Regularized Sparse Kernel SFA with Decorrelation Filtering For Separating Correlated Sources

Advances in digital image processing were increased in the past few years. Blind source separation is one of the important research area with numerous applications in signal processing, image processing, telecommunication and speech recognition. In this paper the Blind Source Separation is performed using Slow Feature Analysis(SFA). It is necessary to use multivariate SFA instead of univariate SFA for separating multi-dimensional signals. This paper makes use of Regularized Sparse Kernel SFA(RSKSFA) instead of multivariate SFA and applies it to the problem of blind source separation in particular to image separation. Here the kernel trick is used in combination with sparsification to provide a powerful function class for large data sets. Sparsity is achieved by a novel matching pursuit approach that can be applied to other tasks as well. For small but complex data sets the kernel SFA approach leads to over-fitting and numerical instabilities. To enforce a stable solution, we introduce regularization to the SFA objective. If the original sources are correlated, it is not possible to achieve perfect separation. So apply a decorrelation filter on the image mixtures before applying SFA for separating the correlated sources. For SFA, when the number of mixtures is greater than or equal to the number of sources, the paper demonstrates how to determine the actual number of sources via regularization technique.