Single pixel imaging is a new imaging technique which is able to obtain imaging information through a single pixel detector. Compared with the traditional array detection imaging techniques, single pixel imaging has the advantages of high sensitivity and anti-interference ability, and has broad application prospects in many fields. Various modulation schemes and reconstruction algorithms for single pixel imaging have been proposed for all kinds of scenario. However, the defect of large time consumption in the modulation and reconstruction process detracts single pixel imaging from practical applications. Recently, many strategies have been proposed to address this problem from the aspects of modulation and reconstruction. The comparison of different modulation schemes and algorithms in various aspects can establish guidelines for practical single pixel imaging.

The single pixel imaging uses a single pixel detector to record the light intensities of the scene illuminated by a sequence of resolved patterns. The spatial information of the scene can be recovered from correlation of the sequential measurements and patterns. The different choice of modulation and algorithms exerts influence on the final imaging result. For modulation devices, liquid crystal spatial light modulator (LC-SLM), digital micromirror device (DMD) and light-emitting diode (LED) array are mainly introduced. Five metrics including programmable, modulation speed, structured detection, grayscale modulation and price are introduced to compare the performance of different popular devices. The pros and cons of different devices are detailed. For sampling schemes, random patterns, Hadamard patterns, Fourier patterns and wavelet patterns are introduced. A simulation is performed to compare the sampling efficiencies of different sampling schemes. For reconstruction algorithms, three categories of algorithms, i.e., non-iterative algorithms, iterative algorithms and deep learning-based algorithms are introduced. Five metrics including running speed, undersampling, applicability, robustness and reconstruction are introduced to compare the performance of different popular reconstruction algorithms for single pixel imaging.

For modulation devices, DMD is the most popular one and outperforms other devices due to its fast modulation speed and programmable characteristics. However, only grayscale patterns can be loaded on DMD and the modulation speed can still be improved further. LC-SLM is an alternative to DMD, taking the advantages of price and ability of grayscale modulation. However, the modulation speed of LC-SLM limits its practical application. LED arrays provide cheaper price and faster modulation speed, so it is a better choice in the future.

For sampling schemes, a simulation is performed to compare the performance of different sampling bases under different sampling rates (Fig. 4). The numerical metric shows that Fourier basis performs the best under all sampling rates. Hadamard basis outperforms wavelet basis under high sampling rates while wavelet basis is better under low sampling rates. Random pattern performs the worst since it is not an orthogonal sampling basis.

For reconstruction algorithms, there exists a trade-off between the non-iterative, iterative and deep leaning-based algorithms. The performances of different algorithms are compared (Fig. 5). Non-iterative algorithms require less computation compared with other algorithms, but the reconstruction quality and robustness are the worst. Iterative algorithms recover good quality of image, even in a low sampling rate. The deep learning-based algorithms require tremendous training dataset and training time in advance, so that in reconstruction, the running speed and reconstruction quality of deep learning-based algorithms are the best.

In this paper, the history and principle of single pixel imaging are briefly reviewed. Different modulation devices, sampling strategies and reconstruction algorithms are compared in different aspects. The performances of different strategies are analyzed and compared in detail. Finally, the future development and application of single pixel imaging are discussed. Our work shows that the optimal combination of modulation schemes, sampling strategies and reconstruction algorithms should be analyzed and selected to achieve perfect and efficient imaging.