Estimation of Time-Scaling Factor for Ultrasound Medical Images Using the Hilbert Transform - Fromageau, Jérémie; Liebgott, Hervé; Brusseau, Elisabeth; Vray, Didier; Delachartre, Philippe (EURASIP journal on advances in signal processing, 2007)
A new formulation for the estimation of thetime-scaling factor between two ultrasound signals is presented.The estimator is derived under the assumptions of a smalltime-scaling factor and signals with constant spectrum over itsbandwidth. Under these conditions, we show that the proposedapproach leads to a simple analytic formulation of thetime-scaling factor estimator. The influences of an increase of thetime-scaling factor and of signal-to-noise ratio (SNR) arestudied. The mathematical developments of the expected mean andbias of the estimator are presented. An iterative version is alsoproposed to reduce the bias. The variance is calculated andcompared to the Cramer-Rao lower bound (CRLB). The estimatorcharacteristics are measured on flat-spectra simulated signals andexperimental ultrasound scanner signals and are compared to thetheoretical mean and variance. Results show that the estimator isunbiased and that variance tends towards the CRLB for SNR higher than20 dB. This is in agreement with typical ultrasound signals usedin the medical field, as shown on typical examples. Effects of thesignal spectrum shape and of the bandwidth size are evaluated.Finally, the iterative version of the estimator improves thequality of the estimation for SNR between 0 and 20 dB as well asthe time-scaling factor estimation validity range (up to 15%).