On the Darmois-Skitovich Theorem and Spatial Independence in Blind Source Separation

Abstract

In many signal processing applications, one may come across the need to individually recover unobserved signals which are also combined in an unknown manner. This problem is widely known as blind source separation (BSS). One of the most prominent set of BSS techniques, known as independent component analysis (ICA), owes much of its development and theoretical understanding to the Darmois-Skitovich theorem. Although this theorem is implicitly used in BSS to establish source separability conditions in ICA, little emphasis is given in the literature to its derivation and to the interpretation of its consequences. The goal of this paper is to revisit, in a more intuitive manner, the Darmois-Skitovich theorem and its derivation in the BSS context.