Application of the wavelet transforms on axial strain calculation in ultrasound elastography

In ultrasound elastography, the axial strain distribution within biological tissues is calculated as the numerical derivative (differentiation) of the estimated axial displacement field. Unfortunately, the numerical derivative is unstable because it can greatly amplify the noises, especially at high frequencies. This work focuses on the axial strain calculation from the estimated axial displacements using wavelet transforms (WTs), including continuous wavelet transforms (CWTs) and discrete wavelet transforms (DWTs). The feasibility of the WT-based method using the quadratic spline function is verified by computer simulations and some phantom data. Results indicate that the WT-based method can effectively reduce the noise amplification in axial strain calculation.