Methods of Fair Comparison of Performance of Linear ICA Techniques in Presence of Additive Noise

Linear ICA model with additive Gaussian noise is frequently considered in many practical applications, because it approaches the reality often much better than the noise-free alternate. In this paper, a number important differences between noisy and noiseless ICA are discussed. It is shown that estimation of the mixing/demixing matrix should not be the main goal, in the noisy case. Instead, it is proposed to compare the outcome of ICA algorithms with a minimum mean square (MMSE) separation, derived for known mixing model. The signal-to-interference-plus-noise ratio is suggested as the most meaningful performance criterion. A simulation study that compares a few well known ICA algorithms applied to noise data is included