Regularization schemes for non-contact mapping with a medical device

A method for determining a voltage distribution on a surface of a tissue, comprising:

• receiving a plurality of voltages collected by a plurality of electrodes adjacent to the surface;
• introducing one or more regularization terms to an error minimization formulation;
• and
• solving, by a processor, the voltage distribution according to said plurality of voltages and according to said regularization terms of the error minimization formulation;
• wherein one of said regularization terms comprises a confidence matrix, wherein one or more terms of said confidence matrix are associated with one or more of a known probability that one or more of said plurality of voltages accurately measures a portion of said voltage distribution, a known likelihood that a portion of said voltage distribution has relatively high or low values, and a known homogeneity of a portion of said voltage distribution.

A method for determining a voltage distribution on a surface of a tissue, comprising:

• receiving a plurality of voltages collected by a plurality of electrodes adjacent to the surface;
• introducing one or more regularization terms to an error minimization formulation;
• and
• solving, by a processor, the voltage distribution according to said plurality of voltages and according to said regularization terms of the error minimization formulation;
• wherein one of said regularization terms comprises a linear operator that interpolates said plurality of voltages to said voltage distribution, wherein said linear operator is other than an identity matrix.