Efficient spectral single-pixel imaging via Morton frequency-domain scanning [Invited]

Single-pixel imaging (SPI) captures two-dimensional images utilizing a sequence of modulation patterns and measurements recorded by a single-pixel detector. However, the sequential measurement of a scene is time-consuming, especially for high-spatial-resolution imaging. Furthermore, for spectral SPI, the enormous data storage and processing time requirements substantially diminish imaging efficiency. To reduce the required number of patterns, we propose a strategy by optimizing a Hadamard pattern sequence via Morton frequency domain scanning to enhance the quality of a reconstructed spectral cube at low sampling rates. Additionally, we expedite spectral cube reconstruction, eliminating the necessity for a large Hadamard matrix. We demonstrate the effectiveness of our approach through both simulation and experiment, achieving sub-Nyquist sampling of a three-dimensional spectral cube with a spatial resolution of 256 × 256 pixels and 181 spectral bands and a reduction in reconstruction time by four orders of magnitude. Consequently, our method offers an efficient solution for compressed spectral imaging.