When a linear mixture of independent sources is contaminated by multiplicative noise, the problems of blind source separation and feature extraction are highly complex. Specifically, the approach followed by the independent component analysis does not produce proper results. This is because the output of a linear transformation of the noisy data cannot be independent. However, the statistic of this output possesses a special structure that can be used to obtain the original mixture. In this paper, this statistical structure is studied and a general approach to solving the problem is stated, studying how the strategies followed by the standard ICA methods can be adapted in this case. To illustrate the analysis, the results of two different methods that follow the general approach are presented, where the improvement with respect the standard ICA method is clear. (c) 2006 Elsevier B.V. All rights reserved.