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 here 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? Thank you for your help!