Single-pixel imaging represents an emerging imaging technology that employs a single-point detector rather than traditional multi-pixel detectors to capture object images. The fundamental principle involves utilizing a spatial light modulator to generate sequential projection patterns with specific spatial structures onto the object. A single-pixel detector measures the corresponding scattered light intensity, and reconstruction algorithms recover the two-dimensional object image from these one-dimensional light intensity signals. Single-pixel imaging has attracted considerable attention due to its distinctive advantages. The technology offers a cost-effective and structurally simple alternative to conventional multi-pixel array systems, particularly beneficial for high-cost and harsh environmental imaging applications. Furthermore, single-pixel detectors demonstrate superior sensitivity, enabling enhanced imaging performance in extremely low light and scattering media conditions. However, the technology inherently trades temporal efficiency for spatial information, requiring numerous projection samples and resulting in extended imaging time. To address this limitation, researchers have implemented orthogonal projection bases and compressed sensing theories to reduce sampling requirements while preserving imaging quality. Consequently, a comprehensive analysis of different orthogonal bases' performance under undersampling conditions becomes essential.

This study examines single-pixel imaging performance utilizing different orthogonal bases under undersampling conditions, specifically analyzing the Laguerre-Gaussian (LG), Fourier, and Hadamard bases. Through comprehensive simulation and experimental validation, we evaluate the imaging quality, algorithm performance, and noise robustness of these methods across various undersampling rates. The study also examines the enhancement effects of the Tval3 compressed sensing algorithm on these three imaging methods. Additionally, we evaluate the imaging results at different distances and analyze the performance of Laguerre-Gaussian single-pixel imaging under varying beam waist radii. These comparative analyses aim to provide strategic insights for optimizing single-pixel imaging technology across diverse application scenarios.

This paper presents a comprehensive comparative analysis of imaging quality, algorithm performance, and noise robustness for Laguerre-Gaussian single-pixel imaging (LGSI), Fourier single-pixel imaging (FSI), and Hadamard single-pixel imaging (HSI) methods under undersampling conditions, supported by simulation and experimental data. The findings reveal that LGSI achieves superior central resolution despite reduced noise robustness. FSI and HSI maintain uniform resolution throughout their fields of view. Without the Tval3 compressed sensing algorithm, FSI demonstrates superior overall performance. Upon application of the Tval3 algorithm, HSI achieves comparable imaging quality to FSI while exhibiting enhanced robustness. The study analyzes the distinctions between pure amplitude LGSI and complex amplitude LGSI, examining the transmission characteristics of various LG interference fields through simulations and experiments (Figs. 3 and 20). Furthermore, we compare the imaging results of LGSI, FSI, and HSI methods at different distances. Experimental results demonstrate that complex amplitude LGSI achieves clear imaging at various distances without requiring physical focusing (Fig. 21). Analysis of varying beam waist radius effects on LGSI imaging reveals that this parameter provides flexible optimization between field of view and resolution according to specific imaging requirements (Fig. 22).

This paper presents a comparative analysis of imaging quality, algorithm performance, and noise robustness for LGSI, FSI, and HSI methods under undersampling conditions. Based on simulation and experimental data, the key findings are as follow. 1) Regarding imaging quality, LGSI’s field of view expands progressively with increasing sample numbers, achieving superior central resolution, particularly suitable for centrally focused objects. FSI and HSI maintain balanced image quality, appropriate for uniformly distributed content. Among these methods, HSI exhibits superior noise robustness, while LGSI demonstrates significant noise sensitivity. 2) Regarding algorithm performance, the Tval3 algorithm produces superior imaging results compared to Hadamard inverse transform and SOC algorithms, though its enhancement of FSI remains minimal. Without compressed sensing algorithms, inverse Fourier transform demonstrates favorable imaging performance. In noisy conditions, the Tval3 algorithm significantly enhances both HSI and FSI performance, with HSI showing the most substantial improvement, indicating strong robustness and recovery capability for high-noise images. However, under lower SNR conditions, Tval3 algorithm performance in LGSI remains inferior to the SOC method. 3) Regarding imaging flexibility, LGSI achieves clear images at various distances without precise physical focusing requirements, and enables balance between field of view and resolution through beam waist radius adjustment, offering enhanced flexibility and adaptability.