title: Application of L1-norm regularization to epicardial potential reconstruction based on gradient projection.
abstract: The epicardial potential (EP)-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 the L2-norm penalty function inherently leads to considerable smoothing of the solution, which reduces the accuracy of distinguishing abnormalities and locating diseased regions. Directly using the L1-norm penalty function, however, may greatly increase computational complexity due to its non-differentiability. We propose an 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 bound-constrained 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.
authors: Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong. lswang@cse.cuhk.edu.hk
authors: Liansheng
authors: L
authors: Wang
authors: Jing
authors: J
authors: Qin
authors: Tien Tsin
authors: TT
authors: Wong
authors: Pheng Ann
authors: PA
authors: Heng
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004562:Electrocardiography / Q000379:methods*; D056149:Epicardial Mapping / Q000379:methods*; D006329:Heart Conduction System / Q000000981:diagnostic imaging* / Q000473:pathology; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008955:Models, Cardiovascular; D011859:Radiography; D059629:Signal-To-Noise Ratio; D013997:Time Factors