An approach to convolutive backward-model blind source separation based on joint diagonalization

A convolutive frequency-domain backward-model blind source separation (BSS) for directly estimating the unmixing matrix by solving a block-by-block least-squares approximate joint diagonalization (AJD) problem is presented. In the new backward-model BSS, the inverse of an exponentially weighted cross-spectral density matrix of the observed signal is calculated at each frequency bin. The expansion of the inverse matrix can lead to a criterion for applying the alternating least-squares with projection (ALSP) algorithm to the backward-model BSS. Introducing the block-processing technique into the least-squares AJD (LS-AJD) problem is effective to reduce computational burden per iteration at each block frame. This new BSS does not need to solve the scaling ambiguity by other methods due to the scale constraint. The interfrequency correlation is used to prevent misalignment permutation for the new BSS. Finally, we compare it with the conventional forward-model BSS in both low and high signal-to-noise ratio (SNR) environments and show that this new BSS improves robustness.