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心脏磁场源重构, 即通过人体胸腔表面的磁场阵列测量信号反演产生该磁场的电流源分布, 是一种无创地研究心脏电活动的方法. 本文用线性化方程描述测量磁场与心脏内部电流源的关系, 并通过一种贪婪优化的方法得到了源重构的稀疏解. 通过近似正交化过程和改变迭代算法中原子的选择方式, 降低了优化算法的复杂度, 可在保证源重构精度的情况下, 快速搜索源空间中强度比较大的位置. 文中通过一组正常人的心磁测量数据, 说明了源重构方法的有效性. 这组数据的研究结果表明, 强度大于65%的重构电流源的空间移动轨迹与心脏除极和复极电活动的传导过程基本符合. 其QRS 和ST-T 段的实测心磁图与重构电流源产生的磁场图的平均拟合优度分别为99.36%和99.78%.Current source reconstruction, i.e., reconstructing current dipole distribution through measured array signals of cardiac magnetic field on body surface, is a method for non-invasively study on the heart electrical activity. In this paper, the relationship between measured magnetic signals and current dipole distribution is described by a linear equation, and a sparse solution of current source reconstruction is achieved using a fast greedy method. This method can significantly decrease the computational complexity of or- thogonal matching pursuit (OMP) algorithm by means of approximating orthogonalisation and improving the selection vector strategy per iteration. Thereby, the sources with large dipole strength can be fast searched out with high accuracy. A set of magnetocardiogram (MCG) data of normal subject is used to demonstrate the effectiveness of this method that the trajectory of reconstructed dominant sources, whose strengths are more than 65%, is almost consistent with conduction process in depolarization and repolarization. The average goodness of fit (GOFs) of measured MCG and the magnetic field map generated by the reconstructed current sources during QRS complex and ST-T segment are 99.36% and 99.78%, respectively.
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Keywords:
- magnetocardiography (MCG) /
- inverse problem /
- sparse solution /
- orthogonal matching pursuit (OMP)
[1] He B 2003 Modeling and Imaging of Bioelectrical Activity: Principles and applications (Minnesota: Kluwer Academic/Plenum Press)
[2] Gutierrez D, Nehorai A, Dogandzic A 2006 IEEE Transactions on Biomedical Engineering 53 840
[3] Moiseev A, Gaspar J M, Schneider J A, Herdman A T 2011 Neuroimage 58 481
[4] Gorodnitsky I F, George J S, Rao B D 1995 Electroencephalography and clinical Neurophysiology 95 231
[5] Melis M D, Tanaka K, Uchikawa Y 2010 IEEE Transactions on magnetics 38 1203
[6] Michel C M, Murray M 2004 Clinical Neurophysiology 115 2195
[7] Davis G 1994 Ph. D. Dissertation (U.S.A: New York University)
[8] Chen S S, Donoho D L, Saunders M A 1998 SIAM Journal of Scientific Computing 20 33
[9] Liu H S, Schimpf P H, Dong G Y, Gao X R, Yang F S, Gao S K 2005 IEEE Transactions on Biomedical Engineering 52 1681
[10] Xu P, Tian Y, Chen H F, Yao D Z 2007 IEEE Transactions on Biomedical Engineering 54 400
[11] Manoharana A, Morana J E, Bowyera S M, Masona K M, Tepleya N, Smitha B J, Barkleya G L 2007 International Congress Series. Eng. 1300 665
[12] Bing L, Jiang S Q, 2012 International Conference on System Simulation Shanghai, China, April 4-6, 2012 p298
[13] Mallat S, Zhang Z 1993 IEEE Transactions on Signal Processing 41 3397
[14] Pati Y C, Rezaiifar R, Krishnaprasad S 1993 27th Annum Asilomar Conference on Signals Systems and Computers California, U.S.A, November 1-3, 1993 p101
[15] Mallat S, Davis G, Zhang Z 1994 SPIE Journal of Optical Engineering 33 2183
[16] Blumensath T, Davies M 2008 IEEE Transactions on Signal Processing 56 2370
[17] Donoho D, Tsaig Y, Drori I, Starck J 2006 Tech. Rep. (U.S.A: Stanford University Press)
[18] Zhu J J, Jiang S Q 2012 International Conference on System Simulation Shanghai, China, April 4-6, 2012 p302
[19] Davies M E, Blumensath T 2008 Proceedings of the third International Symposium on Communications, Control and Signal Processing Malta, March 12-14, 2008 p774
[20] Wang C S 2007 Cardiac conduction system (Beijing: Qinghua University Press) p84 (in Chinese) [王成山 2007 心脏传导系统基础与临床 (北京: 清华大学出版社) 第84页]
[21] Yasunaga H, Yasunaga H, Harumizu S, Naomi I, Seiko K, Tohru S, Masayasu H 2002 Journal of Electrocardiology 35 p105
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[1] He B 2003 Modeling and Imaging of Bioelectrical Activity: Principles and applications (Minnesota: Kluwer Academic/Plenum Press)
[2] Gutierrez D, Nehorai A, Dogandzic A 2006 IEEE Transactions on Biomedical Engineering 53 840
[3] Moiseev A, Gaspar J M, Schneider J A, Herdman A T 2011 Neuroimage 58 481
[4] Gorodnitsky I F, George J S, Rao B D 1995 Electroencephalography and clinical Neurophysiology 95 231
[5] Melis M D, Tanaka K, Uchikawa Y 2010 IEEE Transactions on magnetics 38 1203
[6] Michel C M, Murray M 2004 Clinical Neurophysiology 115 2195
[7] Davis G 1994 Ph. D. Dissertation (U.S.A: New York University)
[8] Chen S S, Donoho D L, Saunders M A 1998 SIAM Journal of Scientific Computing 20 33
[9] Liu H S, Schimpf P H, Dong G Y, Gao X R, Yang F S, Gao S K 2005 IEEE Transactions on Biomedical Engineering 52 1681
[10] Xu P, Tian Y, Chen H F, Yao D Z 2007 IEEE Transactions on Biomedical Engineering 54 400
[11] Manoharana A, Morana J E, Bowyera S M, Masona K M, Tepleya N, Smitha B J, Barkleya G L 2007 International Congress Series. Eng. 1300 665
[12] Bing L, Jiang S Q, 2012 International Conference on System Simulation Shanghai, China, April 4-6, 2012 p298
[13] Mallat S, Zhang Z 1993 IEEE Transactions on Signal Processing 41 3397
[14] Pati Y C, Rezaiifar R, Krishnaprasad S 1993 27th Annum Asilomar Conference on Signals Systems and Computers California, U.S.A, November 1-3, 1993 p101
[15] Mallat S, Davis G, Zhang Z 1994 SPIE Journal of Optical Engineering 33 2183
[16] Blumensath T, Davies M 2008 IEEE Transactions on Signal Processing 56 2370
[17] Donoho D, Tsaig Y, Drori I, Starck J 2006 Tech. Rep. (U.S.A: Stanford University Press)
[18] Zhu J J, Jiang S Q 2012 International Conference on System Simulation Shanghai, China, April 4-6, 2012 p302
[19] Davies M E, Blumensath T 2008 Proceedings of the third International Symposium on Communications, Control and Signal Processing Malta, March 12-14, 2008 p774
[20] Wang C S 2007 Cardiac conduction system (Beijing: Qinghua University Press) p84 (in Chinese) [王成山 2007 心脏传导系统基础与临床 (北京: 清华大学出版社) 第84页]
[21] Yasunaga H, Yasunaga H, Harumizu S, Naomi I, Seiko K, Tohru S, Masayasu H 2002 Journal of Electrocardiology 35 p105
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