A reduced-rank square root filtering framework for noninvasive functional imaging of volumetric cardiac electrical activity

To noninvasively reconstruct transmembrane potential (TMP) dynamics throughout the 3D myocardium using body surface potential recordings, it is necessary to combine prior physiological models and patient's data with regard to their respective uncertainties. To fulfill model-data melding for this large-scale and high-dimensional system, data assimilation with proper computational reduction is needed for computational feasibility and efficiency. In this paper, we develop a reduced-rank square root TMP estimation algorithm, using dominant components of estimation uncertainties to guide a more efficient model-data coupling in the square root structure. The SVD-based reduced-rank error covariance is used to represent and track the dominant estimation errors, and unified into an integrated square root filtering framework. Phantom experiments demonstrate the ability of this framework to bring substantial computational reduction at slight expense of degraded estimation accuracy. It therefore improves the efficiency and applicability of the volumetric myocardial TMP imaging in practice.