Use of genetic algorithm for selection of regularization parameters in multiple constraint inverse ECG problem

Abstract

Tikhonov regularization is one of the most widely used regularization approaches in literature to overcome the ill-posedness of the inverse electrocardiography problem. However, the resulting solutions are biased towards the constraint used for regularization. One alternative to obtain improved results is to employ multiple constraints in the cost function. This approach has been shown to produce better results; however finding appropriate regularization parameters is a serious limitation of the method. In this study, we propose estimating multiple regularization parameters using a genetic algorithm based approach. Applicability of the approach is demonstrated here using two and three constraints. The results show that GA based multiple constraints approach improves the Tikhonov regularization solutions.

Bayesian Optimization for the Inverse Problem in Electrocardiography

“…Some examples of the mentioned models are a multipolar array, one or two moving dipoles, multiple fixed location dipoles, the epicardial potential distribution, and isochrones of activation at the surface of the heart [3]. The most common regularization technique used in the inverse problem of electrocardiography is Tikhonov regularization: this technique seeks to achieve a good balance between the adjustment to the measures and a priori information about the solution [5], [13], [20]. Previous works focused on using two-step algorithms with genetic programming [21] and particle swarm optimization [22], but these approaches require a considerable amount of function evaluations, which explode in number as the geometry becomes more dense.…”

“…Several solutions have been proposed for the inverse problem of electrocardiography, for example using ECG signal processing methods [4], [7], single/multi-layer approaches [2], [8], and machine learning [9]- [11]. One of the most common techniques used in practice, however, is still Tikhonov regularization [5], [6], [12], [13]. Despite the great number of approaches proposed, finding stable solutions for the inverse problem of electrocardiography remains, at the time of writing, an open problem.…”

Accuracy of electrocardiographic imaging using the method of fundamental solutions

“…There are also alternative methods for solving the inverse problem of electrocardiology that do not rely on regularisation techniques. These include using: genetic algorithms [14,15,16]; partial differential equation constrained optimisation [17,18]; Twomey regularisation for wave-front based ECG imaging [19], and Bayesian estimation [20]. Some more recent methods for solving the inverse problem of electrocardiology include a Steklov-Poincaré variational formulation, [21], the factorisation method of boundary value problems [22], and methods that use electrical and mechanical measurements [23].…”