Multiresolution blind deconvolution of symmetric point-spread functions from bioelectrical potentials

Cardiac muscle tissue consists of multiple, electrically-active layers, whose electrical potentials can be reconstructed from surface measurements as a volume conductor inverse problem. These are useful in diagnosis following myocardial infarction. The measurements include an unknown point-spread function, which must be blindly deconvolved from the bioelectrical potentials. We present a new divide-and-conquer approach to this problem: (1) unwrap the 2-D problem into a huge 1-D problem; (2) perform a multiresolution (subband) decomposition of the huge 1-D problem into small 1-D problems; (3) solve the small 1-D problems by finding the null vector of a Toeplitz-plus-Hankel matrix. Depending on the noise level, the polynomial Euclidian algorithm or structured total least squares may be used