Multichannel blind deconvolution of colored signals via eigenvalue decomposition

Abstract

We prove that a MIMO (multiple input multiple output) blind deconvolution problem for n colored uncorrelated signals can be converted to n SIMO (single input multiple output) problems, using eigenvalue decomposition of a special covariance matrix, depending on L-dimensional parameter b, if appropriate covariance matrices have sets of eigenvalues with empty pairwise intersection. We present a sufficient condition for this conversion and discuss how to End such parameters. We prove that the parameters b for which this is possible, form an open subset of IR/sup L/, whose complement has a Lebesgue measure zero.