Space-time treatment of inverse bioelectric field problems

Inverse bioelectric field problems require estimation of a matrix representing the space-time distribution of source-layer strength-which is formally the quotient of a space-time data matrix and a spatial transfer matrix (the latter being ill-conditioned and noise-corrupted). A nonlinear estimation formulation results from imposition of constraints on the form of the solution time series (e.g. as a cardiac action potential, or a cerebral epileptogenic spike). In the absence of such constraints, the optimal (linear) estimation algorithm is based on the novel concept of a “Virtual-SVD”,, which we present herein