The proposed project aims at development of existing methods of blind source separation and blind separation of convolutive mixtures that are important in biomedicine, acoustics and speech processing, and in wireless communications. It will extend previous results of the appplicants in this area. In particular, goals of the project include design of computationally effective methods of approximate joint diagonalization of sets of matrices, improved algorithms for estimation of mutual information of two or more random variables from their random realizations, design of algorithms of the blind separation that combine either non Gaussianity and nonstationarity or nonstationarity and spectral diversity to estimate the mixing mechanism. These methodswill be applied in novel methods for blind separation of convolutive mixtures of acoustic and speech signals, and for artifact removal in biomedical signals, namely in electroencephalogram.