I have a mixed discrete signal $$ A(t_i) = [s(t_i) + a f(t_i+\delta)] \circ g(t_i) $$ for n number of temporal points where $s(t_i)$, $a$, $\delta$ are unknown. $\circ g(t)$ is a convolution, where the shape of $g(t)$ is known, e.g., $g(t)$ is a Gaussian with unknown FWHM. $f(t_i)$ is known. $s(t_i)$ and $f(t_i)$ has Poisson noise.
I have done introductory readings on PCA and ICA and I think ICA techniques can be implemented for this problem. However, given that there is a lot of approaches to ICA geared for different scenarios I am not sure exactly which ICA is best suited for my case. What is the best (ICA or similar) approach to recover the unknown signal $s(t_i) \circ g(t_i)$?