Time and frequency based sparse bounded component analysis algorithms for convolutive mixtures

•Time-based and frequency-based methods were proposed for sparse, bounded signals.•The methods don’t assume statistical independence in space, time or frequency domain.•An application for blind speech separation in a reverberant scene was studied.•The proposed algorithms outperform over some state of the art algorithms. In this paper, we introduce time-domain and frequency-domain versions of a new Blind Source Separation (BSS) approach to extract bounded magnitude sparse sources from convolutive mixtures. We derive algorithms by maximization of the proposed objective functions that are defined in a completely deterministic framework, and prove that global maximums of the objective functions yield perfect separation under suitable conditions. The derived algorithms can be applied to temporal or spatially dependent sources as well as independent sources. We provide experimental results to demonstrate some benefits of the approach, also including an application on blind speech separation.