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

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 ).