Multivariate techniques for preprocessing noisy data for source separation using ICA

Independent component analysis (ICA) is a popular technique for separating sources from observed linear mixtures of the sources. If the measured signals are corrupted by noise, then they are generally preprocessed before applying ICA. We make use of a recently developed technique known as the iterative principal component analysis (IPCA) to preprocess the noisy signals and estimate the signal subspace prior to application of ICA. This preprocessing technique is consistent with the assumptions made in ICA, is invariant to any scaling of the data, and accounts for heteroscedastic errors. Through a simulated example, we show that if the measured signals are contaminated with a high-level of additive noise and outliers, the use of the proposed preprocessing technique results in more precise extraction of the independent sources as compared to the use of PCA as a preprocessing method. Application of the technique to an experimental chemometric data set shows that pure species spectra are more accurately extracted from mixture spectra using ICA, if the data is preprocessed using IPCA.