Applications of Sparse Regularization to Inverse Problem of Electrocardiography

The epicardial potentials (EPs) targeted inverse problem of electrocardiography (ECG) has been widely investigated as it is demonstrated that EPs reflect underlying myocardial activity. It is a well-known ill-posed problem as small noises in input data may yield a highly unstable solution. Traditionally, L2-norm regularization methods have been proposed to solve this ill-posed problem. But L2-norm penalty function inherently leads to considerable smoothing of the solution, which reduces the accuracy of distinguishing abnormalities and locating diseased regions. In this thesis, we propose three new techniques in order to achieve more accurate reconstruction results of EPs and applied these techniques to a clinical application. We first propose a L1-norm regularization method in order to reduce the computational complexity and make rapid convergence possible. Variable splitting is employed to make the L1- norm penalty function differentiable based on the observation that both positive and negative potentials exist on the epicardial surface. Then, the inverse problem of ECG is further formulated as a boundconstrained quadratic problem, which can be efficiently solved by gradient projection in an iterative manner. Extensive experiments conducted on both synthetic data and real data demonstrate that the proposed method can handle both measurement noise and geometry noise and obtain more accurate results than previous L2- and L1- norm regularization methods, especially when the noises are large.;Although L1 norm regularization achieves better reconstructed results compared with L2 norm regularization, L1 norm is still an approximation of L0 norm which is more accurate than L1 norm. We further presented a smoothed L0 norm technique in order to directly solve the L0 norm constrained problem. Our method employs a smoothing function to make the L0 norm continuous. Extensive experiments showed that the proposed method reconstructs more accurate epicardial potentials compared with L1 norm and L2 norm.;In current research of ECG inverse problem, epicardial potentials are reconstructed from a static heart model which blocks the techniques to clinic applications. A novel strategy is presented to recover epicardial potentials using a dynamic heart model built from MRI image sequences and ECG data. We used MRI images to estimate the current density and visualize it on the surface of the heart model. The ECG data also be used to achieve the time synchronization when the propagation of the current density. Experiments are conducted on a set of real time MRI images, also with the real ECG data, and we get favorable results.;Finally, a non-invasive system is presented for enhancing the diagnosis of Bundle Branch Block (BBB). In this system, epicardial potential is estimated and visualized in the 3D heart model to improve the diagnosis of BBB. Using patient CT and BSPM data, the system is able to reconstruct details of the complete electrical activity of BBB on the 3D heart model. Through the analysis of the epicardial potential mapping in this system, patients with BBB are easily and accurately distinguished instead of from empirically checking ECG. Therefore the diagnosis of BBB is improved using this system.