I am new to Signal Processing, and am interested in compression sensing for audio files. CS is based on the algorithm that, given some sampling of a signal $f$ in order to obtain a smaller (compressed) signal $b$ such that:
$$b = \phi f$$ such that $$f = \Psi c$$
and $f$ can be expressed by a linear combination of basis functions $\Psi$ and its coefficients $c$ by doing a nonlinear constrained optimization on the L1 norm of such that :
$$\phi f = b$$
I understand how $f$ can be extracted from a sample without reaching the Nyquist limit, but I'm interested in the application of Compressed Sensing to blind source separation. With blind source seapration, to use standard notation
$$A = \phi\Psi , c = x $$
Thus, L1 norm minization can be represented as
$$Ax = b$$ I have looked at Cleve Moler - Magic Reconstruction: Compressed Sensing for an example How can we adapt compressed sensing when we don't know A (since the whole point of BSS is that you do not know the mixing matrix) and we have to reconstruct more than one signal from b?