Fourier transform profilometry using single-pixel detection based on two-dimensional discrete cosine transform

•Fourier transform profilometry using single-pixel detection based on two-dimensional discrete cosine transform for obtaing three-dimensional (3D) maps was proposed.•A sparse sampling strategy was utilized to reduce the number of measurements.•Experiments of reconstructing 3D maps of simple or complex objects were performed, the minimum ratios of the number of measurements to the number of pixels of 3D maps for acceptable 3D reconstruction were explored.•3D maps obtained by the proposed approach were compared with those obtained with the current 3D reconstruction based on single-pixel imaging scheme.