pith. sign in

arxiv: 2606.18887 · v1 · pith:XVYK6QIPnew · submitted 2026-06-17 · 📡 eess.IV · physics.med-ph

Efficient Image Registration for Ultrasound Localization Microscopy by Obtaining Gradients via Integration Across Iterations

Jipeng Yan , Chang Liu , Hengchang Liu , Biao Huang , Meng-Xing Tang , Yingxiang Liu , Ying Tan This is my paper

Pith reviewed 2026-06-26 19:22 UTC · model grok-4.3

classification 📡 eess.IV physics.med-ph
keywords ultrasound localization microscopyimage registrationextremum seeking controlmotion correctionsuper-resolution imagingaffine registrationB-spline registration
0
0 comments X

The pith

Extremum seeking control supplies effective descent directions for image registration by integrating perturbed similarity metrics across iterations instead of computing explicit gradients.

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

The paper establishes that extremum seeking control can replace standard gradient-based optimization in parametric image registration for ultrasound localization microscopy. Descent directions are obtained by perturbing motion parameters and integrating the resulting demodulated similarity responses over successive iterations, avoiding the need to differentiate the similarity metric with respect to parameters at each step. On simulated motions from a beating ex vivo porcine heart, this yields registration accuracy and convergence comparable to gradient descent while cutting per-iteration computational cost by a factor of approximately 3.5. The method is then embedded in a two-stage pipeline that first applies affine correction for global motion and then B-spline correction for local deformation, enabling super-resolution ULM imaging that reaches 219 micrometers spatial resolution.

Core claim

By using extremum seeking control, which approximates gradient descent through integration of perturbed and demodulated image similarity metrics over iterations, the method performs affine and B-spline registration without explicit differentiation, reducing computational cost by 3.5 times while maintaining accuracy, and enabling 219 μm resolution in ex vivo heart ULM.

What carries the argument

Extremum seeking control that obtains descent information via integration of perturbed and demodulated image similarity metrics across iterations.

If this is right

  • ESC matches GD accuracy and convergence behavior for affine registration using simulated ground-truth motions from the ex vivo porcine heart dataset.
  • Per-iteration computational cost is reduced by a factor of approximately 3.5 compared with explicit gradient evaluation.
  • A two-stage pipeline of affine followed by B-spline registration corrects both global tissue motion and residual local deformation.
  • The corrected images support ULM reconstruction at 219 micrometers spatial resolution, below the 321 micrometer half-wavelength diffraction limit for 2.4 MHz diverging-wave imaging.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The integration-based descent mechanism may extend to other parametric registration tasks where repeated differentiation of complex similarity metrics is the dominant cost.
  • Lower per-iteration expense could enable registration at higher temporal sampling rates or on larger volumetric datasets without proportional increases in compute.
  • Because the approach separates the perturbation and demodulation steps from the underlying image metric, it could be paired with alternative similarity measures or added regularization without altering the core optimization loop.

Load-bearing premise

Integrating perturbed and demodulated image similarity metrics across iterations reliably supplies descent directions equivalent to explicit gradients for both affine and B-spline parametric registration on the tested datasets.

What would settle it

A case on the porcine heart dataset in which extremum seeking control and explicit gradient descent produce final motion parameters that differ by more than the reported registration error, or yield a final image similarity score markedly lower for the extremum seeking approach.

Figures

Figures reproduced from arXiv: 2606.18887 by Biao Huang, Chang Liu, Hengchang Liu, Jipeng Yan, Meng-Xing Tang, Ying Tan, Yingxiang Liu.

Figure 1
Figure 1. Figure 1: A basic ESC framework. ESC perturbs the parameters [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Diagram of the two-stage image registration method based on ESC. Transformation and deformation is only [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Diagram of the comparison between ESC and GD for affine image registration. Affine motions are estimated [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Normalized GARE versus gain K in the iterations for GD and ESC. The optimal gains K are found by the coarse and fine search as 1000 and 10 for GD and ESC respectively. The equivalence and differences between GD and ESC are illustrated in Figs. 5, 6, and 7 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Normalized motion estimation error after optimization for all the simulated frames. The initial motion is [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Convergence curves of two methods for the 27 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Computation efficiency analysis. a) Box plot of iterations required to reach 25%, 50%, and 75% thresholds. [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: ULM density maps reconstructed from acquired 5-seconds CEUS sequence without and with the two-stage [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FRC analysis on images without (wo) and with (w) tissue motion correction. Note that the half wavelength [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
read the original abstract

Tissue motion correction through image registration is essential for ultrasound localization microscopy (ULM). Parametric image registration is commonly formulated as an optimization problem where motion parameters are iteratively updated to maximize image similarity, and used optimization algorithms typically rely on gradient information, the explicit evaluation of which can become computationally demanding. This work investigates Extremum Seeking Control (ESC) as an alternative to explicit derivative evaluation in image registration. By obtaining descent information via integrating perturbed and demodulated image similarity metric across iterations, ESC avoids differentiation of the image similarity metric with respect to motion parameters in each iteration. The classical ESC, whose optimization behavior approximates that of classical gradient descent (GD), is first compared with GD for affine image registration using simulated ground-truth motions derived from a beating ex vivo porcine heart dataset. The results show that ESC achieves registration accuracy and convergence behavior comparable to GD while reducing per-iteration computational cost by approximately 3.5-fold. ESC is subsequently employed in a two-stage motion correction pipeline, where affine registration compensates for global tissue motion and B-spline registration corrects residual local deformation. The proposed method is applied to ULM imaging of a beating ex vivo porcine heart and achieves a spatial resolution of 219 um, substantially below the half-wavelength diffraction limit of 321 um associated with 2.4 MHz diverging-wave imaging. These results demonstrate that ESC provides an effective alternative to explicit derivative evaluation in ULM image registration, enabling accurate motion correction and high-quality super-resolution imaging.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The manuscript proposes Extremum Seeking Control (ESC) as an alternative to explicit gradient evaluation in parametric image registration for ultrasound localization microscopy (ULM). It first compares classical ESC to gradient descent (GD) for affine registration on simulated ground-truth motions derived from an ex vivo porcine heart dataset, claiming comparable accuracy and convergence with ~3.5-fold per-iteration cost reduction. It then deploys ESC in a two-stage pipeline (affine global correction followed by B-spline local correction) and reports a spatial resolution of 219 μm in ULM imaging of a beating ex vivo heart, below the 321 μm half-wavelength diffraction limit at 2.4 MHz.

Significance. If the ESC-to-GD equivalence extends reliably to the B-spline stage on real data, the approach would offer a practical route to lower the per-iteration cost of non-rigid registration in dynamic ULM without explicit differentiation of similarity metrics. The reported sub-diffraction resolution on a beating-heart dataset would strengthen the case for ESC in motion-corrected super-resolution ultrasound. The use of externally derived ground-truth simulated motions for the affine validation is a positive element of the experimental design.

major comments (3)
  1. [Abstract; two-stage pipeline description] Abstract and results on two-stage pipeline: the headline claim that ESC supplies descent directions whose accuracy and convergence match explicit GD is demonstrated only for affine registration on simulated motions; the B-spline stage on real beating-heart data has no direct GD baseline or perturbation-sensitivity analysis, leaving the full-pipeline performance claim without the same level of support.
  2. [ESC description and parameter selection] Methods on ESC formulation: no derivation or ablation is provided for how perturbation frequency/amplitude and demodulation window interact with the non-convex NCC or MI metrics, nor whether residual local deformations after affine correction remain inside the linearization regime assumed by classical ESC.
  3. [Results and abstract] Experimental results: the abstract states comparable accuracy and 3.5-fold cost reduction, yet reports no error bars, statistical tests, or implementation details (e.g., exact perturbation parameters, similarity-metric implementation) that would allow independent verification of the central performance numbers.
minor comments (1)
  1. [Methods] The manuscript would benefit from an explicit statement of the exact similarity metric (NCC or MI) used in each stage and the precise definition of the demodulation operation.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments and positive assessment of the experimental design. We address each major comment below with proposed revisions to improve clarity and support for the claims.

read point-by-point responses

  1. Referee: [Abstract; two-stage pipeline description] Abstract and results on two-stage pipeline: the headline claim that ESC supplies descent directions whose accuracy and convergence match explicit GD is demonstrated only for affine registration on simulated motions; the B-spline stage on real beating-heart data has no direct GD baseline or perturbation-sensitivity analysis, leaving the full-pipeline performance claim without the same level of support.

    Authors: We agree that the direct equivalence demonstration between ESC and GD (accuracy and convergence) is limited to the affine stage on simulated ground-truth motions. The B-spline stage applies ESC to real data without a parallel GD baseline, primarily because explicit gradient computation for the large number of B-spline parameters is computationally prohibitive. The two-stage pipeline result (219 μm resolution) is presented as an application outcome rather than a matched GD comparison. We will revise the abstract and results to explicitly delineate the scope of the GD validation and note that the B-spline stage uses ESC without direct benchmarking. This clarifies the evidential basis without overstating equivalence for the full pipeline. revision: yes

  2. Referee: [ESC description and parameter selection] Methods on ESC formulation: no derivation or ablation is provided for how perturbation frequency/amplitude and demodulation window interact with the non-convex NCC or MI metrics, nor whether residual local deformations after affine correction remain inside the linearization regime assumed by classical ESC.

    Authors: The manuscript employs the classical ESC formulation as an approximation to gradient descent, with parameters chosen via empirical tuning for the NCC metric on the dataset. No full derivation or ablation study of the perturbation parameters with respect to metric non-convexity or the linearization assumption is included. In revision we will add the exact perturbation frequency, amplitude, and demodulation window values used, along with a concise discussion of the post-affine residual deformation scale and why it is expected to remain compatible with the small-signal linearization of classical ESC. A brief reference to supporting ESC theory will also be included. revision: yes

  3. Referee: [Results and abstract] Experimental results: the abstract states comparable accuracy and 3.5-fold cost reduction, yet reports no error bars, statistical tests, or implementation details (e.g., exact perturbation parameters, similarity-metric implementation) that would allow independent verification of the central performance numbers.

    Authors: We acknowledge the absence of error bars, statistical tests, and full implementation details in the current version. The reported 3.5-fold per-iteration cost reduction derives from the number of similarity-metric evaluations (ESC requires two evaluations per parameter versus the higher cost of finite-difference or analytic gradients). We will expand the methods section with the precise perturbation parameters, NCC implementation details, and add error bars or standard deviations computed across the multiple simulated motion trials. Where appropriate, simple statistical comparisons will be added to support the accuracy claims. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical method comparison and application remain independent of inputs.

full rationale

The paper introduces ESC as a known classical technique whose behavior approximates GD, then performs direct experimental comparison of ESC vs. GD on affine registration using externally simulated ground-truth motions from an ex vivo dataset. The subsequent two-stage pipeline applies ESC to B-spline registration on real data without any derivation that reduces the claimed accuracy or resolution improvement to a fitted parameter or self-citation chain. No equations redefine outputs as inputs, no predictions are statistically forced by construction, and the central claims rest on reported empirical metrics rather than tautological equivalence. This is the standard case of a self-contained empirical study.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract only; no explicit free parameters, invented entities, or non-standard axioms are stated. The method implicitly assumes that the similarity metric admits a demodulable perturbation response that approximates gradient information.

axioms (1)
  • domain assumption The image similarity metric admits a demodulable perturbation response that approximates gradient information for the registration optimization.
    Core premise enabling ESC to replace explicit differentiation.

pith-pipeline@v0.9.1-grok · 5814 in / 1178 out tokens · 22833 ms · 2026-06-26T19:22:19.636049+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

35 extracted references

  1. [1]

    Ultrafast ultrasound localization microscopy for deep super-resolution vascular imaging,

    C. Errico, J. Pierre, S. Pezet, Y. Desailly, Z. Lenkei, O. Couture, and M. Tanter, “Ultrafast ultrasound localization microscopy for deep super-resolution vascular imaging,”Nature, vol. 527, no. 7579, pp. 499–502, 2015

    2015

  2. [2]

    In vivo acoustic super-resolution and super-resolved velocity mapping using microbubbles,

    K. Christensen-Jeffries, R. J. Browning, M.-X. Tang, C. Dunsby, and R. J. Eckersley, “In vivo acoustic super-resolution and super-resolved velocity mapping using microbubbles,”IEEE Transactions on Medical Imaging, vol. 34, no. 2, pp. 433–440, 2014

    2014

  3. [3]

    Super-resolution ultrasound imaging,

    K. Christensen-Jeffries, O. Couture, P. A. Dayton, Y. C. Eldar, K. Hynynen, F. Kiessling, M. O’Reilly, G. F. Pinton, G. Schmitz, M.-X. Tanget al., “Super-resolution ultrasound imaging,”Ultrasound in medicine & biology, vol. 46, no. 4, pp. 865–891, 2020

    2020

  4. [4]

    Super-resolution ultrasound microvascular imaging: Is it ready for clinical use?

    P. Song, J. M. Rubin, and M. R. Lowerison, “Super-resolution ultrasound microvascular imaging: Is it ready for clinical use?”Zeitschrift f¨ ur Medizinische Physik, vol. 33, no. 3, pp. 309–323, 2023

    2023

  5. [5]

    Quantitative image markers of super-resolution ultrasound,

    C. A. Smith, H. Wilson, J. Yan, and M.-X. Tang, “Quantitative image markers of super-resolution ultrasound,” EBioMedicine, vol. 124, 2026. 10 Figure 7: Computation efficiency analysis. a) Box plot of iterations required to reach 25%, 50%, and 75% thresholds. b) Box plot of computational cost required to reach 25%, 50%, and 75% thresholds

    2026

  6. [6]

    Dynamic myocardial ultrasound localization angiography,

    P. Cormier, J. Por´ ee, C. Bourquin, and J. Provost, “Dynamic myocardial ultrasound localization angiography,”IEEE Transactions on Medical Imaging, vol. 40, no. 12, pp. 3379–3388, 2021

    2021

  7. [7]

    Coronary flow assessment using 3-dimensional ultrafast ultrasound localization microscopy,

    O. Demeulenaere, Z. Sandoval, P. Mateo, A. Dizeux, O. Villemain, R. Gallet, B. Ghaleh, T. Deffieux, C. Dem´ en´ e, M. Tan- teret al., “Coronary flow assessment using 3-dimensional ultrafast ultrasound localization microscopy,”Cardiovascular Imaging, vol. 15, no. 7, pp. 1193–1208, 2022

    2022

  8. [8]

    Transthoracic ultrasound localization microscopy of myocardial vasculature in patients,

    J. Yan, B. Huang, J. Tonko, M. Toulemonde, J. Hansen-Shearer, Q. Tan, K. Riemer, K. Ntagiantas, R. A. Chowdhury, P. D. Lambiaseet al., “Transthoracic ultrasound localization microscopy of myocardial vasculature in patients,”Nature Biomedical Engineering, vol. 8, pp. 689–700, 2024

    2024

  9. [9]

    In vivo motion correction in super-resolution imaging of rat kidneys,

    I. Taghavi, S. B. Andersen, C. A. V. Hoyos, M. B. Nielsen, C. M. Sørensen, and J. A. Jensen, “In vivo motion correction in super-resolution imaging of rat kidneys,”IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 68, no. 10, pp. 3082–3093, 2021

    2021

  10. [10]

    Transcranial ultrafast ultrasound localization microscopy of brain vasculature in patients,

    C. Demen´ e, J. Robin, A. Dizeux, B. Heiles, M. Pernot, M. Tanter, and F. Perren, “Transcranial ultrafast ultrasound localization microscopy of brain vasculature in patients,”Nature Biomedical Engineering, vol. 5, no. 3, pp. 219–228, 2021

    2021

  11. [11]

    Super-resolution ultrasound: from data acquisition and motion correction to localization, tracking, and evaluation,

    S. Dencks, M. Lowerison, J. Hansen-Shearer, Y. Shin, G. Schmitz, P. Song, and M.-X. Tang, “Super-resolution ultrasound: from data acquisition and motion correction to localization, tracking, and evaluation,”IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2025

    2025

  12. [12]

    Subwavelength motion-correction for ultrafast ultrasound localization microscopy,

    V. Hingot, C. Errico, M. Tanter, and O. Couture, “Subwavelength motion-correction for ultrafast ultrasound localization microscopy,”Ultrasonics, vol. 77, pp. 17–21, 2017

    2017

  13. [13]

    A pyramidal optical flow method based on dense sift feature maps for motion correction in ultrafast power doppler imaging,

    X. Wei, L. Huang, H. Lan, and J. Luo, “A pyramidal optical flow method based on dense sift feature maps for motion correction in ultrafast power doppler imaging,” in2024 IEEE International Symposium on Biomedical Imaging (ISBI). IEEE, 2024, pp. 1–4

    2024

  14. [14]

    Deformable medical image registration: A survey,

    A. Sotiras, C. Davatzikos, and N. Paragios, “Deformable medical image registration: A survey,”IEEE transactions on medical imaging, vol. 32, no. 7, pp. 1153–1190, 2013

    2013

  15. [15]

    Two-stage motion correction for super-resolution ultrasound imaging in human lower limb,

    S. Harput, K. Christensen-Jeffries, J. Brown, Y. Li, K. J. Williams, A. H. Davies, R. J. Eckersley, C. Dunsby, and M.-X. Tang, “Two-stage motion correction for super-resolution ultrasound imaging in human lower limb,”IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency control, vol. 65, no. 5, pp. 803–814, 2018

    2018

  16. [16]

    Nonrigid registration using free-form deformations: application to breast mr images,

    D. Rueckert, L. I. Sonoda, C. Hayes, D. L. Hill, M. O. Leach, and D. J. Hawkes, “Nonrigid registration using free-form deformations: application to breast mr images,”IEEE transactions on medical imaging, vol. 18, no. 8, pp. 712–721, 2002

    2002

  17. [17]

    A survey on deep learning in medical image registration: New technologies, uncertainty, evaluation metrics, and beyond,

    J. Chen, Y. Liu, S. Wei, Z. Bian, S. Subramanian, A. Carass, J. L. Prince, and Y. Du, “A survey on deep learning in medical image registration: New technologies, uncertainty, evaluation metrics, and beyond,”Medical Image Analysis, vol. 100, p. 103385, 2025. 11 Figure 8: ULM density maps reconstructed from acquired 5-seconds CEUS sequence without and with ...

    2025

  18. [18]

    Stability of extremum seeking feedback for general nonlinear dynamic systems,

    M. Krsti´ c and H.-H. Wang, “Stability of extremum seeking feedback for general nonlinear dynamic systems,”Automatica, vol. 36, no. 4, pp. 595–601, 2000

    2000

  19. [19]

    K. B. Ariyur and M. Krstic,Real-time optimization by extremum-seeking control. John Wiley & Sons, 2003

    2003

  20. [20]

    On non-local stability properties of extremum seeking control,

    Y. Tan, D. Neˇ si´ c, and I. Mareels, “On non-local stability properties of extremum seeking control,”Automatica, vol. 42, no. 6, pp. 889 – 903, 2006

    2006

  21. [21]

    100 years of extremum seeking: A survey,

    A. Scheinker, “100 years of extremum seeking: A survey,”Automatica, vol. 161, p. 111481, 2024

    2024

  22. [22]

    Engineering and algorithm design for an image processing api: a technical report on itk-the insight toolkit,

    T. Yoo, V. Chalana, and W. Schroeder, “Engineering and algorithm design for an image processing api: a technical report on itk-the insight toolkit,”Studies in health technology and informatics, 2002

    2002

  23. [23]

    Improved optimization for the robust and accurate linear registration and motion correction of brain images,

    M. Jenkinson, P. Bannister, M. Brady, and S. Smith, “Improved optimization for the robust and accurate linear registration and motion correction of brain images,”Neuroimage, vol. 17, no. 2, pp. 825–841, 2002

    2002

  24. [24]

    Solving smooth and nonsmooth multivariable extremum seeking problems by the methods of nonlinear programming,

    A. R. Teel and D. Popovic, “Solving smooth and nonsmooth multivariable extremum seeking problems by the methods of nonlinear programming,” inProceedings of the 2001 American Control Conference, vol. 3, 2001, pp. 2394–2399

    2001

  25. [25]

    H. K. Khalil,Nonlinear systems. Third edition Prentice Hall, Upper Saddle River, New Jersey, 2002

    2002

  26. [26]

    Evaluation of optimization methods for nonrigid medical image registration using mutual information and b-splines,

    S. Klein, M. Staring, and J. P. Pluim, “Evaluation of optimization methods for nonrigid medical image registration using mutual information and b-splines,”IEEE transactions on image processing, vol. 16, no. 12, pp. 2879–2890, 2007

    2007

  27. [27]

    So you think you can das? a viewpoint on delay-and-sum beamforming,

    V. Perrot, M. Polichetti, F. Varray, and D. Garcia, “So you think you can das? a viewpoint on delay-and-sum beamforming,” Ultrasonics, vol. 111, p. 106309, 2021. 12

    2021

  28. [28]

    Fast 3d super-resolution ultrasound with adaptive weight-based beamforming,

    J. Yan, B. Wang, K. Riemer, J. Hansen-Shearer, M. Lerendegui, M. Toulemonde, C. J. Rowlands, P. D. Weinberg, and M.-X. Tang, “Fast 3d super-resolution ultrasound with adaptive weight-based beamforming,”IEEE Transactions on Biomedical Engineering, vol. 70, no. 9, pp. 2752–2761, 2023

    2023

  29. [29]

    Super-resolution ultrasound through sparsity-based deconvolution and multi-feature tracking,

    J. Yan, T. Zhang, J. Broughton-Venner, P. Huang, and M.-X. Tang, “Super-resolution ultrasound through sparsity-based deconvolution and multi-feature tracking,”IEEE Transactions on Medical Imaging, vol. 41, no. 8, pp. 1938–1947, 2022

    1938

  30. [30]

    Measuring image resolution in ultrasound localization microscopy,

    V. Hingot, A. Chavignon, B. Heiles, and O. Couture, “Measuring image resolution in ultrasound localization microscopy,” IEEE transactions on medical imaging, vol. 40, no. 12, pp. 3812–3819, 2021

    2021

  31. [31]

    A unifying approach to extremum seeking: Adaptive schemes based on estimation of derivatives,

    D. Neˇ si´ c, Y. Tan, W. H. Moase, and C. Manzie, “A unifying approach to extremum seeking: Adaptive schemes based on estimation of derivatives,” inProceedings of the 49th IEEE Conference on Decision and Control (CDC), Atlanta, GA, USA, 2010, pp. 4625–4630

    2010

  32. [32]

    Nonsmooth extremum seeking control with user-prescribed fixed-time convergence,

    J. I. Poveda and M. Krsti´ c, “Nonsmooth extremum seeking control with user-prescribed fixed-time convergence,”IEEE Transactions on Automatic Control, vol. 66, no. 12, pp. 6156–6163, 2021

    2021

  33. [33]

    Fast extremum seeking control for a class of generalized hammerstein systems with the knowledge of relative degree

    H. Liu, Y. Tan, T. Bacek, D. Kulic, D. Oetomo, and C. Manzie, “Fast extremum seeking control for a class of generalized hammerstein systems with the knowledge of relative degree.” inACC, 2023, pp. 2405–2410

    2023

  34. [34]

    Online 4d ultrasound- guided robotic tracking enables 3d ultrasound localisation microscopy with large tissue displacements,

    J. Yan, Q. Tan, S. Kawara, J. Zhu, B. Wang, M. Toulemonde, H. Liu, Y. Tan, and M.-X. Tang, “Online 4d ultrasound- guided robotic tracking enables 3d ultrasound localisation microscopy with large tissue displacements,”IEEE transactions on medical imaging, 2025

    2025

  35. [35]

    Real-time super-resolution ultrasound imaging using the erythrocytes,

    S. K. Præsius, L. T. Jørgensen, and J. A. Jensen, “Real-time super-resolution ultrasound imaging using the erythrocytes,” IEEE Transactions on Ultrasonics, 2026. 13

    2026