A comparison of higher-order generalized eigensystem techniques and tikhonov regularization for the inverse problem of electrocardiography^*

^*This work was supported in part by NSF grant numbers BES-9410385 and BES-9622158, and the National Center for Supercomputing Applications under grant BCS930005N. It utilized the Power Challenge Array at NCSA, University of Illinois at Urbana-Champaign.

Abstract

In a recent series of papers we proposed a new class of methods, the generalized eigensystem (GES) methods, for solving the inverse problem of electrocardiography. In this paper, we compare zero, first, and second order regularized GES methods to zero, first, and second order Tikhonov methods. Both optimal results and results from parameter estimation techniques are compared in terms of relative error and accuracy of epicardial potential maps. Results from higher order regularization depend heavily on the exact form of the regularization operator, and operators generated by finite element techniques give the most accurate and consistent results. In the optimal parameter case, the GES techniques produce smaller average relative errors than the Tikhonov techniques. However, as the regularization order increases, the difference in average relative errors between the two techniques becomes less pronounced. We introduce the minimum distance to the origin (MDO) technique to choose the number of expansion modes for the GES techniques. This produces average relative errors similar to those obtained using the composite residual and smoothing operator (CRESO) with Tikhonov regularization. Second order regularization gives the smallest average relative errors but over-smoothes important epicardial features. In general, GES with MDO resolves the epicardial features better than Tikhonov with CRESO for the data set studied.

Keywords:

• Electrocardiography
• numerical methods
• regularization methods
• inverse problems

^*This work was supported in part by NSF grant numbers BES-9410385 and BES-9622158, and the National Center for Supercomputing Applications under grant BCS930005N. It utilized the Power Challenge Array at NCSA, University of Illinois at Urbana-Champaign.

^†Corresponding [email protected]

^*This work was supported in part by NSF grant numbers BES-9410385 and BES-9622158, and the National Center for Supercomputing Applications under grant BCS930005N. It utilized the Power Challenge Array at NCSA, University of Illinois at Urbana-Champaign.

^†Corresponding [email protected]

Notes

^*This work was supported in part by NSF grant numbers BES-9410385 and BES-9622158, and the National Center for Supercomputing Applications under grant BCS930005N. It utilized the Power Challenge Array at NCSA, University of Illinois at Urbana-Champaign.

^†Corresponding [email protected]