Open Access

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

  • Jérémie Fromageau1Email author,
  • Hervé Liebgott2,
  • Elisabeth Brusseau2,
  • Didier Vray2 and
  • Philippe Delachartre2
EURASIP Journal on Advances in Signal Processing20062007:080735

Received: 20 April 2006

Accepted: 20 September 2006

Published: 20 December 2006


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 ).


Ultrasound ScannerSignal SpectrumIterative VersionFactor EstimationSimulated Signal


Authors’ Affiliations

Laboratory of Biorheology and Medical Ultrasonics (LBUM), University of Montreal Hospital, Montréal, Canada
Centre de Recherche et d’Applications en Traitement de l’Image et du Signal (CREATIS), CNRS UMR 5515, Inserm U 630, INSA de Lyon, Villeurbanne Cedex, France


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© Jérémie Fromageau et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.