Abstract
Regularization is a key step for solving the ill-posed inverse problem of electrocardiography (ECG). In this paper, a novel regularization technique (LSQR-Tik) which combines the least square QR (LSQR) method with a Tikhonov-like prior information term is proposed. This technique needs to select two parameters, the Tikhonov-like regularization parameter (λ) and the iteration number of LSQR-Tik (k), which can be determined by a modified L-curve technique. The performance of the LSQR-Tik method for solving the inverse ECG problem was evaluated based on a realistic heart-torso model simulation protocol. The results show that the LSQR-Tik method could overcome the ill-pose property effectively and get better inverse solutions than those of Tikhonov and LSQR methods, especially in the case of body surface potential with large noises.
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References
Rudy, Y., Messinger, R.: The Inverse Problem in Electrocardiography: Solutions in Terms of Epicardial Potentials. CRC Crit. Rev. Biomed. Eng. 16, 215–268 (1988)
Seger, M., Fischer, G., Modre, R., Messnarz, B., Hanser, F., Tilg, B.: Lead Field Computation for The Electrocardiographic Inverse Problem-Finite Elements Versus Boundary Elements. Computer Methods and Programs in Biomedicine 77, 241–252 (2005)
Calvetti, D., Reichel, L.: Tikhonov Regularization of Large Linear Problems BIT Numerical Mathematics 43, 263–283 (2003)
Johnston, P.R., Gulrajani, R.M.: Selecting the Corner in the L-Curve Approach to Tikhonov Regularization. IEEE Trans. Biomed. Eng. 47, 1293–1296 (2000)
Hansen, P.C., OLeary, D.P.: The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems. SIAM J. Sci. Comput. 14, 1487–1503 (1993)
Golub, G.H., Von, M.U.: Generalized Cross-Validation for Large-Scale Problems. J. Comput. Graph. Statist. 6, 1–34 (1997)
Bazan, F.S.V.: CGLS-GCV: A Hybrid Algorithm for Low-Rank-Deficient Problems. Applied Numerical Mathematics 47, 91–108 (2003)
Jacobsen, M., Hansen, P.C., Saunders, M.A.: Subspace Preconditioned LSQR for Discrete Ill-Posed Problems. BIT Numerical Mathematics 43, 975–989 (2003)
Angelika, B.G., Valia, G.O.: An Improved Preconditioned LSQR for Discrete Ill-Posed Problems. Mathematics Computers in Simulation 73, 65–75 (2006)
Jiang, M., Xia, L., Shou, G., Tang, M.: Combination of the LSQR Method and A Genetic Algorithm for Solving The Electrocardiography Inverse Problem. Phys. Med. Biol. 52, 1277–1294 (2007)
Paige, C.C., Saunders, M.A., LSQR,: An Algorithm for Sparse Linear Equations and Sparse Least Squares. ACM Trans. Math. Software 8, 43–71 (1982)
Youmaran, R., Adler, A.: Combining Regularization Frameworks for Image Deblurring: Optimization of Combined Hyper-Parameters. Canadian Conference on Electrical and Computer Engineering 2, 723–726 (2004)
Xia, L., Huo, M., Wei, Q., Liu, F., Crozier, S.: Analysis of Cardiac Ventricular Wall Motion Based on A Three-Dimensional Electromechanical Biventricular Model. Phys. Med. Biol. 50, 1901–1917 (2005)
Xia, L., Huo, M., Wei, Q., Liu, F., Crozie, S.: Electrodynamic Heart Model Construction and ECG Simulation. Methods of Information in Medicine 45, 564–573 (2006)
Xia, L., Zhang, Y., Zhang, H., Wei, Q., Liu, F., Crozier, S.: Simulation of Brugada Syndrome Using Cellular and Three-Dimensional Whole-Heart Modeling Approaches. Phsiological Measurement 27, 1125–1142 (2006)
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Jiang, M., Xia, L., Shou, G. (2007). Combining Regularization Frameworks for Solving the Electrocardiography Inverse Problem. In: Huang, DS., Heutte, L., Loog, M. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Contemporary Intelligent Computing Techniques. ICIC 2007. Communications in Computer and Information Science, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74282-1_136
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DOI: https://doi.org/10.1007/978-3-540-74282-1_136
Publisher Name: Springer, Berlin, Heidelberg
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