Abstract
Compressed sensing has been discussed separately in spatial and temporal domains. Compressive holography has been introduced as a method that allows 3D tomographic reconstruction at different depths from a single 2D image. Coded exposure is a temporal compressed sensing method for high speed video acquisition. In this work, we combine compressive holography and coded exposure techniques and extend the discussion to 4D reconstruction in space and time from one coded captured image. In our prototype, digital in-line holography was used for imaging macroscopic, fast moving objects. The pixel-wise temporal modulation was implemented by a digital micromirror device.
Our work exploits both spatial and temporal redundancy in natural scenes and generalizes to a 4D (3D positon with time) system model. We show that by combining digital holography and coded exposure techniques using a CS framework, it is feasible to reconstruct a 4D moving scene from a single 2D hologram. We demonstrate a temporal super resolution of 10×. Note that this increase in frame rate can be achieved for any sensor, regardless of the native frame rate, as long as the spatial-temporal modulator operates at a higher frame rate. We anticipate approximately 1 cm resolution with optical sectioning. As a test case, we focus on macroscopic scenes exhibiting fast motion of small objects (vibrating bars or small particles, etc.).