Joint Diagonalization Learning Algorithm for Nonlinear Blind Source Separation

Recovering independent source signals from their nonlinear mixtures is a very important issue in many fields. Joint approximate diagonalization of eigenmatrices (JADE) is an efficient method which utilizes fourth-order cumulants of signals. However it cannot deal with nonlinear problem. This paper proposes a robust radial basis function network (RBFN) approach by using higher-order cumulants when observations are suffered from noise and nonlinear distortion. The higherorder cumulants can measure the departure of a random vector from a Gaussian random vector for extracting the nonGaussian part of a signal. The proposed method can efficiently recover the nonlinearly mixed signals suffered high-level noise simultaneously. The proposed method is divided into two steps. First, the radial basis function helps us to transform the mixed signals to high-dimensional space. Then in the second step, we can linearly separate the mixtures in the high-dimensional space by jointing approximate diagonalization of eigenmatrics. We consider artificial signal and acoustic signal separation and denoising applications. Furthermore, a comparison between the traditional RBF-based method, original JADE and proposed algorithm is produced, from which we can see the proposed algorithm is more suitable and applicable for unsupervised nonlinear signal denoising problem.