Comparison of temporal dimensionality reduction methods for constrained inverse in cardiac electrical imaging

Cardiac electrical imaging, that is, reconstructing cardiac electrical activity from body surface measurements, is a technology with great potential. However, ill-posedness of this problem hinders its routine usage in clinical environment and continues to motivate the search for improvements on current methods. Messnarz et al. introduced an algorithm that constraints the reconstructed transmembrane potential (TMP) to be non-decreasing over time during QRS-complex. This physiologically meaningful constraint reduces the solution space of the problem and regularizes the solution. However, this approach is computationally extensive and can become prohibitive as spatial and temporal resolution of the problem increase. Here we compare three distinct options to reduce the computational load: downsampling the measurements in time, downsampling the measurements after filtering with an algorithm based on principal component analysis and non-linearly interpolating the potentials with a spline-based method. The data used were simulated TMPs that were forward propagated to the body surface in a densely sampled geometry. The resulting body surface potential simulations were corrupted with noise and the inverse computed using a much coarser mesh to take geometry errors into account. The results indicate that reducing the dimension of the signal in time does not reduce the quality of the solutions obtained, while the computational requirements decrease considerably, especially for the spline method.