Academic Journal
Applying constraint to minimum variance problem to provide a computationally efficient beamformer for medical ultrasound imaging.
| Title: | Applying constraint to minimum variance problem to provide a computationally efficient beamformer for medical ultrasound imaging. |
|---|---|
| Authors: | Sadeghi M; Department of Biomedical Engineering, Qom Branch, Islamic Azad University, Qom, Iran. Masume.sadeghi@iau.ac.ir.; Production and Recycling of Materials and Energy Research Center, Qom Branch, Islamic Azad University, Qom, Iran. Masume.sadeghi@iau.ac.ir. |
| Source: | Journal of medical ultrasonics (2001) [J Med Ultrason (2001)] 2026 Jan; Vol. 53 (1), pp. 3-18. Date of Electronic Publication: 2025 Oct 15. |
| Publication Type: | Journal Article |
| Language: | English |
| Journal Info: | Publisher: Springer Verlag Country of Publication: Japan NLM ID: 101128385 Publication Model: Print-Electronic Cited Medium: Internet ISSN: 1613-2254 (Electronic) Linking ISSN: 13464523 NLM ISO Abbreviation: J Med Ultrason (2001) Subsets: MEDLINE |
| Imprint Name(s): | Original Publication: Tokyo, Japan : Springer Verlag, c2001- |
| MeSH Terms: | Image Processing, Computer-Assisted*/methods, Ultrasonography/methods ; Phantoms, Imaging ; Computer Simulation ; Algorithms ; Humans |
| Abstract: | Purpose: Minimum variance (MV) beamforming was introduced in ultrasound imaging to improve image quality. It solves a minimization problem where the closed-form solution imposes huge computational load due to the matrix inversion requirement. The MV problem can be iteratively solved to avoid this requirement. Methods: This paper shows that the weight vector at the first iteration is proportional to the covariance matrix elements. It is proposed that this proportionality be considered as a constraint in the main MV problem. Inspired by the idea of the exact line search method, solving the proposed constrained MV (CMV) problem leads to an adaptive beamforming with considerably lower computational load. As an interesting point, the unknown coefficients can be directly calculated through entries of a covariance matrix by a simple operation. Result: The proposed method was investigated on several simulation and experimental data sets. It was found that it required 93% fewer flops than the MV method, which represents a dramatic computational gain. Conclusion: This study showed how only two features, the mean and trace of the covariance matrix, are enough to achieve adaptive beamforming. The proposed beamformer provides approximately the same resolution as the MV method. (© 2025. The Author(s), under exclusive licence to The Japan Society of Ultrasonics in Medicine.) |
| Competing Interests: | Declarations. Conflict of interest: Masume Sadeghi declares that she has no conflicts of interest. Ethical approval: This article does not contain any studies with human or animal subjects. |
| References: | Ramm V, Smith SW. Beam steering with linear arrays. IEEE Trans Biomed Eng. 1983;30:438–52. (PMID: 10.1109/TBME.1983.325149) Parker K. Correspondence: apodization and windowing functions. IEEE Trans Ultrason Ferroelectr Freq Control. 2013;60:1263–71. (PMID: 10.1109/TUFFC.2013.269125004491) Sasso M, Bacrie C. Medical imaging using the fully adaptive beamformer. Proc IEEE Int conf Acoust Speech Signal Process. 2005;2:489–92. Synnevag JF, Austeng A, Holm S. Adaptive beamforming applied to medical ultrasound imaging. IEEE Trans Ultrason Ferroelect Freq Control. 2007;54:1606–13. (PMID: 10.1109/TUFFC.2007.431) Synnevag JF, Austeng A, Holm S. Benefits of minimum-variance beamforming in medical ultrasound imaging. IEEE Trans Ultrason Ferroelect Freq Control. 2009;56:1868–77. (PMID: 10.1109/TUFFC.2009.1263) Holfort LK, Gran F, Jensen JA. Broadband minimum variance beamforming for ultrasound imaging. IEEE Trans Ultrason Ferroelectr Freq Control. 2009;56:314–25. (PMID: 10.1109/TUFFC.2009.104019251518) Asl BM, Mahloojifar A. A low-complexity adaptive beamformer for ultrasound imaging using structured covariance matrix. IEEE Trans Ultrason Ferroelectr Freq Control. 2012;59:660–7. (PMID: 10.1109/TUFFC.2012.224422547277) Nilsen CIC, Hafizovic I. Beamspace adaptive beamforming for ultrasound imaging. IEEE Trans Ultrason Ferroelectr Freq Control. 2009;56:97. Zeng X, Wang Y, Yu J, et al. Beam domain eigenspace based minimum variance beamformer for medical ultrasound imaging. IEEE Trans Ultrason Ferroelectr Freq Control. 2013;60:2670–6. (PMID: 10.1109/TUFFC.2013.286624297032) Kim K, Park S, Kim J, et al. A fast minimum variance beamforming method using principal component analysis. IEEE Trans Ultrason Ferroelectr Freq Control. 2014;61:930–45. (PMID: 10.1109/TUFFC.2014.298924859657) Choi YH. Subspace based adaptive beamforming methodwith low complexity. Electron Lett. 2011;47:529–30. (PMID: 10.1049/el.2011.0512) Deylami AM, Asl BM. Low complex subspace minimum variance beamformer for medical ultrasound imaging. Ultrasonics. 2016;66:43–53. (PMID: 10.1016/j.ultras.2015.11.01226678788) Park J, Wi SM, Lee JS. Computationally efficient adaptive beamformer for ultrasound imaging based on QR decomposition. IEEE Trans Ultrason Ferroelectr Freq Control. 2016;63:65. Asl BM, Deylami AM. A low complexity minimum variance beamformer for ultrasound imaging using dominant mode rejection. Ultrasonics. 2018;85:49–60. (PMID: 10.1016/j.ultras.2017.12.01229331226) Afrakhteh S, Behnam H. Low-complexity adaptive minimum variance ultrasound beam-former based on diagonalization. Biomed Signal Process Control. 2020;62:1–17. (PMID: 10.1016/j.bspc.2020.102110) Nagaoka R, Omura M, Hasegawa H. Effects from imaging parameters of sub-aperture averaging in minimum variance adaptive beamforming using outputs of delay-and-sum beamformer. Jpn J Appl Phys. 2023;62:SJ8007. (PMID: 10.35848/1347-4065/acbb88) Hasegawa H, Kanai H. Effect of Subaperture Beamforming on Phase Coherence Imaging. IEEE Trans Ultrason Ferroelectr Freq Control. 2014;61:1779–90. (PMID: 10.1109/TUFFC.2014.00636525389157) Hasegawa H, Kanai H. Effect of element directivity on adaptive beamforming applied to high frame rate ultrasound. IEEE Trans Ultrason Ferroelectr Freq Control. 2015;62:511–23. (PMID: 10.1109/TUFFC.2015.00697325768817) Xu M, Yang X, Ding M, et al. Spatio-temporally smoothed coherence factor for ultrasound imaging. IEEE Trans Ultrason Ferroelectr Freq Control. 2014;61:189–97. (PMID: 10.1109/TUFFC.2014.6689786) AlMukaddim R, Ahmed R, Varghese T. Sub-aperture processing based adaptive beamforming for photoacoustic imaging. IEEE Trans Ultrason Ferroelectr Freq Control. 2021;68:2336–50. (PMID: 10.1109/TUFFC.2021.3060371) Mukaddim RA, Ahmed R, Varghese T. Improving Minimum Variance Beamforming with Sub-Aperture Processing for Photoacoustic Imaging. 43rd Annu Int Conf IEEE Eng Med Biol Soc. (EMBC). 2021; 2879–82. Deylami AM, Asl BM. Iterative minimum variance beamformer with low complexity for medical ultrasound imaging. Ultrasound Med Biol. 2018;44:1882–90. (PMID: 10.1016/j.ultrasmedbio.2018.04.01629880249) Yang XS. Introduction to algorithms for data mining and machine learning. New York: Academic Press; 2019. p. 1–18. (PMID: 10.1016/B978-0-12-817216-2.00008-9) Sadeghi M, Mahloojifar A. A novel adaptive apodization to improve the resolution of phased subarray imaging in medical ultrasound. J Med Ultrasonics. 2020;47:13–24. (PMID: 10.1007/s10396-019-00970-2) Widrow B, Stearns SD. Adaptive signal processing. Hoboken: Prentice Hall; 1985. Meza JC. Steepest descent. New York: Wiley; 2010. p. 719–22. https://doi.org/10.1002/wics.117 . (PMID: 10.1002/wics.117) Vignon F, Burcher M. Capon beamforming in medical ultrasound imaging with focused beams. IEEE Trans Ultrason Ferroelectr Freq Control. 2008;55:619–28. (PMID: 10.1109/TUFFC.2008.68618407851) Shan TJ, Kailath T. Adaptive beamforming for coherent signals and interferences. IEEE Trans Acoust Speech Signal Process. 1985;33:527–36. (PMID: 10.1109/TASSP.1985.1164583) Synnevag JF, Nilsen CIC. Holm S. Speckle statistics in adaptive beamforming. In: Proc. IEEE Ultrason Symp. 2007;1545–48. Jensen J. Field: a program for simulating ultrasound systems. Med Biol Eng Comput. 1996;34:351–3. Silverstein SD. Ultrasound scattering model: 2D cross correlation and focusing criteria theory, simulations, and experiments. IEEE Trans Ultrason Ferroelecr Freq Control. 2001;48:1023–30. (PMID: 10.1109/58.935719) O’Donnell M, Flax SW. Phase-aberration correction using signals from point reflectors and diffuse scatterers: measurements. IEEE Trans Ultrason Ferroelectr Freq Control. 1988;35:768–74. (PMID: 10.1109/58.933418290214) Krishnan S, Rigby KW, O’Donnell M. Improved estimation of phase aberration profiles. IEEE Trans Ultrason Ferroelectr Freq Control. 1997;44:701–13. (PMID: 10.1109/58.658333) Golub GH, Van Loan CF. Matrix computations. Baltimore: The Johns Hopkins Univ. Press; 1996. |
| Contributed Indexing: | Keywords: Computational load; Constrained beamformer; Minimum variance beamformer; Ultrasound |
| Entry Date(s): | Date Created: 20251015 Date Completed: 20260110 Latest Revision: 20260111 |
| Update Code: | 20260130 |
| DOI: | 10.1007/s10396-025-01523-6 |
| PMID: | 41094315 |
| Database: | MEDLINE |
Be the first to leave a comment!