Messnarz Bernd, Tilg Bernhard, Modre Robert, Fischer Gerald, Hanser Friedrich
University for Health Informatics and Technology Tyrol, Innsbruck 6020, Austria.
IEEE Trans Biomed Eng. 2004 Feb;51(2):273-81. doi: 10.1109/TBME.2003.820394.
The single-beat reconstruction of electrical cardiac sources from body-surface electrocardiogram data might become an important issue for clinical application. The feasibility and field of application of noninvasive imaging methods strongly depend on development of stable algorithms for solving the underlying ill-posed inverse problems. We propose a novel spatiotemporal regularization approach for the reconstruction of surface transmembrane potential (TMP) patterns. Regularization is achieved by imposing linearly formulated constraints on the solution in the spatial as well as in the temporal domain. In the spatial domain an operator similar to the surface Laplacian, weighted by a regularization parameter, is used. In the temporal domain monotonic nondecreasing behavior of the potential is presumed. This is formulated as side condition without the need of any regularization parameter. Compared to presuming template functions, the weaker temporal constraint widens the field of application because it enables the reconstruction of TMP patterns with ischemic and infarcted regions. Following the line of Tikhonov regularization, but considering all time points simultaneously, we obtain a linearly constrained sparse large-scale convex optimization problem solved by a fast interior point optimizer. We demonstrate the performance with simulations by comparing reconstructed TMP patterns with the underlying reference patterns.
从体表心电图数据进行心脏电活动源的单搏重建可能成为临床应用中的一个重要问题。非侵入性成像方法的可行性和应用领域在很大程度上取决于用于解决潜在不适定逆问题的稳定算法的发展。我们提出了一种用于重建表面跨膜电位（TMP）模式的新型时空正则化方法。通过在空间和时间域中对解施加线性约束来实现正则化。在空间域中，使用一个类似于表面拉普拉斯算子的算子，并由一个正则化参数加权。在时间域中，假定电位具有单调非递减行为。这被表述为一个附带条件，无需任何正则化参数。与假定模板函数相比，较弱的时间约束拓宽了应用领域，因为它能够重建具有缺血和梗死区域的TMP模式。沿着蒂霍诺夫正则化的思路，但同时考虑所有时间点，我们得到了一个由快速内点优化器求解的线性约束稀疏大规模凸优化问题。我们通过将重建的TMP模式与潜在的参考模式进行比较，用模拟来证明其性能。
