Why do we need deterministic measurement matrices in compressed sensing? I recently introduced myself into the field of CS, but I do not understand why some people try to find deterministic measurement matrices?
If I am correct, gaussian random matrices are very powerful with their properties. They are easy to create, their reconstruction power is very good (having a low RIP constant) and so on.
As far as I know there are two reasons:

In sensing part: For practical implementation, usage of random matrices
is hard, so people try to come up with simpler matrices that are fixed,
this is thought to be helpful for designing efficient hardware.
In reconstruction part: To find deterministic matrices which their
structure can be exploited for faster signal recovery. Using a
structured matrix, might pave the way for efficient recovery. The
goal is to achieving something like FFT for compressive recovery.