A system comprising: one or more processors programmed to: define a simulated measurement matrix V SM representative of a unit matrix; decompose the simulated measurement matrix V SM into a plurality of basis element vectors V SMBEI for a plurality of electrodes, each of the plurality of electrodes to measure electrical potentials non-invasively from a location of a patient's body surface; compute, using a regularization technique, a plurality of simulated estimations of electrical potentials to provide simulated solution vectors V SSi for a plurality of locations on a surface of interest based on the plurality of basis element vectors V SMBEI and a transfer matrix, wherein the value of each simulated solution vector V SSi represents a simulated estimated electrical potential at the plurality of locations on the surface of interest if a given electrode of the electrodes measured a respective value while all other electrodes of the plurality of electrodes measured a zero or are effectively turned off, the transfer matrix having been precomputed to represent a geometrical relationship between a location of each of the electrodes where the measured electrical potentials are to be measured and the locations on the surface of interest for which the electrical potentials are being estimated; and create a transfer matrix based on the simulated solution vectors V SSi to represent a relative influence that each location for the measured electrical potential has on the estimation of the electrical potentials on the surface of interest; and calculate an estimation of electrical potentials on the surface of interest (Vs) by multiplying the transfer matrix C by measured electrical potentials (V M), where V S =C*V M. define a simulated measurement matrix V SM representative of a unit matrix; decompose the simulated measurement matrix V SM into a plurality of basis element vectors V SMBEI for a plurality of electrodes, each of the plurality of electrodes to measure electrical potentials non-invasively from a location of a patient's body surface; compute, using a regularization technique, a plurality of simulated estimations of electrical potentials to provide simulated solution vectors V SSi for a plurality of locations on a surface of interest based on the plurality of basis element vectors V SMBEI and a transfer matrix, wherein the value of each simulated solution vector V SSi represents a simulated estimated electrical potential at the plurality of locations on the surface of interest if a given electrode of the electrodes measured a respective value while all other electrodes of the plurality of electrodes measured a zero or are effectively turned off, the transfer matrix having been precomputed to represent a geometrical relationship between a location of each of the electrodes where the measured electrical potentials are to be measured and the locations on the surface of interest for which the electrical potentials are being estimated; and create a transfer matrix based on the simulated solution vectors V SSi to represent a relative influence that each location for the measured electrical potential has on the estimation of the electrical potentials on the surface of interest; and calculate an estimation of electrical potentials on the surface of interest (Vs) by multiplying the transfer matrix C by measured electrical potentials (V M), where V S =C*V M.