Single-pixel imaging of dynamic objects using multi-frame motion estimation

Single-pixel imaging (SPI) enables the visualization of objects with a single detector by using a sequence of spatially modulated illumination patterns. For natural images, the number of illumination patterns may be smaller than the number of pixels when compressed-sensing algorithms are used. Nonetheless, the sequential nature of the SPI measurement requires that the object remains static until the signals from all the required patterns have been collected. In this paper, we present a new approach to SPI that enables imaging scenarios in which the imaged object, or parts thereof, moves within the imaging plane during data acquisition. Our algorithms estimate the motion direction from inter-frame cross-correlations and incorporate it in the reconstruction model. Moreover, when the illumination pattern is cyclic, the motion may be estimated directly from the raw data, further increasing the numerical efficiency of the algorithm. A demonstration of our approach is presented for both numerically simulated and measured data.