Blind Separation Of Underdetermined Mixtures Of Sources

The goal of Blind Sources Separation (BSS) is to recover the original sources given only sensor observations that are unknown linear mixtures of the unobserved source signals. There are many potential exciting applications of blind sources separation in science and technology, especially in biomedical signal processing, wireless communication, audio and acoustics, image enhancement, sonar and radar systems; it has been one of the most active research areas in the modem signal processing. In the earlier research of the BSS, generally, most of the methods to BSS assume that the number of sources is known and the number of observed signals is not less than that of source signals. In practice, however, the number of the sources does not often hold and the number of mixing signals usually is less than that of sources. In this dissertation, we investigate the problem of underdetermined blind sources separation (UBSS) with an unknown source number, i.e. the number of observed signals is less than that of source signals. The primary contributions of the dissertation are summarized blow:1. Based on the sparse mixture models, a potential function method based on the Lapulacial potential function is proposed for UBSS. When the source signals are assumed to be sparse sufficiently, the number of sources and mixing matrix can be obtained by estimating the local maximum of the Lapulacial potential function. When the source signals are sparse insufficiently, the normal vectors of the concentration hyperplanes can be obtained by estimating the local maximum of the potential function, and then the number of sources and mixing matrix can be estimated by finding the intersection of the concentration hyperplanes. In order to increase the robustness to the noise and the outlier, the clustering algorithm is exploited to estimate the local maximum of the potential function instead of directly estimating the local maximum of the potential function.2. With unknown the number of sources, the Robust Competitive Agglomeration (RCA) algorithm is proposed to UBSS in the presence of noise. When the source signals are assumed to be sparse sufficiently, we can select the prototype parameters of clusters with larger cardinality as the estimation of mixing matrix's column vectors and then we can restructure the mixing matrix. The number of column of the estimated mixing matrix can be regarded as the estimated number of the source signals. When the source signals are sparse insufficiently, the RCA algorithm can be extended to estimate the normal vectors of the concentration hyperplanes, and then the number of sources and mixing matrix can be also estimated by finding the intersection of the concentration hyperplanes. 3. When the sources are nonnegative, a novel algorithm is proposed for over or well determined BSS based on the Nonnegative Matrix Factorization (NMF) methods with the least correlated component constraints. The algorithm relaxes the source independence assumption and has low-complexity algebraic computations, and thus is computationally efficient. The algorithm can be also used to blind separation of convolutive mixed sources.4. In generally, the problem of UBSS can not be solved by using the standard NMF methods. With the assumption of that the source signals are nonnegative and sparse; a tri-NMF algorithm is proposed to recover the source signals for UBSS. Based on the theory of Compressive Sampling (CS), the problem of NMF can be converted to a tri-NMF model. By incorporating the regularization and sparse penalty into the cost function, a novel multiplicative update rules is proposed to solve the problem of UBSS based on tri-NMF.