Blind separation of multi-dimensional components via subspace decomposition: Performance analysis

A prevalent approach to blind separation of multi-dimensional data is a two-step procedure. In the first step, the data are assigned a one-dimensional model. A separating algorithm is applied according to this model. This step corresponds to classical blind source separation (BSS). In the second step, the output is assigned into groups, representing the multi-dimensional components. In this paper, we consider an even more general case, in which the subpartition of the components in the first step may be into elements of any dimension, not necessarily one. We consider a piecewise stationary model and assume that the number and dimensions of the underlying multi-dimensional components are known. We obtain a closed-form analytical expression for the mean-square error (MSE) in the estimation of the multi-dimensional components using this two-step procedure. As expected, this approach is suboptimal in the presence of finite data-size errors. Therefore, we can predict the expected gain from using the correct model of the components, over any finer decomposition thereof. In addition, we demonstrate the dependence of this gain on the model parameters.