Conclusions

We presented an algorithm to invert the nonlinearities in the problem of post-nonlinear underdetermined BSS of sparse sources. The algorithm consists of two steps: firstly, a spectral clustering algorithm is applied to identify the active sources and secondly a set of MLPs are trained to identify the inverse nonlinearity. After these two steps, the outputs of the MLPs provide a ``linearized'' underdetermined BSS problem, which can easily be solved.

The presented method requires sparse sources and invertible nonlinearities that are linear for small input values. Simulation results were included for 2-measurement and 3-measurement cases, and as long as the contributions of the different sources do not overlap in the mixtures, there is no restriction on the number of sources or mixtures.