Sparse Independent Component Analysis with Interpolation for Blind Source Separation

The separation of a super position of multiple signals is accomplished by taking into account the structure of the mixing process and by making assumptions about the sources. By assuming that the sources can be represented sparsely in a given basis, recent research has demonstrated that better results can be obtained. In this paper, we will show that increasing the size of mixture of signals by estimating new data points using the technique of interpolation can be used to increase the accuracy of Blind Source Separation (BSS) methods. We propose a four step BSS technique for instantaneous case which increases the accuracy of the sparse BSS methods. These steps include Interpolation, Sparse Decomposition, Independent Component Analysis (ICA) algorithm, and Downsampling. The idea is to use the combination of interpolation and sparsing as preprocessing for ICA. Although the method works for both one dimensional and two dimensional signals, it is best suitable for two dimensional signals like images. Results of the proposed method on one dimensional and two dimensional signals have been presented.