Untrained networks for compressive lensless photography

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.