Flexible multichannel blind deconvolution, an investigation

In this paper, we consider the issue of devising a flexible nonlinear function for multichannel blind deconvolution. In particular, we consider the underlying assumption of the source probability density functions. We consider two cases, when the source probability density functions are assumed to be uni-modal, and multimodal respectively. In the unimodal case, there are two approaches: Pearson function and generalized exponential function. In the multimodal case, there are three approaches: mixture of Gaussian functions, mixture of Pearson functions, and mixture of generalized exponential functions. It is demonstrated through an illustrating example that the assumption on the source probability density functions gives rise to different performances of source separation algorithms for the multichannel blind deconvolution problem. Further it is observed that these performance differences are not large, indicating that the current formulation of multichannel blind deconvolution problems is robust with respect to the underlying assumption of source probability density functions. It is further speculated that one of the discriminating features among various source separation algorithms appears to be the relative computational efficiencies of various approximation schemes. In other words, the discriminating feature of various source separation algorithms based on assumptions on the source probability density function appears to be an implementation issue rather than one of a theoretical concern.