Study On Joint Diagonalization In Blind Source Separation

Blind source separation (BSS) consists of recovering mutually independent(uncorrelated) but otherwise unavailable source signals only from their mixtureswithout a priori knowledge of the channel. On one hand, BSS methods restore thesource signals without lots of prior knowledge about them, which makes it a practicaltechnique in signal processing fields. On the other hand, due to the generality of BSSmodel most of the measurements fit this model quite well. Therefore, the BSS methodshave a broad application perspective. This dissertation focuses on the blind sourceseparation of linear mixtures, and we investigate the more efficient and robust blindsource separation method. The primary contributions in this dissertation aresummarized as follows.1. We investigated the adaptive online algorithms for blind source separation in thecontext of prewhitening. On one hand, equivariant source separation is a desiredproperty for most of BSS algorithms. To achieve this, we presented an adaptiverecursive least-squares (RLS) algorithm for blind source separation withequivariant property. The proposed algorithm has two benefits, firstly, it providesuniform separation performance; secondly, it easily links with the adaptivewhitening algorithms, which ultimately results in one step blind separation. On theother hand, to maintain the orthogonality of the separating matrix, we analyzed theoptimal solutions of the existing RLS algorithms based on the estimating functiontheory. We further pointed out the relationship between these optimal solutions.Through choosing a proper normalizer, we can hold the orthogonality of theseparating matrix at each iteration, which results in the robust convergencebehavior for the adaptive RLS algorithms.2. We investigated the batch off-online algorithms for BSS based on orthogonal joint(zero) diagonalization. On one hand, we proposed the concept of matrix powerconcentration. From this point of view, we presented an orthogonal jointdiagonalization algorithm based on bilateral Householder transform. Due to the useof unsymmetrical diagonalizers, the performance of the proposed algorithm doesnot degrade severely when the diagonal matrices which are used to produce targetmatrices are interfered by noise. On the other hand, we investigated the blindidentifiability of BSS algorithms via orthogonal joint diagonal zero diagonalization. The proposed identifiability conditions provide the theory foundation for BSSalgorithms. Moreover, we presented a joint diagonal zero diagonalization algorithmbased on dimension reduction Householder transform, which will yield betterperformance when we focus the BSS solution in time frequency domain.3. We investigated the batch algorithms for BSS based on nonorthogonal joint (zero)diagonalization. As is known that BSS algorithms using prewhitening usuallyperform robust, but may suffer from a serious loss of accuracy due to the introducedwhitening error. BSS algorithms based on nonorthogonal joint diagonalization canavoid the prewhitening process. Therefore, the separation performance will begreatly improved. The existing nonorthogonal joint diagonalization algorithmsusually have high computational load, we presented several efficient algorithmsbased on LU factorization and QR factorization to reduce the computational load ofnonorthogonal joint diagonalization. Moreover, to avoid the undesired solutions innonorthogonal joint zero diagonalization (JZD), we proposed an iterative algorithmfor nonorthogonal JZD. Compared with the existing iterative JZD algorithm, theproposed algorithm can avoid the singular solutions. While compared with thenoniterative JZD algorithm, the proposed algorithm requires much less targetmatrices to achieve the same (even better) separation performance.4. We investigated the batch algorithm for blind separation of linear convolutivemixtures of sources based on nonorthogonal joint block diagonalization (JBD)technique. The convolutive mixture model can be transformed to an instantaneousone by using proper delay structures, then the correlation matrix of the transformedsource vector has a block diagonal structure, which can be exploited to identify theseparating filters. Since the singular solutions may also occur in blockdiagonalization context, we presented a fast nonorthogonal JBD algorithm toeliminate the potential singular solutions. Simulation results show that the proposedalgorithm guarantees the complete separation of all the sources.