Analysis of cost function based on Kullback-Leibler divergence in independent component analysis for two uniformly distributed source signals

Independent component analysis plays a central role in blind source separation, leading to many applications of signal processing such as telecommunications, speech processing, and biomedical signal processing. Although the independent component analysis requires cost functions for evaluation of mutual independence of observed signals, little has been reported on theoretical investigation of the characteristics of such cost functions. In this paper, we mathematically analyze the cost function based on Kullback-Leibler divergence in independent component analysis. Our analysis proves that the cost function becomes unimodal when the number of source signals is two and both of the source signals have uniform distributions. In order to derive this result, we make use of whitening of observed signals and we describe the cost function in closed-form.