Optimal compressive multiphoton imaging at depth using single-pixel detection

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. In this Letter, we explore the random Morlet basis as an optimal set for compressive multiphoton imaging, based on its ability to minimize the space-frequency uncertainty. We implement this approach for wide-field multiphoton microscopy with single-pixel detection, which allows imaging through turbid media without correction. The Morlet basis promises a route for rapid acquisition with lower photodamage.