Gram-Schmidt Orthonormalization to the Adaptive ICA Function for Fixing the Permutation Ambiguity

Yoshitatsu Matsuda, Kazunori Yamaguchi

Abstract: Recently, we have proposed a new objective function of ICA called the adaptive ICA function (AIF). AIF is a summation of weighted 4th-order statistics, where the weights are determined by adaptively estimated kurtoses. In this paper, the Gram-Schmidt orthonormalization is applied to the optimization of AIF. The proposed method is theoretically guaranteed to extract the independent components in the unique order of the degree of non-Gaussianity. Consequently, it enables us to fix the permutation ambiguity. Experimental results on blind image separation problems show the usefulness of the proposed method.