  We implement a compressive quantum state tomography capable of reconstructing
any arbitrary low-rank spectral-temporal optical signal with extremely few
measurement settings and without any \emph{ad hoc} assumptions about the
initially unknown signal. This is carried out with a quantum pulse gate, a
device that flexibly implements projections onto arbitrary user-specified
optical modes. We present conclusive experimental results for both temporal
pulsed modes and frequency bins, which showcase the versatility of our
randomized compressive method and thereby introduce a universal optical
reconstruction framework to these platforms.
