Elastographic Image Reconstruction: A Stochastic State Space Approach

A stochastic model-based filtering approach is developed to reconstruct the elastographic images in this paper. The advantage of this model-based reconstruction algorithm over the conventional strain-based approaches is:strain-based approaches can only provide the distribution of relative elasticity because of the assumption of uniformed internal stress distribution, while our model-based algorithm can provide the distribution of real elasticity using realistic finite element (FE) or bio-mechanical model constraints.However, how to define a realistic model constraint in the environment of elastography, especially static ultrasound elastography, is really a challenge because of the disc repancies between the model and image data. In this paper, a stochastic state space approach is proposed to generate the elastographic image through the simultaneous estimation of materials properties and kinematic functions from 1 ultrasound elastographic data using the constitutive law of linear elastic isotropic material, which has been well adopted in static elastography. Upon the state space approach, the discrepancies between the bio-mechanical model and data is modeled as process noises, and the realistic bio-mechanical model constraint is obtained from a filtering identification process, which is to recursively estimate the real material properties for particular ultrasound data according to the minimum mean square error (MMSE) criteria. In our implementation of thesis stochastic state approach, the linear isotropic bio-mechanical model, obeyed the constitutive law of linear elastic isotropic material, is transformed into a system equation, and the ultrasound-derived measurements is assimilated through an observation equation. The optimal estimation of kinematic functions, i.e. the full displacement and velocity field, and the distribution of Young's modulus are computed simultaneously through an extended Kalman filter (EKF). Further, the model-data discrepancy is modeled as uncertainties, i.e. Gaussian white noise, and the measurement noise is treated as another independent Gaussian white noise in the EKF. The accuracy and robustness of our proposed framework is first evaluated in synthetic data in controlled condition, and the performance of this framework is then evaluated in the real data collected from elastography phantom and patients using the ultrasound machine with favorable results.