A Study of the Effect of Source Sparsity for Various Transforms on Blind Audio Source Separation Performance

In this paper, the problem of blind separation of underdetermined noisy mixtures of audio sources is considered. The sources are assumed to be sparsely represented in a transform domain. The sparsity of their analysis coefficients is modelled by the Student t distribution. This prior allows for robust Bayesian estimation of the sources, the mixing matrix, the additive noise variance as well as hyperparameters of the Student t priors, using a Gibbs sampler (a standard Monte Carlo Markov Chain simulation method). The performances resulting from the use of various transforms, orthonormal as well as overcomplete, are compared. More precisely, we present extensive separation results of 2× 3 mixtures of various sets of sources (speech, musical and percussion sources) using various orthonormal transforms Discrete Cosine Transform (DCT), Modified Discrete Cosine Transform (MDCT), Discrete Wavelet Transforms (DWT), and overcomplete transforms Short-Time Discrete Cosine Transform (STDCT) and union of MDCT and DWT. In general, the MDCT is found to be a good transform to use on the various types of audio signals. However, the DWT is the best transform to use on the percussion signals as they contain more transients than tonals. The provided results show that the separation performance is indeed correlated to the sparsity of the analysis coefficients of the sources in the transform domain. Our results also show that the use of overcomplete transforms does not lead to significant improvement in performance, because they fail to improve the sparsity measure.