A prewhitening-induced bound on the identification error in independent component analysis

In this paper, we derive a prewhitening-induced lowerbound on the Frobenius norm of the difference between the true mixing matrix and its estimate in independent component analysis. This bound applies to all algorithms that employ a prewhitening. Our analysis allows one to assess the contribution to the overall error of the partial estimation errors on the components of the singular value decomposition of the mixing matrix. The bound indicates the performance that can theoretically be achieved. It is actually reached for sufficiently high signal-to-noise ratios by good algorithms. This is illustrated by means of a numerical experiment. A small-error analysis allows to express the bound on the average precision in terms of the second-order statistics of the estimator of the signal covariance.