  Compressive sensing can overcome the Nyquist criterion and record images with
a fraction of the usual number of measurements required. However, conventional
measurement bases are susceptible to diffraction and scattering, prevalent in
high-resolution microscopy. Here, we explore the random Morlet basis as an
optimal set for compressive multiphoton imaging, based on its ability to
minimise the space-frequency uncertainty. We implement this approach for the
newly developed method of wide-field multiphoton microscopy with single-pixel
detection (TRAFIX), which allows imaging through turbid media without
correction. The Morlet basis is well-suited to TRAFIX at depth, and promises a
route for rapid acquisition with low photodamage.
