Hartley‐Domain Parallel Single‐Pixel Imaging for Real‐Time 3D Shape Measurement: Breaking the Bottleneck of Data Volume and Computational Efficiency

ABSTRACT Recent parallel single‐pixel imaging (PSI) has emerged as a promising alternative to conventional structured‐light techniques in complex reflection and transmission scenarios. However, its real‐time measurement capability is severely restricted by the substantial data throughput and computational cost, hindering its practical deployment. To overcome this limitation, we propose a real‐time 3D measurement method based on Hartley‐domain parallel single‐pixel imaging (HPSI). This work enables, for the first time, the transition from offline reconstruction to online real‐time 3D imaging. Specifically, a real‐valued Hartley basis replaces Fourier modulation, which circumvents multi‐step phase shifting and reduces the number of projected patterns. A hybrid non‐uniform sampling strategy is then designed to produce an aperiodically enhanced light transport coefficient (LTC), facilitating fast global identification of the direct‐light component without epipolar‐assisted search for periodic‐replica disambiguation. In addition, a dual‐LTC 1D slice localization is developed, which reduces the search complexity from two‐dimensional global search to one‐dimensional profile analysis. Experiments show that HPSI maintains high accuracy under complex global illumination while slashing the acquisition data to only 21 patterns and reducing the computational complexity from quadratic to linear scale, showing great potential in online industrial inspection and dynamic biomedical imaging.