Compressed data separation via dual frames based split-analysis with Weibull matrices

In this paper, we consider data separation problem, where the original signal is composed of two distinct subcomponents, via dual frames based Split-analysis approach. We show that the two distinct subcomponents, which are sparse in two different general frames respectively, can be exactly recovered with high probability, when the measurement matrix is a Weibull random matrix (not Gaussian) and the two frames satisfy a mutual coherence property. Our result may be significant for analysing Split-analysis model for data separation.