Abstract:
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The electrocardiographic imaging (ECGI) inverse problem is highly
ill-posed and regularization is needed to stabilize the problem and to provide a
unique solution. When Tikhonov regularization is used, choosing the regularization
parameter is a challenging problem. Mathematically, a suitable value for this
parameter needs to fulfill the Discrete Picard Condition (DPC). In this study, we
propose two new methods to choose the regularization parameter for ECGI with
the Tikhonov method: i) a new automatic technique based on the DPC, which we
named ADPC, and ii) the U-curve method, introduced in other fields for cases
where the well-known L-curve method fails or provides an over-regularized solution,
and not tested yet in ECGI. We calculated the Tikhonov solution with the
ADPC and U-curve parameters for in-silico data, and we compared them with
the solution obtained with other automatic regularization choice methods widely
used for the ECGI problem (CRESO and L-curve). ADPC provided a better correlation
coefficient of the potentials in time and of the activation time (AT) maps,
while less error was present in most of the cases compared to the other methods.
Furthermore, we found that for in-silico spiral wave data, the L-curve method
over-regularized the solution and the AT maps could not be solved for some of
these cases. U-curve and ADPC provided the best solutions in these last cases. |