A novel direct approach for blind source separation based on the characteristic function

We propose a new "direct-form" algorithm for blind source separation. In contrast to "iterative-form" algorithms, in a "direct-form" algorithm the mixing matrix is estimated directly from the observed data, using a single pass to collect some statistics. The statistics exploited by our algorithm are the empirical second-derivative matrices of the second joint characteristic function of the observations, evaluated at selected points, termed "processing points". Applying approximate joint diagonalization to these matrices yields a consistent estimate of the mixing matrix (under some mild regularity conditions) in the noiseless as well as in the noisy case, whenever the noise is Gaussian and spatially white. For spatially correlated Gaussian noise, a slightly modified version of the algorithm can still produce consistent estimates. The performance depends strongly on the choice of processing points, and can compare favorably to other BSS algorithms.