Single-pixel imaging of a randomly moving object.

Single-pixel imaging enjoys advantages of low budget, broad spectrum, and high imaging speed. However, existing methods cannot clearly reconstruct the object that is fast rotating or randomly moving. In this work, we put forward an effective method to image a randomly moving object based on geometric moment analysis. To the best of our knowledge, this is the first work that reconstructs the shape and motion state of the target without prior knowledge of the speed or position. By using the cake-cutting order Hadamard illumination patterns and low-order geometric moment patterns, we obtain a high-quality video stream of the target which moves at high and varying translational and rotational speeds. The efficient method as verified by simulation and experimental results has great potential for practical applications such as Brownian motion microscopy and remote sensing.