Application of L1-Norm Regularization to Epicardial Potential Solution of the Inverse Electrocardiography Problem
By Subham Ghosh, Yoram Rudy. 2009
130 citations recorded by the source corpus.
The electrocardiographic inverse problem of computing epicardial potentials from multi-electrode body-surface ECG measurements, is an ill-posed problem. Tikhonov regularization is commonly employed, which imposes penalty on the L2-norm of the potentials (zero-order) or their derivatives. Previous work has indicated superior results using L2-norm of the normal derivative of the solution (a first order regularization). However, L2-norm penalty function can cause considerable smoothing of the solution. Here, we use the L1-norm of the normal derivative of the potential as a penalty function. L1-norm solutions were compared to zero-order and first-order L2-norm Tikhonov solutions and to measured ‘gold standards’ in previous experiments with isolated canine hearts. Solutions with L1-norm penalty function (average relative error [RE] = 0.36) were more accurate than L2-norm (average RE = 0.62). In addition, the L1-norm method localized epicardial pacing sites with better accuracy (3.8 ± 1.5 mm) compared to L2-norm (9.2 ± 2.6 mm) during pacing in five pediatric patients with congenital heart disease. In a pediatric patient with Wolff–Parkinson–White syndrome, the L1-norm method also detected and localized two distinct areas of early activation around the mitral valve annulus, indicating the presence of two left-sided pathways which were not distinguished using L2 regularization.
Subfields: Biomedical Engineering, Electrical and Electronic Engineering, Radiology, Nuclear Medicine and Imaging
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Citations in the corpus
- Comparative studies on damage identification with Tikhonov regularization and sparse regularization (2016, background): “Even though the sparsity constraint has been exploited and adopted in solving inverse problems in other disciplines [9,10], only until very recently it has begun to attract some attention in structural health monitoring applications.”
- Identification of isolated structural damage from incomplete spectrum information using l1-norm minimization (2014, background): “Even though the concept of sparsity has been exploited to solve inverse problems in other disciplines [18,19], only until very recently it has begun to attract some attention in structural health monitoring applications [20].”
- Noninvasive Transmural Electrophysiological Imaging Based on Minimization of Total-Variation Functional (2014, background): “This result is consistent with other studies that compared L1-regularization with L2- versus L1-based data-fidelity term [15], [16], as would be expected because of the fundamental assumption behind a L1 data-fidelity term to handle measurement errors that are mostly small but occasionally large in ”