Lensless imaging is an important and challenging problem. One notablesolution to lensless imaging is a single pixel camera which benefits from ideascentral to compressive sampling. However, traditional single pixel camerasrequire many illumination patterns which result in a long acquisition process.Here we present a method for lensless imaging based on compressive ultrafastsensing. Each sensor acquisition is encoded with a different illuminationpattern and produces a time series where time is a function of the photon'sorigin in the scene. Currently available hardware with picosecond timeresolution enables time tagging photons as they arrive to an omnidirectionalsensor. This allows lensless imaging with significantly fewer patterns comparedto regular single pixel imaging. To that end, we develop a framework fordesigning lensless imaging systems that use ultrafast detectors. We provide analgorithm for ideal sensor placement and an algorithm for optimized activeillumination patterns. We show that efficient lensless imaging is possible withultrafast measurement and compressive sensing. This paves the way for novelimaging architectures and remote sensing in extreme situations where imagingwith a lens is not possible.
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