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Estimation of Time-Scaling Factor for Ultrasound Medical Images Using the Hilbert Transform

EURASIP Journal on Advances in Signal Processing volume 2007, Article number: 080735 (2006) Cite this article

Abstract

A new formulation for the estimation of the time-scaling factor between two ultrasound signals is presented. The estimator is derived under the assumptions of a small time-scaling factor and signals with constant spectrum over its bandwidth. Under these conditions, we show that the proposed approach leads to a simple analytic formulation of the time-scaling factor estimator. The influences of an increase of the time-scaling factor and of signal-to-noise ratio (SNR) are studied. The mathematical developments of the expected mean and bias of the estimator are presented. An iterative version is also proposed to reduce the bias. The variance is calculated and compared to the Cramer-Rao lower bound (CRLB). The estimator characteristics are measured on flat-spectra simulated signals and experimental ultrasound scanner signals and are compared to the theoretical mean and variance. Results show that the estimator is unbiased and that variance tends towards the CRLB for SNR higher than 20 dB. This is in agreement with typical ultrasound signals used in the medical field, as shown on typical examples. Effects of the signal spectrum shape and of the bandwidth size are evaluated. Finally, the iterative version of the estimator improves the quality of the estimation for SNR between 0 and 20 dB as well as the time-scaling factor estimation validity range (up to).

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Authors and Affiliations

  1. Laboratory of Biorheology and Medical Ultrasonics (LBUM), University of Montreal Hospital, 2099 Pavilion J. A. de Sève, Montréal, QC, H2L 2W5, Canada

    Jérémie Fromageau

  2. Centre de Recherche et d’Applications en Traitement de l’Image et du Signal (CREATIS), CNRS UMR 5515, Inserm U 630, INSA de Lyon, 7 Avenue Jean Capelle, Villeurbanne Cedex, 69 621, France

    Hervé Liebgott, Elisabeth Brusseau, Didier Vray & Philippe Delachartre

Authors
  1. Jérémie Fromageau
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  2. Hervé Liebgott
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  3. Elisabeth Brusseau
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  4. Didier Vray
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  5. Philippe Delachartre
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Correspondence to Jérémie Fromageau.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://doi.org/creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Fromageau, J., Liebgott, H., Brusseau, E. et al. Estimation of Time-Scaling Factor for Ultrasound Medical Images Using the Hilbert Transform. EURASIP J. Adv. Signal Process. 2007, 080735 (2006). https://doi.org/10.1155/2007/80735

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  • DOI: https://doi.org/10.1155/2007/80735

Keywords

  • Ultrasound Scanner
  • Signal Spectrum
  • Iterative Version
  • Factor Estimation
  • Simulated Signal