Contrast functions for deterministic blind source separation

Blind source separation (BSS) is often carried out under the assumption that sources are statistically mutually independent, at least in the sense of cumulants of given order. However, this assumption is not mandatory, and can be replaced by some assumption on the source distribution, even if all sources are identically distributed. Contrast functions are optimization criteria that satisfy some identifiability conditions. We define a distance to any discrete constellation, and prove that this family of criteria indeed defines contrast functions. The advantage of such criteria is that they are deterministic, and do not involve the estimation of sample statistics, such as moments or cumulants, hence they have a potentially shorter convergence time.