  Limited throughput is a key challenge in in-vivo deep-tissue imaging using
nonlinear optical microscopy. Point scanning multiphoton microscopy, the
current gold standard, is slow especially compared to the wide-field imaging
modalities used for optically cleared or thin specimens. We recently introduced
'De-scattering with Excitation Patterning or DEEP', as a widefield alternative
to point-scanning geometries. Using patterned multiphoton excitation, DEEP
encodes spatial information inside tissue before scattering. However, to
de-scatter at typical depths, hundreds of such patterned excitations are
needed. In this work, we present DEEP$^2$, a deep learning based model, that
can de-scatter images from just tens of patterned excitations instead of
hundreds. Consequently, we improve DEEP's throughput by almost an order of
magnitude. We demonstrate our method in multiple numerical and physical
experiments including in-vivo cortical vasculature imaging up to four
scattering lengths deep, in alive mice.
