Robust recovery of myocardial kinematics using dual ℋ ∞ $\mathcal {H}_{\infty }$ criteria

Abstract

Accurate estimation of myocardial motion can help to better understand the pathophysiological processes of ischemic heart diseases. However, because of partial and noisy image-derived measurements on the cardiac kinematics, the performance of model-based motion estimation relies heavily on the assumption of noise distribution on the measurement data. While existing studies of model-based motion estimation have often adopted the $\mathcal {H}_{2}$ criteria (e.g. least square error) based on fixed model constraints from mathematical or mechanical nature, we present a robust estimation framework with an adaptive biomechanical model constraint using dual $\mathcal {H}_{\infty }$ criteria for the first time. Comparing to the minimization of average gaussian error in $\mathcal {H}_{2}$ criteria, our $\mathcal {H}_{\infty }$ criteria aims to minimize the maximum error without regarding the noise distribution. In this work, our dual estimation framework consists of two iterative $\mathcal {H}_{\infty }$ filters: One filter for the kinematics estimation and another one for the elasticity estimation. At each time step, heart kinematics is estimated with sub-optimal fixed material parameters, followed by an elasticity property recovering given these sub-optimal kinematic state estimates. Such coupled estimation processes are iteratively repeated as necessary until convergence. We evaluate the performance of dual estimation framework on synthetic data, cine image sequences, and human image sequence. Our dual estimation framework shows a higher tolerance of noise than the conventional extended Kalman filter. The results obtained by both synthetic data of varying noises and magnetic resonance image sequences demonstrate the accuracy and robustness of the proposed strategy.