IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES Blind Separation of Time/Position Varying Mixtures

We address the fascinating open engineering problem of blindly separating time/position varying mixtures, and attempt to separate the sources from such mixtures without having prior information about the sources or the mixing system. Unlike studies concerning instantaneous or convolutive mixtures, we assume that the mixing system (medium) is changing in time/position. Attempts to solve this problem have mostly utilized, so far, online algorithms based on tracking the mixing system by methods previously developed for the instantaneous or convolutive mixtures. In contrast with these attempts, we develop a batch algorithm in the form of Staged Sparse Component Analysis (SSCA). Accordingly, we assume that the sources are either sparse or can be ’sparsified’. In the first stage we estimate the mixing system filters, based on the scatter plot of the sparse mixtures’ data, using a proper grouping and curve/surface fitting. In the second stage, the mixing system is inverted, yielding the estimated sources. We use the SSCA approach for solving three types of mixtures: time/position varying instantaneous mixtures, single-path mixtures and multi-path mixtures. Real image mixtures and simulated mixtures are used to test our approach. Index Terms Blind Source Separation (BSS), Sparse Component Analysis (SCA), Time/Position Varying Mixing/Unmixing.