Spatial frequency characteristics of single-pixel imaging and correlative-manipulation filtering

The understanding of single-pixel imaging has long been confined to the spatial domain, lacking a description of its spatial frequency characteristics. This leads to an unclear relationship between patterns and the reconstructed image, which prevents active manipulation of the reconstructed image by controlling the patterns, thus limiting its function to passive imaging and hindering its expansion into active manipulation. To this end, we derive the formalism of single-pixel imaging in the spatial frequency domain, establish its optical transfer function, and propose the concept of correlative-manipulation, i.e., the modulation can be transferred from patterns to the reconstructed image. The experimental results show that the slit filtering based on correlative-manipulation exhibits good performance, demonstrating the transfer characteristic of correlative-manipulation. Such characteristic enables manipulation of the reconstructed image by modulating patterns, meaning that various transformations of the reconstructed image only require one single-pixel measurement, laying a solid foundation for extending single-pixel imaging toward manipulation-based applications.