Smoothing-Spline based Strain Estimation in Ultrasound Elastography

In ultrasound elastography, the strains in the axial direction are usually calculated by applying gradient operator on the estimated axial displacements. Unfortunately, the direct gradient operation also amplifies the noises. In this paper a novel smoothing-spline based strain estimation (SSSE) method for estimating the distribution of the soft tissue axial strains from displacement estimates is presented. First, a cubic smoothing-spline is estimated to approximate the axial displacements and then axial strains are calculated as derivative of the estimated spline. The simulation and experimental results showed that the new method can improve the elastographic contrast-to-noise ratio (CNR_e) and signal-to-noise ratio (SNR_e) of the estimated elastogram without sacrificing spatial resolution or being very time consuming.