  The proposed method re-frames traditional inverse problems of
electrocardiography into regression problems, constraining the solution space
by decomposing signals with multidimensional Gaussian impulse basis functions.
Impulse HSPs were generated with single Gaussian basis functions at discrete
heart surface locations and projected to corresponding BSPs using a volume
conductor torso model. Both BSP (inputs) and HSP (outputs) were mapped to
regular 2D surface meshes and used to train a neural network. Predictive
capabilities of the network were tested with unseen synthetic and experimental
data. A dense full connected single hidden layer neural network was trained to
map body surface impulses to heart surface Gaussian basis functions for
reconstructing HSP. Synthetic pulses moving across the heart surface were
predicted from the neural network with root mean squared error of $9.1\pm1.4$%.
Predicted signals were robust to noise up to 20 dB and errors due to
displacement and rotation of the heart within the torso were bounded and
predictable. A shift of the heart 40 mm toward the spine resulted in a 4\%
increase in signal feature localization error. The set of training impulse
function data could be reduced and prediction error remained bounded. Recorded
HSPs from in-vitro pig hearts were reliably decomposed using space-time
Gaussian basis functions. Predicted HSPs for left-ventricular pacing had a mean
absolute error of $10.4\pm11.4$ ms. Other pacing scenarios were analyzed with
similar success. Conclusion: Impulses from Gaussian basis functions are
potentially an effective and robust way to train simple neural network data
models for reconstructing HSPs from decomposed BSPs. The HSPs predicted by the
neural network can be used to generate activation maps that non-invasively
identify features of cardiac electrical dysfunction and can guide subsequent
treatment options.

Quantitative Methods;Machine Learning