High-Order Contrasts for Self-Adaptive Source Separation

Abstract

SUMMARYThis paper is concerned with the problem of separating independent non-Gaussian sources. This is done by adaptively maximizing a contrast function based on fourth-order cumulants of the (mixed) observations. The first class of solutions involves a first stage where the signal vector is adaptively whitened. In order to implement in the second stage the proper separating task, new contrast functions are proposed, especially when all the source kurtosises have the same sign. These contrasts involve only self-cumulants of the outputs. The second class of solutions requires a single separating stage. However, the associated contrasts involve cross-cumulants in addition to self-cumulants. They essentially apply to correlated vectors with normalized powers (rather than to white vectors). The resulting adaptive one-stage and twostage systems achieve satisfactory separation performance independently of the statistics of sources and of the kind of linear mixture.

One-Bit-Matching Conjecture for Independent Component Analysis

“…Finally, we show that maximizing the weighted sum will recover the sources up to a permutation and sign indeterminacy. Meantime, as a by-product, we also show that the kurtosis maximization (Moreau & Macchi, 1996)-based ICA can be taken as a special case of the ICA based on equation 1.3.…”

A theoretical discussion on the foundation of Stone’s blind source separation

“…There exist many possible performance criterion in the literature [34][35][36]. The numerical manner that we have used for BSS performance evaluation is the index defined on the global matrix G [36].…”

“…The numerical manner that we have used for BSS performance evaluation is the index defined on the global matrix G [36]. The global matrix is obtained by multiplication of mixing and de-mixing matrices G = W A.…”

Blind source separation with unknown and dynamically changing number of source signals

“…In the process of updating B = DP A † , the initial separating matrix B(0) = 0.5I m×m , and φ i (y i ), i = 1, 2, · · ·, m takes the adaptive nonlinear function (16). The constants in (14) are carefully chosen as η 0 = 100T , t 0 = 400 and T d = 15T , respectively.…”