A stochastic filtering approach to recover strain images from quasi-static ultrasound elastography

BACKGROUND: Model-based reconstruction algorithms have shown potentials over conventional strain-based methods in quasi-static elastographic image by using realistic finite element (FE) or bio-mechanical model constraints. However, it is still difficult to properly handle the discrepancies between the model constraint and ultrasound data, and the measurement noise. METHODS: In this paper, we explore the usage of Kalman filtering algorithm for the estimation of strain imaging in quasi-static ultrasound elastography. The proposed strategy formulates the displacement distribution through biomechanical models, and the ultrasound-derived measurements through observation equations. Through this filtering strategy, the discrepancies are quantitatively modelled as one Gaussian white noise, and the measurement noise of ultrasound data is modelled as another independent Gaussian white noise. The optimal estimation of kinematic functions, i.e. the full displacement and velocity field, are computed through this Kalman filter. Then the strain images can be easily calculated from the estimated displacement field. RESULTS: The accuracy and robustness of our proposed framework is first evaluated in synthetic data in controlled conditions, and the performance of this framework is then evaluated in the real data collected from elastography phantoms and patients with favourable results. CONCLUSIONS: The potential of our algorithm is to provide the distribution of mechanically meaningful strain under a proper biomechanical model constraint. We address the model-data discrepancy and measurement noise by introducing process noise and measurement noise in our framework, and then the mechanically meaningful strain is estimated through the Kalman filter in the minimum mean square error (MMSE) sense.