Blind convolution using signal reconstruction from partial higher order cepstral information

A blind deconvolution scheme for the reconstruction of a signal that propagates in the presence of reverberation and additive noise is presented. The reconstruction employs data collected by two receivers placed well apart from each other. Each received sequence consists of the convolution of the transmitted signal with a channel. Applying the bicepstrum iterative reconstruction algorithm on the differences of the cepstra coefficients of the two received sequences, the cepstra coefficients of the transmission channels can be computed and used for the reconstruction of the transmitted signal. The deconvolution can be performed even if the data sequences are corrupted by additive noise. The computation of the cepstra coefficients is based on the cross-bispectrum if the noise processes present in the observation sequences are zero mean and uncorrelated, while the bicepstrum of each observation is used if the noise processes are zero mean correlated with a symmetric probability density function