  Compressive lensless imagers enable novel applications in an extremely
compact device, requiring only a phase or amplitude mask placed close to the
sensor. They have been demonstrated for 2D and 3D microscopy, single-shot
video, and single-shot hyperspectral imaging; in each of these cases, a
compressive-sensing-based inverse problem is solved in order to recover a 3D
data-cube from a 2D measurement. Typically, this is accomplished using convex
optimization and hand-picked priors. Alternatively, deep learning-based
reconstruction methods offer the promise of better priors, but require many
thousands of ground truth training pairs, which can be difficult or impossible
to acquire. In this work, we propose the use of untrained networks for
compressive image recovery. Our approach does not require any labeled training
data, but instead uses the measurement itself to update the network weights. We
demonstrate our untrained approach on lensless compressive 2D imaging as well
as single-shot high-speed video recovery using the camera's rolling shutter,
and single-shot hyperspectral imaging. We provide simulation and experimental
verification, showing that our method results in improved image quality over
existing methods.
