Title :
Blind Separation of Multi-Dimensional Components via Subspace Decomposition: Performance Analysis
Author :
Lahat, Dana ; Cardoso, Jean-Francois ; Messer, Hagit
Author_Institution :
GIPSA-Lab., St. Martin d´Hères, France
Abstract :
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.
Keywords :
blind source separation; decomposition; mean square error methods; BSS; MSE; blind source separation; closed-form analytical expression; finite data-size error; mean-square error; multidimensional data component; one-dimensional model; piecewise stationary model; subspace decomposition; two-step procedure; Algorithm design and analysis; Blind source separation; Data models; Educational institutions; Joints; Signal processing algorithms; Vectors; Blind source separation; independent component analysis; independent subspace analysis; joint block diagonalization; multi-dimensional components; performance analysis; second-order methods;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2014.2315164