Second-Order Blind Source Separation Based on Multi-dimensional Autocovariances

SOBI is a blind source separation algorithm based on time decorrelation. It uses multiple time autocovariance matrices, and performs joint diagonalization thus being more robust than previous time decorrelation algorithms such as AMUSE. We propose an extension called mdSOBI by using multidimensional autocovariances, which can be calculated for data sets with multidimensional parameterizations such as images or fMRI scans. mdSOBI has the advantage of using the spatial data in all directions, whereas SOBI only uses a single direction. These findings are confirmed by simulations and an application to fMRI analysis, where mdSOBI outperforms SOBI considerably. Blind source separation (BSS) describes the task of recovering the unknown mixing process and the underlying sources of an observed data set. Currently, many BSS algorithm assume independence of the sources (ICA), see for instance [1,2] and references therein. In this work, we consider BSS algorithms based on time-decorrelation. Such algorithms include AMUSE [3] and extensions such as SOBI [4] and the similar TDSEP [5]. These algorithms rely on the fact that the data sets have non-trivial autocorrelations. We give an extension thereof to data sets, which have more than one direction in the parametrization, such as images, by replacing one-dimensional autocovariances by multi-dimensional autocovariances. The paper is organized as follows: In section 1 we introduce the linear mixture model; the next section 2 recalls results on time decorrelation BSS algorithms. We then define multidimensional autocovariances and use them to propose mdSOBI in section 3. The paper finished with both artificial and real-world results in section 4.