Conventional imaging uses a set of lenses to form an image on the sensor plane. This pure hardware-based approach doesn't use any signal processing, nor the extra information in the time of arrival of photons to the sensor. Recently, modern compressive sensing techniques have been applied for lensless imaging. However, this computational approach tends to depend as much as possible on signal processing (for example, single pixel camera) and results in a long acquisition time. Here we propose using compressive ultrafast sensing for lensless imaging. We use extremely fast sensors (picosecond time resolution) to time tag photons as they arrive to an omnidirectional pixel. Thus, each measurement produces a time series where time is a function of the photon source location in the scene. This allows lensless imaging with significantly fewer measurements compared to regular single pixel imaging (33× less measurements in our experiments). To achieve this goal, we developed a framework for using ultrafast pixels with compressive sensing, including an algorithm for ideal sensor placement, and an algorithm for optimized active illumination patterns. We show that efficient lensless imaging is possible with ultrafast imaging and compressive sensing. This paves the way for novel imaging architectures, and remote sensing in extreme situations where imaging with a lens is not possible.

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