Single-pixel imaging (SPI) uses a single-pixel detector instead of a detector array with a lot of pixels in traditional imaging techniques to realize two-dimensional or even multi-dimensional imaging. For SPI using compressed sensing, the target to be imaged is illuminated by a series of patterns with spatial resolution, and then the reflected or transmitted intensity is compressively sampled by the single-pixel detector to reconstruct the target image while breaking the limitation of the Nyquist sampling theorem. Recently, in the area of signal processing using compressed sensing, many measurement matrices as well as reconstruction algorithms have been proposed. It is necessary to explore the application of these methods in SPI. Therefore, this paper reviews the concept of compressive sensing SPI and summarizes the main measurement matrices and reconstruction algorithms in compressive sensing. Further, the performance of their applications in SPI through simulations and experiments is explored in detail, and then their advantages and disadvantages are summarized. Finally, the prospect of compressive sensing with SPI is discussed.

Wavefront single‐pixel imaging (WSPI) has emerged as a promising approach for simultaneous amplitude and phase reconstruction, especially in spectral wavebands where cameras are immature or even unavailable. However, conventional WSPIs suffer from limited imaging speed & range, and heavy pattern‐data storage. Here, we demonstrate a wavefront line‐scan imaging (WLSI) technique that integrates 1D spatial light modulation with single‐pixel detection, enabling faster imaging in a large rectangular range with minimal pattern‐data storage. A theoretical model is developed and validated by simulations and experiments. A digital micromirror device (DMD) worked in 1D, achieving a modulation rate of 90.9 kHz, enabling line‐scan imaging at 2.8 ms per line without compressive down‐sampling. Consequently, the WLSI achieves over 4‐fold enhancement in imaging speed and significantly reduces the pattern‐data storage to more than 5 orders of magnitude as compared to the WSPI, when reconstructing a wavefront of 256 × 256 pixels at full sampling. The push‐broom WLSI extends the imaging range, enabling continuous acquisition in a long rectangular range. Combining the advantages of WSPI with the flexibility of line‐scan imaging, we offer a potential solution for high‐throughput amplitude and phase imaging of biological samples, defect detection of optical components, wavefront detection in special spectra, etc.