Independent Component Analysis and Signal Separation

Abstract

The estimation of relevant information theoretical quantities , such as entropy, mutual information, and various divergences is computationally expensive in high dimensions. However, for this task, one may apply pairwise Euclidean distances of sample points, which suits random projection (RP) based low dimensional embeddings. The Johnson-Lindenstrauss (JL) lemma gives theoretical bound on the dimension of the low dimensional embedding. We adapt the RP technique for the estimation of information theoretical quantities. Intriguingly, we find that embeddings into extremely small dimensions, far below the bounds of the JL lemma, provide satisfactory estimates for the original task. We illustrate this in the Independent Subspace Analysis (ISA) task; we combine RP dimension reduction with a simple ensemble method. We gain considerable speed-up with the potential of real-time parallel estimation of high dimensional information theoretical quantities.

Review of spectral imaging technology in biomedical engineering: achievements and challenges

“…They also performed Raman spectral imaging to show the distribution of nucleic acids, lipids, and proteins within the cell. 227 There are also some other applications that have been demonstrated in separating multiple fluorescence signals, 120,141 separating autofluorescence and fluorescence signals, 12,85 extracting dye distributions from the images, 228 FRET imaging, 53,229 and tissue imaging. 45 These studies show that spectral imaging is best appreciated as a tool for detecting spectral changes in fluorescence and eliminating problems associated with autofluorescence.…”