Abstract

cation of a new approach to total-variation (TV) minimization for reconstruction problems on geometrically-complex and unstructured volumetric mesh. The driving application of thisstudy is the reconstruction of 3D ischemic regions in the heartfrom noninvasive body-surface potential data, where the use of a TV-prior can be expected to promote the reconstruction of two piecewise smooth regions of healthy and ischemic electricalproperties with localized gradient in between. Compared to TV minimization on regular grids of pixels/voxels, the com-plex unstructured volumetric mesh of the heart poses unique challenges including the impact of mesh resolutions on the TVprior and the difficulty of gradient calculation. In this paperintroduce a variational TV-prior and, when combined with the iteratively re-weighted least-square concept, a new algorithm tTV minimization that is computationally efficient and robust tothe discretization resolution. In a large set of simulation stuas well as two initial real-data studies, we show that the use of the proposed TV prior outperforms L2-based penalties in reconstruct ischemic regions, and it shows higher robustness and efficiency compared to the commonly used discrete TV prior. We also investigate the performance of the proposed TV-prior in combination with a L2versus L1-based data fidelity term. The proposed method can extend TV-minimization to a border range of applications that involves physical domains of complex shape and unstructured volumetric mesh. I. I NTRODUCTION Myocardial ischemia, a precursor of myocardial infarction, occurs when the oxygen supply to the heart is insufficient. Myocardial infarction creates substrate for ventricular arrhythmias and increase the risk of sudden cardiac death [8]. Nowadays, 12-lead electrocardiograms (ECG) is routinely used for monitoring and identifying myocardial ischemia [22], although its low sensitivity and inability to locate ischemic region has been noted in [1]. Some tomographic techniques can also be used for ischemia imaging, such as perfusion scintigraphy [1]. However, high cost and long procedure time limit the wide application of such techniques in the clinic [9]. Alternatively, much effort has been devoted to computational approaches that reconstruct ischemic regions from body-surface ECG data, mostly through the reconstruction of potential sequence on the epicardium [2]. These approaches define location and extent of ischemic regions on the heart surface only, without information on the transmurality or 3D morphology of ischemic myocardium. Transition to 3D