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REVIEW 4 major objections 5 minor 28 references

Coherence Based Sound Speed Aberration Correction -- with clinical validation in fetal ultrasound

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Estimating a distributed average sound speed map directly from channel data — without solving the ill-posed local sound speed inversion — corrects focusing delays and improves fetal B-mode image quality in a 172-image clinical evaluation.

desk verdict A serious, clinically grounded sound-speed aberration correction paper whose headline 72.5% is a weaker composite than it looks; worth reviewing, but the straight-ray assumption needs quantification. read the letter →

arxiv 2411.16551 v2 pith:2EVYFEDZ submitted 2024-11-25 eess.IV physics.med-ph

Anders Emil Vr{aa}lstad , Peter Fosodeder , Karin Ulrike Deibele , Siri Ann Nyrnes , Ole Marius Hoel Rindal , Vibeke Skoura-Torvik , Martin Mienkina , Svein-Erik M{aa}s{o}y This is my paper · ORCID
classification eess.IVphysics.med-ph
keywords soundspeedaberrationcorrectioncoherencefactordistributedaveragefetalultrasoundREFoCUSbeamformingrankfilteringTenengradsharpnessclinicalvalidation
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

Ultrasound image quality depends on the assumed speed of sound, and the standard 1540 m/s value is often wrong, especially in fetal imaging where maternal fat can lower the actual speed. This paper aims to show that the resulting blur can be corrected without solving the ill-posed problem of reconstructing a local sound speed map: the authors beamform the same stored channel data at 21 candidate sound speeds, measure a coherence factor per pixel (how well the delayed channel signals agree in phase), and keep the sound speed that maximizes coherence for each pixel. That produces a distributed average sound speed map, and the focusing delays are computed directly from that map using a straight-ray travel-time model. The paper validates the map against ground truth in simulations and a phantom, then applies the correction to 172 fetal B-mode images from a commercial matrix-array system; three clinicians preferred the corrected image or rated it equivalent to the uncorrected 1540 m/s image in 72.5% of evaluations, and a lateral-sharpness metric rose with the estimated deviation from 1540 m/s (Pearson r = 0.67). If the claim holds, stored fetal channel data can be re-focused with patient-specific sound speed maps, and the clinical default of 1540 m/s may be too high for many pregnancies.

What carries the argument

The load-bearing object is the distributed average sound speed map $c_{\mathrm{avg}}(\mathbf{r})$ of Eq. (1), formed from the one-way harmonic averages $c_{\mathrm{har}}(\mathbf{r}, e)$ of Eq. (2) along straight rays between each array element and each pixel. Estimation uses the coherence factor $C_R$ from Eq. (7), computed per pixel at 21 candidate sound speeds; a 90th-percentile rank filter expands the main lobe of the point-spread function so pixels near strong scatterers still pick the correct speed, and pixel-grid compensation (Eqs. 5-6) keeps structures stationary while the sound speed changes. REFoCUS retrospective beamforming makes the speed estimate independent of the transmit sound speed and focus, and the final B-mode is formed with the same travel-time expression using the estimated map.

What would settle it

On a phantom with a known strongly refracting layer (for example a wedge of material near 1450 m/s over a 1540 m/s background) and a grid of point targets, the assumption would be settled: if coherence maximization over the 1440-1640 m/s candidates yields a speed map whose corrected image is sharp at some targets but visibly defocused at others, or whose global estimate is biased well beyond the roughly 5 m/s in-silico error, then refraction cannot be treated as second order.

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Extended reading notes

Core claim

The paper's central claim is that the two-way travel-time aberration correction can be computed directly from the observed distributed average sound speed, bypassing the ill-posed local sound speed inversion. The map used for focusing is $c_{\mathrm{avg}}(\mathbf{r})$, the mean over all transmit and receive elements of the one-way harmonic average sound speed along straight rays (Eqs. 1-2), and it is estimated pixel-by-pixel by beamforming the channel data at 21 constant speeds and selecting the speed that maximizes the coherence factor $C_R$ (Eq. 7). The authors report that the estimate is unbiased against the sound speed assumed on transmission, matches the true average map in simulation (MAE about 4-5 m/s) and in a 1540 m/s phantom (MAE about 1 m/s), and, when used to re-beamform 172 fetal B-mode images, increases measured sharpness and is preferred or rated equivalent to the standard 1540 m/s image by three clinicians in 72.5% of evaluations.

Load-bearing premise

The method assumes ultrasound travels in straight lines without bending (refraction), so every focusing error is read as a speed-of-sound error; if ray bending through fat or other tissue is significant, the estimated speed map will be biased even where coherence is maximized.

Editorial extensions

If this is right

  • Stored fetal channel data can be re-beamformed with patient-specific sound speed maps, so the correction does not require a new scan or a change in acquisition.
  • The default fetal ultrasound sound speed may need to be lowered from 1540 m/s toward 1500 m/s, matching the estimated global values in this cohort and earlier clinical findings.
  • Because the estimator is unbiased against the transmit sound speed, data acquired on scanners that focused at 1540 m/s can still be corrected retrospectively.
  • A lateral Tenengrad sharpness metric can serve as an objective proxy for focusing improvement, with a Pearson correlation of 0.67 between sharpness gain and estimated sound speed deviation.
  • Per-pixel sound speed maps can be smoothed with depth-dependent kernels because the averaging in Eq. (2) makes the true map smooth, which stabilizes the per-pixel selection.

Reading between the lines

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

  • In high-BMI pregnancies, where thick fat layers cause stronger refraction and frequency-dependent phase aberration, the straight-ray assumption may bias the estimated average map; a natural next test is to compare this method with a ray-tracing local sound speed estimate on the same channel data.
  • The same coherence-maximization scheme, without local inversion, should transfer to other matrix-array applications; a testable prediction is that correction gains track the deviation of true tissue sound speed from 1540 m/s.
  • The 'similar quality' category was used very differently by the three evaluators (77, 30, and 6 images), so a standardized equivalence definition would be needed before multi-site deployment of the method.
  • Because images with estimated sound speed close to 1540 m/s were mostly rated 'similar', the 72.5% preference/equivalence figure likely understates the benefit in patients with larger sound speed deviations; stratifying by estimated global sound speed would test this.
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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

4 major / 5 minor

Summary. The paper proposes a coherence-based sound speed aberration correction method for fetal ultrasound. Instead of solving the ill-posed local sound speed inversion, the method estimates a per-pixel average sound speed by beamforming the same channel data at 21 constant candidate sound speeds, selecting for each pixel the speed that maximizes a coherence factor, and then beamforming with the resulting spatially varying average sound speed map. The method is tested in K-wave simulations and on a CIRS phantom, and clinically evaluated on 172 fetal B-mode images with three expert clinicians. The authors report that the corrected images are preferred or rated equivalent to the uncorrected 1540 m/s images in 72.5% of evaluations, and that a Tenengrad sharpness increase correlates with the estimated sound speed deviation (Pearson r = 0.67).

Significance. If the central claims are sustained, the paper offers a practically relevant contribution: retrospective two-way aberration correction that avoids the ill-posed inversion of local sound speed, applied to obstetric imaging with a 2D matrix array. The use of REFoCUS beamforming, the in vitro demonstration that the estimate is largely independent of the transmit sound speed assumption, and the relatively large clinical reader dataset are genuine strengths. The paper also makes its processing pipeline available through the vbeam library and a project website, which supports reproducibility. However, the physical validity of the straight-ray model is the load-bearing assumption, and the current evidence is partly circular and does not yet fully establish the claimed clinical preference.

major comments (4)
  1. [Section 3.1.1, Eqs. (1)-(4)] The in-silico validation is circular with respect to the central modeling assumption. The ground-truth average sound speed maps are computed from the true local maps using Eq. (1), which is exactly the straight-ray harmonic-mean model assumed by the estimator in the TOF expression of Eq. (4). The reported MAEs (4.78, 4.74, and 4.31 m/s) therefore demonstrate that the estimator recovers what the model assumes, not that the model accurately describes wave propagation in tissue. The authors should either provide a simulation ground truth computed without Eq. (1) (e.g., via full-wave travel-time measurements or a different propagation model) or explicitly restrict the claim to internal consistency of the estimator.
  2. [Section 2.1 and Section 5] The aberration ambiguity and the straight-ray assumption are acknowledged in the text and illustrated in Fig. 2, but the magnitude of the resulting error is never quantified. The estimator uses a 10 m/s candidate grid, yet no estimate is given for the travel-time error caused by refraction or frequency-dependent phase aberration relative to the TOF difference corresponding to a 10 m/s step. This matters because Examples G and J in Section 5 show exactly the failure mode predicted by the ambiguity: correction sharpens some structures and defocuses others, which is consistent with coherence maximization selecting a biased average sound speed. The paper should provide a quantitative bound, a simulation with refraction, or an additional validation criterion to rule out this bias.
  3. [Section 3.2.1, Table 4] The headline clinical result of 72.5% is a composite of 'prefer corrected' (50.6%) and 'similar quality' (21.9%), but no confidence interval or formal statistical test is reported. The ratings are also clustered: 172 images are evaluated by three clinicians, and the evaluators use the 'similar' option very differently (6 vs. 77 times), so treating the 516 evaluations as independent overstates precision. The authors should report a confidence interval for the composite proportion, account for clustering by image and evaluator, and separately analyze the forced-choice preference rate between corrected and uncorrected images.
  4. [Section 3.2.2 and Section 5] The Tenengrad sharpness comparison may be confounded by the gain normalization described in Section 5, where each corrected image is 'gained to have the same 80th percentile pixel intensity value as the 80th percentile value of the corresponding uncorrected image.' If this normalization is applied before computing the lateral Sobel magnitude in Eq. (10), then F depends on the global gain, and the reported κ could reflect changes in brightness rather than focusing alone. The authors should state the exact order of operations and, if normalization is applied before F, repeat the analysis with and without normalization.
minor comments (5)
  1. [Section 3.2.2] The abbreviation MAD is used both for 'Mean Abdominal Diameter' in the clinical view list and for 'Mean Absolute Deviation' in the sharpness analysis; this is confusing and should be disambiguated with different symbols.
  2. [Figure 8] The caption states that the 'notch indicate 95% confidence' and that the median of 'similar quality' is 'statistically different by the Wilcoxon rank sum test,' but no p-values or test details are given in the text or caption; please add them.
  3. [Throughout] The probe name is written inconsistently as 'eM6c' and 'eM6C'; please use a single spelling.
  4. [Table 5] The row 'Corrected preferred' uses values 3, 2, 3, 1, etc., that represent counts of clinicians, but this is not stated in the table caption; please clarify the units of the counts.
  5. [Section 3.1.1] The K-wave simulation is described as imaging 'a speckle scene with point targets,' but the exact scatterer configuration is not given; a brief description or figure of the simulated medium would help reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the coherence-based sound speed estimator is not fitted to its own outcome metrics, and independent in vitro and clinician benchmarks anchor the claims.

full rationale

The paper's derivation chain is: assume straight-ray propagation and define the distributed average sound speed in Eqs. (1)-(2), estimate that average sound speed per pixel by maximizing the coherence factor over candidate constant sound speeds (Eq. 7), and then beamform with the resulting map using Eqs. (3)-(4). The sound speed map is not computed from Eq. (1) and is not fitted to the sharpness or clinician-preference outcomes; those are independent evaluation metrics. The 72.5% clinician preference/equivalence result and the Tenengrad sharpness measurements are external consequences, not inputs to the sound speed estimation. The in-silico ground truth is calculated from the true local sound speed map using Eq. (1), which is the same straight-ray definition the method assumes; this makes that validation leg a self-consistency check rather than a test of the no-refraction assumption. That is a limitation in external validity, not a circular reduction, because the coherence estimator is not derived from Eq. (1), and the phantom study (known 1540 m/s) plus the clinician data provide independent grounding. The paper also openly reports mixed in vivo cases (Examples G and J) and discusses the straight-ray, no-refraction assumption. Self-citations ([13], [18], [23]) are used for beamforming implementation, virtual-source correction, and scan-grid compensation details, and are not load-bearing uniqueness theorems or injected ansatz. Therefore no load-bearing step reduces by construction to its own inputs.

Assumptions & free parameters 9 free parameters · 6 assumptions · 0 invented entities

The method's performance depends on hand-chosen processing parameters and on modeling assumptions about straight-ray propagation, coherence as a focusing metric, and the adequacy of the discrete sound speed search. The in-silico ground truth is generated with the same wave model used by the estimator, while the in-vitro and clinical results provide external support. No new physical entities are introduced.

free parameters (9)
  • Sound speed search grid = 1440 to 1640 m/s in 10 m/s steps
    Step 1 restricts per-pixel sound speed estimates to 21 discrete values; estimates outside the grid would be biased or clamped.
  • Coherence threshold = 0.2
    Step 2 replaces coherence values below 0.2 with the mean of values outside the mask; this affects which pixels participate in sound speed selection.
  • Rank filter percentile = 90th percentile
    Section 2.4 and Step 2; kernel size 8x2 mm for simulation and 5x3 degrees by mm for the eM6C probe expands the main lobe to avoid sidelobe-driven sound speed selection.
  • Median filter kernel = 4x6 mm (simulation), 10x10 degrees by mm (eM6C)
    Step 4 removes outliers from the estimated sound speed map; kernel size controls spatial granularity of the correction.
  • Smoothing kernel and growth rates = 18x8 mm with 0.3 mm/mm rates (simulation); 20x10 degrees by mm with 0.803 degrees/mm lateral and 0.6 mm/mm axial (eM6C)
    Step 4 smooths the sound speed map with a depth-dependent kernel; these choices determine how rapidly the correction can vary in space.
  • Nearfield depth and valid sector fraction = 3 mm and 100% (simulation); 10 mm and 80% (probe)
    Step 2 excludes an extreme nearfield region and sector borders from coherence estimation, defining the domain where the method operates.
  • Moving average length over sound speed = 3
    Step 2 smooths coherence along the sound speed dimension, affecting how sharply the maximum is localized.
  • Gaussian smoothing kernel = 6x5 mm (simulation); 10x5 degrees by mm (eM6C)
    Step 2 smooths each coherence image to average measurement noise before rank filtering.
  • Tenengrad ROI depth cutoff = 10 mm
    Section 3.2.2 excludes near-field artifacts from the sharpness metric, influencing the reported correlation of 0.67.
assumptions (6)
  • domain assumption Straight-ray wave propagation with a global per-pixel average sound speed, neglecting refraction.
    Section 2.1, Eqs. (1)-(2) state that refraction is second order and any hyperbolic delay aberration is interpreted as a sound speed error; if refraction is significant the model is biased.
  • domain assumption Coherence factor CR in Eq. (7) is a valid focusing quality metric whose per-pixel maximization selects the true average sound speed.
    Section 2.3; no proof is given that the coherence maximum corresponds to the correct sound speed, and Section 2.4 acknowledges incorrect selection near strong scatterers, motivating the rank filter.
  • domain assumption A discrete set of 21 constant sound speeds from 1440 to 1640 m/s is sufficient to approximate the continuous average sound speed field.
    Step 1; in vivo sound speeds outside this range would be biassed to the grid boundary, and no sensitivity analysis is provided.
  • domain assumption Focused transmit and harmonic imaging suppress reverberations and transmit sidelobes sufficiently for accurate sound speed estimation.
    Section 1 and the method rely on harmonic imaging and focused transmit to reduce clutter; the paper does not quantify how imperfect suppression affects the estimate.
  • domain assumption Pixel-grid compensation via Eqs. (5)-(6), including the Snell scaling of angles, keeps structures stationary while varying sound speed.
    Section 2.2.1 introduces the compensation to avoid bias; it assumes the transmission geometry is computed with c0 and that angle changes follow Snell's law.
  • standard math K-wave simulation is an accurate forward model for pulse-echo ultrasound in heterogeneous media.
    Section 3.1.1 uses K-wave to generate channel data with known local sound speed maps; simulation validity is taken as given.

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Cite this review

Pith. "Pith review of Coherence Based Sound Speed Aberration Correction -- with clinical validation in fetal ultrasound." pith.science (2026). https://pith.science/paper/2EVYFEDZ

@misc{pith2026241116551,
  author       = {Pith},
  title        = {Pith review of: Coherence Based Sound Speed Aberration Correction -- with clinical validation in fetal ultrasound},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2EVYFEDZ}},
  note         = {Machine review of arXiv:2411.16551}
}
read the original abstract

The purpose of this work is to demonstrate a robust and clinically validated method for correcting sound speed aberrations in medical ultrasound. We propose a correction method that calculates focusing delays directly from the observed two-way distributed average sound speed. The method beamforms multiple coherence images and selects the sound speed that maximizes the coherence for each image pixel. The main contribution of this work is the direct estimation of aberration, without the ill-posed inversion of a local sound speed map, and the proposed processing of coherence images which adapts to in vivo situations where low coherent regions and off-axis scattering represents a challenge. The method is validated in vitro and in silico showing high correlation with ground truth speed of sound maps. Further, the method is clinically validated by being applied to channel data recorded from 172 obstetric Bmode images, and 12 case examples are presented and discussed in detail. The data is recorded with a GE HealthCare Voluson Expert 22 system with an eM6c matrix array probe. The images are evaluated by three expert clinicians, and the results show that the corrected images are preferred or gave equivalent quality to no correction (1540m/s) for 72.5% of the 172 images. In addition, a sharpness metric from digital photography is used to quantify image quality improvement. The increase in sharpness and the change in average sound speed are shown to be linearly correlated with a Pearson Correlation Coefficient of 0.67.

Figures

Figures reproduced from arXiv: 2411.16551 by the authors.

Figure 1
Figure 1. Visualization of imaging setup with the co [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Illustration of received signal from a point scat [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Illustration of Point Spread Function (PSF) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: shows the estimated sound speed maps for true constant 1480 m/s and 1610 m/s values [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 7
Figure 7. Figure 7: Distribution of estimated global speed of sound [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 6
Figure 6. Figure 6: Estimated average sound speed maps and Bmode images of two collections of a CIRS 1540 m/s phantom. The recordings differ in the assumed sound speed during transmission. using the Tenengrad image quality metric F from Sec￾tion 3.2.2. The average value of the estimated a…
Figure 10
Figure 10. Figure 10: Example A. In vivo fetal Bmode image using constant 1540 m/s and the estimated average sound speed map. The average sound speed map is shown in the top right corner and the rightmost colorbar indicates the sound speed values. Alternating GIFs are found in the suppleme…
Figure 11
Figure 11. Figure 11: Example B. In vivo fetal Bmode image using constant 1540 m/s and the estimated average sound speed map. The average sound speed map is shown in the top right corner and the rightmost colorbar indicates the sound speed values. Alternating GIFs are found in the suppleme…
Figure 12
Figure 12. Figure 12: Example C. In vivo fetal Bmode and coherence images using constant 1540 m/s and the estimated average sound speed map. The average sound speed map is shown in the top right corner and the rightmost colorbar indicates the sound speed values. Alternating GIFs are found …

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.