Blind separation using convex functions

In this paper, the problem of how to conveniently estimate independence from observations is addressed. Random variables (RVs) are transformed by their respective distribution functions and quantized. Then, the uniformity of the joint probability of the obtained discrete RVs is evaluated using a strictly convex function. An infinite class of new independence measures, named quasientropy (QE), is thus proposed. Unbiased estimates of the values of the distribution functions at the observations are directly utilized in estimating QE. The linear instantaneous blind source separation (BSS) algorithm based on QE can separate signals with arbitrary continuous distributions.