A semi-blind EM algorithm for overcomplete ICA

Overcomplete independent component analysis (ICA) is a challenge of ICA to estimate more sources from less mixtures. The statistical properties of the sources such as sparsity are often assumed to solve the problem. Other available information about the sources such as waveform, however, is scarcely used. Motivated by the fact that semi-blind ICA in complete case can improve the potential of ICA by incorporating source information, this paper proposes a semi-blind algorithm for overcomplete ICA by explicitly utilizing waveform information about some sources. An approximate expectation-maximization (EM) algorithm is explored to provide normal cost function of the semi-blind algorithm while the prior information is utilized to form an extended one. Computer simulations results demonstrate that the proposed algorithm has much improved performance in SNR, convergence speed, and elimination of order ambiguity compared to the original EM algorithm.