Greedy Selection of the Torso Electrodes for the Solution of Inverse Problem with a Single Dipole

Many torso electrodes are used to solve the inverse problem of electrocardiography. We investigate which ones are the most important based on 4 different criteria. Body surface potential measurements in 128 and 192 electrodes from one patient-specific (Bratislava) and two torso tank experimental datasets (Bordeaux, Utah) with the known position of the ventricular stimulation were used as a testbed to analyse inverse solutions with a single dipole. Electrode sets were constructed incrementally according to the singular value decomposition of the transfer matrix. Electrode sets were chosen for 4 optimality criteria: A) minimized condition number,
$B$
) maximized product of singular values,
$C$
) maximized sum of singular values and
$D$
) joint criterion of A and
$B$
. Starting from the initial set of 4 best electrodes, the electrode set was incrementally enlarged by a single electrode at a time in a greedy manner. The accuracy of the inverse solution was determined by the localization error
$(LE)$
. For Bratislava, the best results were achieved for
$C$
and
$D$
, with LE decreasing to 7.1 mm and 7.5 mm (10% and 13% of electrodes). The LE with all electrodes used was 16.0 mm, suggesting beneficial effects of the sparsity enforcement in the electrode space. For Bordeaux the best results were obtained for A (LE 12.3 mm) and Utah for
$C$
(LE 14.2 mm).