Fourier-domain implementation of correlated component analysis, with error estimation

We introduce a Fourier-domain version of the Correlated Component Analysis technique used for blind separation of linearly mixed dependent sources when they exhibit a sufficient degree of spatial autocorrelation and the mixing operator can be identified through a few parameters. The main advantage of this technique when compared to its space-domain version is that possible convolutive mixtures with channel-dependent kernels can be naturally treated with no need for data preprocessing. Like its space-domain counterpart, the new technique is able to estimate both the mixing operator and the spatial structures of the source images, in this case, through their cross-spectra. A further advantage of the Fourier technique is that the ill-conditioned estimation of the power spectra can be regularized by energy or smoothness constraints. The estimated cross-spectra can then be used to help the reconstruction task. A complete derivation of the technique is presented, with some simulations to demonstrate both its capabilities and the validity of the assumptions made. Some strategies to evaluate approximately the variances of the estimated parameters are also proposed.