302,
  author       = {Pith},
  title        = {Pith review of: 3D Wave-Equation-Based Finite-Frequency Tomography for Ultrasound Computed Tomography},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O34AHCVH}},
  note         = {Machine review of arXiv:1908.03302}
}
read the original abstract

Ultrasound Computed Tomography (USCT) has great potential for 3D quantitative imaging of acoustic breast tissue properties. Typical devices include high-frequency transducers, which makes tomography techniques based on numerical wave propagation simulations computationally challenging, especially in 3D. Therefore, despite the finite-frequency nature of ultrasonic waves, ray-theoretical approaches to transmission tomography are still widely used. This work introduces finite-frequency traveltime tomography to medical ultrasound. In addition to being computationally tractable for 3D imaging at high frequencies, the method has two main advantages: (1) It correctly accounts for the frequency dependence and volumetric sensitivity of traveltime measurements, which are related to off-ray-path scattering and diffraction. (2) It naturally enables out-of-plane imaging and the construction of 3D images from 2D slice-by-slice acquisition systems. Our method rests on the availability of calibration data in water, used to linearize the forward problem and to provide analytical expressions of cross-correlation traveltime sensitivity. As a consequence of the finite frequency content, sensitivity is distributed in multiple Fresnel volumes, thereby providing out-of-plane sensitivity. To improve computational efficiency, we develop a memory-efficient implementation by encoding the Jacobian operator with a 1D parameterization, which allows us to extend the method to large-scale domains. We validate our tomographic approach using lab measurements collected with a 2D setup of transducers and using a cylindrically symmetric phantom. We then demonstrate its applicability for 3D reconstructions by simulating a slice-by-slice acquisition systems using the same dataset.

Figures

Figures reproduced from arXiv: 1908.03302 by the authors.

Figure 1
Figure 1. Sensitivity kernel for a band-limited signal with frequencies in the range of 1–3 MHz. The emitter and the receiver are located at positions (-0.095,0,0) m [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Cross-section in xy-plane of the sensitivity kernel in Fig. 1 (a) with [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Acquisition system and an illustration of the tissue mimicking [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: (a) 2D velocity reconstruction and (b) normalized sensitivity coverage. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: (a) Singular value spectrum of the 2D forward operator. The red line [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: PSFs corresponding to point-localized unit perturbations at positions [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: (a) 3D velocity reconstruction using the same dataset as in the 2D example. We show the lateral view of the volumetric reconstruction, the top view [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 9
Figure 9. Figure 9: As expected, the PSFs computed for 8 mm spacing [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]
Figure 8
Figure 8. Figure 8: 3D velocity reconstruction for (a) 3 mm and (b) 8 mm spacing between measurements at different elevations. We show in each case the lateral view, [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: (a), (b) Vertical and horizontal cross sections of PSFs due to perturbations at [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]

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Works this paper leans on

60 extracted references · 57 canonical work pages

  1. [33]

    On the linearity of cross-correlation delay times in finite-frequency tomography,

    E. D. Mercerat and G. Nolet, “On the linearity of cross-correlation delay times in finite-frequency tomography,” Geophysical Journal International, vol. 192, no. 2, pp. 681–687, 12 2012. [Online]. Available: https://doi.org/10.1093/gji/ggs017

    work page doi:10.1093/gji/ggs017 2012

  2. [46]

    USCT reference data base: conclusions from the first SPIE USCT data challenge and future directions,

    N. V . Ruiter, M. Zapf, T. Hopp, H. Gemmeke, K. W. A. van Dongen, J. Camacho, J. L. Herraiz, M. P. Liva, and J. M. Ud ´ıas, “USCT reference data base: conclusions from the first SPIE USCT data challenge and future directions,” Proc. SPIE, vol. 10580, p. 105800Q,

    work page

  3. [1]

    Solid breast nodules: use of sonography to distinguish between benign and malignant lesions

    A. T. Stavros, D. Thickman, C. L. Rapp, M. A. Dennis, S. H. Parker, and G. A. Sisney, “Solid breast nodules: use of sonography to distinguish between benign and malignant lesions.” Radiology, vol. 196, no. 1, pp. 123–134, 1995, pMID: 7784555. [Online]. Available: https://doi.org/10.1148/radiology.196.1.7784555

    work page doi:10.1148/radiology.196.1.7784555 1995

  4. [2]

    Quantitative cross- sectional imaging of ultrasound parameters,

    J. F. Greenleaf, S. A. Johnson, and R. C. Bahn, “Quantitative cross- sectional imaging of ultrasound parameters,” in 1977 Ultrasonics Sym- posium, Oct 1977, pp. 989–995

    work page 1977

  5. [3]

    Empirical relationships between acoustic parameters in human soft tissues,

    T. D. Mast, “Empirical relationships between acoustic parameters in human soft tissues,” Acoustics Research Letters Online , vol. 1, no. 2, pp. 37–42, 2000. [Online]. Available: https://doi.org/10.1121/1.1336896

    work page doi:10.1121/1.1336896

  6. [4]

    Using speed of sound imaging to characterize breast density,

    M. Sak, N. Duric, P. Littrup, L. Bey-Knight, H. Ali, P. Vallieres, M. E. Sherman, and G. L. Gierach, “Using speed of sound imaging to characterize breast density,” Ultrasound in Medicine and Biology, vol. 43, no. 1, pp. 91 – 103, 2017. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0301562916302575

    work page 2017

  7. [5]

    Quantitative assessment of mammographic breast density: Relationship with breast cancer risk,

    J. A. Harvey and V . E. Bovbjerg, “Quantitative assessment of mammographic breast density: Relationship with breast cancer risk,” Radiology, vol. 230, no. 1, pp. 29–41, 2004, pMID: 14617762. [Online]. Available: https://doi.org/10.1148/radiol.2301020870

    work page doi:10.1148/radiol.2301020870 2004

  8. [6]

    Refraction corrected transmission ultrasound computed tomography for application in breast imaging,

    S. Li, M. Jackowski, D. P. Dione, T. Varslot, L. H. Staib, and K. Mueller, “Refraction corrected transmission ultrasound computed tomography for application in breast imaging,” Medical Physics , vol. 37, no. 5, pp. 2233–2246, 2010. [Online]. Available: https: //aapm.onlinelibrary.wiley.com/doi/abs/10.1118/1.3360180

    work page doi:10.1118/1.3360180 2010

Show all 60 references
  1. [7]

    Regularization of image reconstruction in ultrasound computed tomography,

    M. P ´erez-Liva, J. L. Herraiz, L. Medina-Vald´es, J. Camacho, C. Fritsch, B. E. Treeby, and J. M. Ud ´ıas, “Regularization of image reconstruction in ultrasound computed tomography,” in 2015 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC) , Oct 2015, pp. 1–3

    2015

  2. [8]

    3D ultrasound computer tomography: Hardware setup, reconstruction methods and first clinical results,

    H. Gemmeke, T. Hopp, M. Zapf, C. Kaiser, and N. V . Ruiter, “3D ultrasound computer tomography: Hardware setup, reconstruction methods and first clinical results,” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associat...

    2017

  3. [9]

    Diffraction effects upon finite-frequency travel times: A simple 2-D example,

    J. Tong, F. A. Dahlen, G. Nolet, and H. Marquering, “Diffraction effects upon finite-frequency travel times: A simple 2-D example,” Geophys. Res. Lett., vol. 25, pp. 1983–1986, 1998

    1983

  4. [10]

    A guide to the limits of resolution imposed by scattering in ray tomography,

    P. R. Williamson, “A guide to the limits of resolution imposed by scattering in ray tomography,” Geophysics, vol. 56, no. 2, pp. 202–207,

  5. [11]

    Methods for forward and inverse scattering in ultrasound tomography,

    R. J. Lavarello and A. J. Hesford, “Methods for forward and inverse scattering in ultrasound tomography,” in Quantitative Ultrasound in Soft Tissues , J. Mamou and M. L. Oelze, Eds. Dordrecht: Springer Netherlands, 2013, pp. 345–394

    2013

  6. [12]

    Clinical results with ultrasound computed tomography of the breast,

    M. Andr ´e, J. Wiskin, and D. Borup, “Clinical results with ultrasound computed tomography of the breast,” in Quantitative Ultrasound in Soft Tissues , J. Mamou and M. L. Oelze, Eds. Dordrecht: Springer Netherlands, 2013, pp. 395–432

    2013

  7. [13]

    Sound-speed and attenuation imaging of breast tissue using waveform tomography of transmission ultrasound data,

    R. G. Pratt, L. Huang, N. Duric, and P. Littrup, “Sound-speed and attenuation imaging of breast tissue using waveform tomography of transmission ultrasound data,” Proc. SPIE, vol. 6510, p. 65104S, 2007

    2007

  8. [14]

    Time domain reconstruction of sound speed and attenuation in ultrasound computed tomography using full wave inversion,

    M. P ´erez-Liva, J. L. Herraiz, J. M. Ud ´ıas, E. Miller, B. T. Cox, and B. E. Treeby, “Time domain reconstruction of sound speed and attenuation in ultrasound computed tomography using full wave inversion,” The Journal of the Acoustical Society of America, vol. 141, no. 3, pp...

    2017 doi

  9. [15]

    Time-domain spectral-element ultrasound waveform tomography using a stochastic quasi-Newton method,

    C. Boehm, N. Korta Martiartu, N. Vinard, I. J. Balic, and A. Fichtner, “Time-domain spectral-element ultrasound waveform tomography using a stochastic quasi-Newton method,” Proc. SPIE , vol. 10580, pp. 10 580 – 10 580 – 9, 2018. [Online]. Available: https://doi.org/10.1117/12.2293299

    2018 doi

  10. [16]

    3D imaging of the breast using full-waveform inversion,

    O. C. Agudo, L. Guasch, P. Huthwaite, and M. Warner, “3D imaging of the breast using full-waveform inversion,” in Proceedings of the International Workshop on Medical Ultrasound Tomography: 1.-3. Nov. 2017, Speyer, Germany. KIT Scientific Publishing, 2018, p. 99

    2017

  11. [17]

    Frequency domain ultrasound waveform tomography: breast imaging using a ring transducer,

    G. Y . Sandhu, C. Li, O. Roy, S. Schmidt, and N. Duric, “Frequency domain ultrasound waveform tomography: breast imaging using a ring transducer,” Physics in Medicine & Biology , vol. 60, no. 14, p. 5381,

  12. [18]

    A computer simulation study of soft tissue characterization using low-frequancy ultrasonic tomography,

    A. Goncharsky, S. Y . Romanov, and S. Y . Seryozhnikov, “A computer simulation study of soft tissue characterization using low-frequancy ultrasonic tomography,” Ultrasonics, vol. 67, pp. 136–150, 2016

    2016

  13. [19]

    Three-dimensional nonlinear inverse scattering: Quantitative transmission algorithms, refraction corrected reflection, scanner design and clinical results,

    J. Wiskin, D. Borup, S. Johnson, M. Andre, J. Greenleaf, Y . Parisky, and J. Klock, “Three-dimensional nonlinear inverse scattering: Quantitative transmission algorithms, refraction corrected reflection, scanner design and clinical results,” Proceedings of Meetings on Acoustics...

    2013

  14. [20]

    3D frequency-domain ultrasound waveform tomography breast imaging,

    G. Y . Sandhu, E. West, C. Li, O. Roy, and N. Duric, “3D frequency-domain ultrasound waveform tomography breast imaging,” Proc. SPIE , vol. 10139, pp. 10 139 – 10 139 – 14, 2017. [Online]. Available: https://doi.org/10.1117/12.2254399

    2017 doi

  15. [21]

    Medical ultrasound tomography: lessons from exploration geophysics,

    R. G. Pratt, “Medical ultrasound tomography: lessons from exploration geophysics,” in Proceedings of the International Workshop on Medical Ultrasound Tomography: 1.-3. Nov. 2017, Speyer, Germany . KIT Scientific Publishing, 2018, p. 65

    2017

  16. [22]

    Two-dimensional nonlinear inversion of seismic waveforms: Numerical results,

    O. Gauthier, J. Virieux, and A. Tarantola, “Two-dimensional nonlinear inversion of seismic waveforms: Numerical results,”Geophysics, vol. 51, no. 7, pp. 1387–1403, 1986

    1986

  17. [23]

    Multiscale seismic waveform inversion,

    C. Bunks, F. M. Saleck, S. Zaleski, and G. Chavent, “Multiscale seismic waveform inversion,” Geophysics, vol. 60, no. 5, pp. 1457–1473, 1995

    1995

  18. [24]

    Wave-equation traveltime inversion,

    Y . Luo and G. T. Schuster, “Wave-equation traveltime inversion,” Geophysics, vol. 56, no. 5, pp. 645–653, 1991. [Online]. Available: https://doi.org/10.1190/1.1443081

    1991 doi

  19. [25]

    Fresnel zone inversion for lateral heterogeneities in the Earth,

    K. Yomogida, “Fresnel zone inversion for lateral heterogeneities in the Earth,” Pure Appl. Geophys. , vol. 138, pp. 391–406, 1992

    1992

  20. [26]

    Three-dimensional sensitivity kernels for finite-frequency traveltimes: the banana-doughnut paradox,

    H. Marquering, F. Dahlen, and G. Nolet, “Three-dimensional sensitivity kernels for finite-frequency traveltimes: the banana-doughnut paradox,” Geophysical Journal International , vol. 137, no. 3, pp. 805–815,

  21. [27]

    Fr ´echet kernels for finite- frequency traveltimes - I. Theory,

    F. A. Dahlen, G. Nolet, and S.-H. Hung, “Fr ´echet kernels for finite- frequency traveltimes - I. Theory,” Geophysical Journal International , vol. 141, no. 1, pp. 157–174, 04 2000. [Online]. Available: https://dx.doi.org/10.1046/j.1365-246X.2000.00070.x

  22. [28]

    The S-velocity structure of the East Asian mantle from inversion of shear and surface waveforms,

    W. Friederich, “The S-velocity structure of the East Asian mantle from inversion of shear and surface waveforms,” vol. 153, pp. 88–102, 2003

    2003

  23. [29]

    Multi-mode surface wave to- mography for the Australian region using a 3-stage approach in- corporating finite-frequency effects,

    K. Yoshizawa and B. L. N. Kennett, “Multi-mode surface wave to- mography for the Australian region using a 3-stage approach in- corporating finite-frequency effects,” J. Geophys. Res. , vol. 109, p. doi:10.1029/2002JB002254, 2004

    doi

  24. [30]

    Two-stage subduction history under north america inferred from multiple-frequency tomography,

    K. Sigloch, N. McQuarrie, and G. Nolet, “Two-stage subduction history under north america inferred from multiple-frequency tomography,”Nat. Geosc., vol. 1, p. doi:10.1038/ngeo231, 2008

    2008 doi

  25. [31]

    Finite-frequency tomography reveals a variety of plumes in the mantle,

    R. Montelli, G. Nolet, F. A. Dahlen, G. Masters, E. R. Engdahl, and S.-H. Hung, “Finite-frequency tomography reveals a variety of plumes in the mantle,” Science, vol. 303, no. 5656, pp. 338–343, 2004. [Online]. Available: http://science.sciencemag.org/content/303/5656/338

    2004

  26. [32]

    Global upper-mantle structure from finite-frequency surface-wave tomography,

    Y . Zhou, G. Nolet, F. A. Dahlen, and G. Laske, “Global upper-mantle structure from finite-frequency surface-wave tomography,” J. Geophys. Res., vol. 111, p. doi:10.1029/2005JB003677, 2006

    2006 doi

  27. [34]

    Traveltimes of waves in three-dimensional random media,

    A. M. Baig, F. A. Dahlen, and S.-H. Hung, “Traveltimes of waves in three-dimensional random media,” Geophysical Journal International, vol. 153, no. 2, pp. 467–482, 05 2003. [Online]. Available: https://doi.org/10.1046/j.1365-246X.2003.01905.x

    2003 arXiv

  28. [35]

    Validation of first-order diffraction theory for the traveltimes and amplitudes of propagating waves,

    J. Jocker, J. Spetzler, D. Smeulders, and J. Trampert, “Validation of first-order diffraction theory for the traveltimes and amplitudes of propagating waves,” Geophysics, vol. 71, no. 6, pp. T167–T177, 2006. [Online]. Available: https://doi.org/10.1190/1.2358412

    2006 doi

  29. [36]

    Theoretical background for the inversion of seismic waveforms, including elasticity and attenuation,

    A. Tarantola, “Theoretical background for the inversion of seismic waveforms, including elasticity and attenuation,” Pure Appl. Geophys. , vol. 128, pp. 365–399, 1988

    1988

  30. [37]

    Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels,

    J. Tromp, C. Tape, and Q. Liu, “Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels,” Geophysical Journal International, vol. 160, no. 1, pp. 195–216, 01 2005. [Online]. Available: https://doi.org/10.1111/j.1365-246X.2004.02453.x

    2005 arXiv

  31. [38]

    The adjoint method in seismol- ogy - I. Theory,

    A. Fichtner, H.-P. Bunge, and H. Igel, “The adjoint method in seismol- ogy - I. Theory,” vol. 157, pp. 86–104, 2006

    2006

  32. [39]

    A review of the adjoint-state method for computing the gradient of a functional with geophysical applications,

    R.-E. Plessix, “A review of the adjoint-state method for computing the gradient of a functional with geophysical applications,” vol. 167, pp. 495–503, 2006

    2006

  33. [40]

    Linearized inversion of seismic reflection data,

    A. Tarantola, “Linearized inversion of seismic reflection data,” Geophysical Prospecting, vol. 32, no. 6, pp. 998–1015, 1984. [Online]. Available: https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1365-2478. 1984.tb00751.x

    1984 doi

  34. [41]

    Nolet, A Breviary of Seismic Tomography: Imaging the Interior of the Earth and Sun

    G. Nolet, A Breviary of Seismic Tomography: Imaging the Interior of the Earth and Sun . Cambridge University Press, 2008

    2008

  35. [42]

    Toward a practical ultrasound waveform tomography algorithm for improving breast imaging,

    C. Li, G. S. Sandhu, O. Roy, N. Duric, V . Allada, and S. Schmidt, “Toward a practical ultrasound waveform tomography algorithm for improving breast imaging,” Proc. SPIE , vol. 9040, 2014. [Online]. Available: https://doi.org/10.1117/12.2043686

    2014 doi

  36. [43]

    Diffraction effects upon finite-frequency travel times: A simple 2-D example,

    J. Tong, F. A. Dahlen, G. Nolet, and H. Marquering, “Diffraction effects upon finite-frequency travel times: A simple 2-D example,” Geophysical Research Letters , vol. 25, no. 11, pp. 1983–1986, 1998. [Online]. Available: https://agupubs.onlinelibrary.wiley.com/doi/abs/10. 1029...

    1983

  37. [44]

    Fast algorithms for Bayesian uncertainty quantification in large-scale linear inverse problems based on low-rank partial hessian approximations,

    H. Flath, L. Wilcox, V . Akelik, J. Hill, B. van Bloemen Waanders, and O. Ghattas, “Fast algorithms for Bayesian uncertainty quantification in large-scale linear inverse problems based on low-rank partial hessian approximations,” SIAM Journal on Scientific Computing , vol. 33, n...

    2011 doi

  38. [45]

    Resolution analysis by random probing,

    A. Fichtner and T. v. Leeuwen, “Resolution analysis by random probing,” Journal of Geophysical Research: Solid Earth , vol. 120, no. 8, pp. 5549–5573, 2015. [Online]. Available: https: //agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2015JB012106

    2015 doi

  39. [47]

    Multimodal ultrasonic imaging for breast cancer detection,

    J. Camacho, L. Medina, J. F. Cruza, J. M. Moreno, and C. Fritsch, “Multimodal ultrasonic imaging for breast cancer detection,” Archives of Acoustics , vol. 37, no. 3, pp. 253 – 260, 2012. [Online]. Available: https://content.sciendo.com/view/journals/aoa/37/3/article-p253.xml

    2012

  40. [48]

    Implementation of an optimal first-order method for strongly convex total variation regularization,

    T. L. Jensen, J. H. Jørgensen, P. C. Hansen, and S. H. Jensen, “Implementation of an optimal first-order method for strongly convex total variation regularization,” BIT Numerical Mathematics , vol. 52, no. 2, pp. 329–356, Jun 2012. [Online]. Available: https://doi.org/10.1007/s...

    2012 doi

  41. [49]

    An improved 3D Ultrasound Computer Tomography system,

    H. Gemmeke, R. Dapp, T. Hopp, M. Zapf, and N. V . Ruiter, “An improved 3D Ultrasound Computer Tomography system,” in 2014 IEEE International Ultrasonics Symposium , Sept 2014, pp. 1009–1012

    2014

  42. [50]

    Optimal experimental design to position transducers in ultrasound breast imaging,

    N. Korta Martiartu, C. Boehm, N. Vinard, I. Jovanovi ´c Balic, and A. Fichtner, “Optimal experimental design to position transducers in ultrasound breast imaging,” Proc. SPIE, vol. 10139, p. 101390M, 2017. [Online]. Available: https://doi.org/10.1117/12.2252514

    2017 doi

  43. [51]

    Resolution analysis in full waveform inversion,

    A. Fichtner and J. Trampert, “Resolution analysis in full waveform inversion,” Geophysical Journal International , vol. 187, no. 3, pp. 1604–1624, 2011. [Online]. Available: https://onlinelibrary.wiley.com/ doi/abs/10.1111/j.1365-246X.2011.05218.x

    2011 arXiv

  44. [52]

    Development of ultrasound tomography for breast imaging: Technical assessment,

    N. Duric, P. Littrup, A. Babkin, D. Chambers, S. Azevedo, A. Kalinin, R. Pevzner, M. Tokarev, E. Holsapple, O. Rama, and R. Duncan, “Development of ultrasound tomography for breast imaging: Technical assessment,” Medical Physics , vol. 32, no. 5, pp. 1375–1386,

  45. [53]

    H. M. Iyer and K. Hirahara, Seiemic tomography, Theory and Practice . Chapman & Hall, 1993

    1993

  46. [54]

    3- d nonlinear acoustic inverse scattering: Algorithm and quantitative re- sults,

    J. W. Wiskin, D. T. Borup, E. Iuanow, J. Klock, and M. W. Lenox, “3- d nonlinear acoustic inverse scattering: Algorithm and quantitative re- sults,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 64, no. 8, pp. 1161–1174, Aug 2017

    2017

  47. [1991]

    Available: https://doi.org/10.1190/1.1443032

    [Online]. Available: https://doi.org/10.1190/1.1443032

    doi

  48. [1999]

    Available: https://onlinelibrary.wiley.com/doi/abs/10

    [Online]. Available: https://onlinelibrary.wiley.com/doi/abs/10. 1046/j.1365-246x.1999.00837.x

    1999

  49. [2005]

    Available: https://aapm.onlinelibrary.wiley.com/doi/abs/ 10.1118/1.1897463

    [Online]. Available: https://aapm.onlinelibrary.wiley.com/doi/abs/ 10.1118/1.1897463

    doi

  50. [2015]

    Available: http://stacks.iop.org/0031-9155/60/i=14/a= 5381

    [Online]. Available: http://stacks.iop.org/0031-9155/60/i=14/a= 5381

  51. [2016]

    Available: http://www.sciencedirect.com/science/article/ pii/S0168900217307593 11

    [Online]. Available: http://www.sciencedirect.com/science/article/ pii/S0168900217307593 11

  52. [2018]

    Available: https://doi.org/10.1117/12.2293063

    [Online]. Available: https://doi.org/10.1117/12.2293063

    doi

Pith tools

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