Algorithms for blind source seperation/dimensionality reduction

I am trying to extract a low amplitude signal hidden in a high amplitude signal. (I don't know the true low amplitude signal but wan't to find the "best" approximation. Spectrums of the two signals overlap so I cannot just use a filter.

What techniques should I try? I have tried dimensionality reduction using PCA and SVC with OK results, but would like to obtain even better results (specifically I can see residue of the high amplitude signal in the frequency domain)

Thanks!