Mathematical Modelling and Applications

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Compressed Sensing Algorithm for Real-Time Doppler Ultrasound Image Reconstruction

Received: 31 January 2017    Accepted: 06 March 2017    Published: 18 December 2017
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Abstract

A Doppler ultrasound signal has been reconstructed using different compressed sensing algorithms. With compressed sensing it’s possible to reconstruct signals and images using a few numbers of measurements so as to overcome the limitation of sampling in a real-time Doppler ultrasound sonogram. In this work we want to compare different compressed sensing algorithms used for Doppler ultrasound signal reconstruction so as to select the best algorithm that, gives a real-time Doppler ultrasound image and maintain quality. The result shows that regularized orthogonal matching pursuit reconstruction algorithm reconstructs the Doppler signal and gives Doppler spectrum in a real-time with high quality also ℓ1-norm reconstructs the Doppler signal and gives Doppler spectrum with a good quality, but the reconstruction time was very long.

DOI 10.11648/j.mma.20170206.14
Published in Mathematical Modelling and Applications (Volume 2, Issue 6, December 2017)
Page(s) 75-80
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Doppler Ultrasound Signal, Compressed Sensing, Signal Reconstruction, ℓ1-Norm, Regularized Orthogonal Matching Pursuit

References
[1] D. Donoho, “Compressed Sensing”, IEEE Trans. Info. Theory, vol. 52 (4), pp. 1289 - 1306, 2006.
[2] M. Lusting, D. Donoho, J. Pauly, Sparse MR: The Application of Compressed Sensing For Rapid MR Imaging, Magnetic Resonance in Medicine, 58 (6), pp. 1182 - 1182, 2007.
[3] H. Yu, G. Wang, Compressed Sensing Based Interior Tomography, Physics in Medicine and Biology, 54, 2791 - 2805, 2009.
[4] S. Aviyente, Compressed Sensing Framework for EEG Compression, IEEE Statistical Signal Processing / SP 14th Workshop, pp. 181 - 184, 2007.
[5] S. Zobly and Y. Kadah, “Compressed Sensing: Doppler Ultrasound Signal Recovery by Using Non-uniform Sampling & Random Sampling”, Proc IEEE, 2011.
[6] S. Zobly and Y. Kadah, “Novel Doppler Ultrasound Data Acquisition Framework Based on Compressed Sensing”, International Conference on: Advances in Biomedical Engineering, pp. 137 - 138, 2011.
[7] S. Zobly and Y. Kadah, “Orthogonal Matching Pursuit & Compressive Sampling Matching Pursuit for Doppler Ultrasound Signal Reconstruction”, Proc IEEE, 2012.
[8] S. Zobly and Y. Kadah, “Multiple Measurements Vectors Compressed Sensing for Doppler Ultrasound Signal Reconstruction”, International Conference in Computing, Electronics and Electrical Engineering, Proc IEEE, 2013.
[9] E. Candes, J. Remborg and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Info. Theory, vol. 52 (2), pp. 489 – 509, 2006.
[10] J. Tropp and A. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit”, IEEE Trans. Info. Theory, vol. 53 (12), 2007.
[11] D. Needell, J. Tropp, COSAMP: Iterative Signal Recovery from Incomplete and Inaccurate sampling, ACM Technical Report 2008-01, California Institute of Technology, 2008.
[12] D. Needell, R. Vershynin, Signal Recovery from Incomplete and Inaccurate Measurements via Regularized Orthogonal Matching Pursuit, IEEE J. Select. Top. Signal Processing, 4 (2), pp. 310 - 316, 2010.
[13] I. Gorodnitsky and B. Rao, “Sparse Signal Reconstruction from Limited Data using FOCUSS: A re-weighted minimum norm Algorithm”, IEEE Transaction on Signal Processing, vol. 45 (3), pp. 600 - 616, 1997.
[14] S. Beaker, J. Boben, E. Candes, A fast and Accurate First-order methods for sparse recovery. Available: https://www.eecs.berkeley.edu/~yang/paper/YangA_ICIP2010.pdf.
[15] D. Needell, J. Tropp, R. Vershynin, “Greedy Signal Recovery Review,” 2008. Available: www.acm.caltech.edu/~jtropp/conf/NTV08-greedy-signal-asilomar.pdf.
[16] S. Zobly, Y. Kadah, Processing Methodologies for Doppler Ultrasound, PhD Thesis, 2012.
[17] H. Lu, X. Long and J. Lv, “A Fast Algorithm for Recovery of Jointly Sparse Vector Based on the Alternating Direction Methods”, International Conference on Artificial Intelligence and Statistic, vol. 15, pp. 461- 469, 2011.
Author Information
  • Department of Medical Physics & Instrumentation, National Cancer Institute, University of Gezira, Wad Medani, Sudan

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  • APA Style

    Sulieman Mohammed Salih Zobly. (2017). Compressed Sensing Algorithm for Real-Time Doppler Ultrasound Image Reconstruction. Mathematical Modelling and Applications, 2(6), 75-80. https://doi.org/10.11648/j.mma.20170206.14

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    ACS Style

    Sulieman Mohammed Salih Zobly. Compressed Sensing Algorithm for Real-Time Doppler Ultrasound Image Reconstruction. Math. Model. Appl. 2017, 2(6), 75-80. doi: 10.11648/j.mma.20170206.14

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    AMA Style

    Sulieman Mohammed Salih Zobly. Compressed Sensing Algorithm for Real-Time Doppler Ultrasound Image Reconstruction. Math Model Appl. 2017;2(6):75-80. doi: 10.11648/j.mma.20170206.14

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  • @article{10.11648/j.mma.20170206.14,
      author = {Sulieman Mohammed Salih Zobly},
      title = {Compressed Sensing Algorithm for Real-Time Doppler Ultrasound Image Reconstruction},
      journal = {Mathematical Modelling and Applications},
      volume = {2},
      number = {6},
      pages = {75-80},
      doi = {10.11648/j.mma.20170206.14},
      url = {https://doi.org/10.11648/j.mma.20170206.14},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.mma.20170206.14},
      abstract = {A Doppler ultrasound signal has been reconstructed using different compressed sensing algorithms. With compressed sensing it’s possible to reconstruct signals and images using a few numbers of measurements so as to overcome the limitation of sampling in a real-time Doppler ultrasound sonogram. In this work we want to compare different compressed sensing algorithms used for Doppler ultrasound signal reconstruction so as to select the best algorithm that, gives a real-time Doppler ultrasound image and maintain quality. The result shows that regularized orthogonal matching pursuit reconstruction algorithm reconstructs the Doppler signal and gives Doppler spectrum in a real-time with high quality also ℓ1-norm reconstructs the Doppler signal and gives Doppler spectrum with a good quality, but the reconstruction time was very long.},
     year = {2017}
    }
    

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    AU  - Sulieman Mohammed Salih Zobly
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    AB  - A Doppler ultrasound signal has been reconstructed using different compressed sensing algorithms. With compressed sensing it’s possible to reconstruct signals and images using a few numbers of measurements so as to overcome the limitation of sampling in a real-time Doppler ultrasound sonogram. In this work we want to compare different compressed sensing algorithms used for Doppler ultrasound signal reconstruction so as to select the best algorithm that, gives a real-time Doppler ultrasound image and maintain quality. The result shows that regularized orthogonal matching pursuit reconstruction algorithm reconstructs the Doppler signal and gives Doppler spectrum in a real-time with high quality also ℓ1-norm reconstructs the Doppler signal and gives Doppler spectrum with a good quality, but the reconstruction time was very long.
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