Source separation arises in a variety of signal processing applications, ranging from speech processing to medical image analysis. The separation of a superposition of multiple signals is accomplished by taking into account the structure of the mixing process and by making assumptions about the sources. When the information about the mixing process and sources is limited, the problem is called ''blind'. By assuming that the sources can be represented sparsely in a given basis, recent research has demonstrated that solutions to previously problematic blind source separation problems can be obtained. In some cases, solutions are possible to problems intractable by previous non-sparse methods. Indeed, sparse methods provide a powerful approach to the separation of linear mixtures of independent data. This paper surveys the recent arrival of sparse blind source separation methods and the previously existing nonsparse methods, providing insights and appropriate hooks into theliterature along the way.

Discovering a representation that allows auditory data to be parsimoniously represented is useful for many machine learning and signal processing tasks. Such a representation can be constructed by Non-negative Matrix Factorisation (NMF), a method for finding parts-based representations of non-negative data. Here, we present an extension to convolutive NMF that includes a sparseness constraint, where the resultant algorithm has multiplicative updates and utilises the beta divergence as its reconstruction objective. In combination with a spectral magnitude transform of speech, this method discovers auditory objects that resemble speech phones along with their associated sparse activation patterns. We use these in a supervised separation scheme for monophonic mixtures, finding improved separation performance in comparison to classic convolutive NMF.

Discovering a representation which allows auditory data to be parsimoniously represented is useful for many machine learning and signal processing tasks. Such a representation can be constructed by Non-negative Matrix Factorisation (NMF), a method for finding parts-based representations of non-negative data. We present an extension to NMF that is convolutive and includes a sparseness constraint. In combination with a spectral magnitude transform, this method discovers auditory objects and their associated sparse activation patterns.

Abstract. Robust clustering of data into overlapping linear subspaces is a common problem. Here we consider one-dimensional subspaces that cross the origin. This problem arises in blind source separation, where the subspaces correspond directly to columns of a mixing matrix. We present an algorithm that identifies these subspaces using an EM procedure, where the E-step calculates posterior probabilities assigning data points to lines and M-step repositions the lines to match the points assigned to them. This method, combined with a transformation into a sparse domain and an L1-norm optimisation, constitutes a blind source separation algorithm for the under-determined case.

Robust clustering of data into linear subspaces is a common problem. Here we treat clustering into one-dimensional subspaces that cross the origin. This problem arises in blind source separation, where the subspaces correspond directly to columns of a mixing matrix. We present an algorithm that identifies these subspaces using a modified k-means procedure, where line orientations and distances from a line replace the cluster centres and distance from cluster centres of conventional k-means. This method, combined with a transformation into a sparse domain and an L1-norm optimisation, constitutes a blind source separation algorithm for the under-determined case.