Compressed Hermite–Gaussian differential single-pixel imaging

In contrast to the array detector, the single-pixel detector (SD) has a range of advantages, including heightened quantum efficiency, attenuated dark noise, and expedited response time. These advantages engender the extensive utility of single-pixel imaging (SPI) within numerous imaging fields. Traditional single-pixel imaging (SPI) encounters challenges such as a high sampling redundancy and poor imaging quality, constraining its widespread application. Despite a range of orthogonal modulation modes having been employed in structured illumination to enhance imaging performance, some encoding issues still persist in information sampling, impeding the further progression of SPI. We propose an SPI method based on orthogonal Hermite–Gaussian (HG) moments, achieving improved imaging reconstruction through differential modulation of HG basis patterns and linear weighting of the acquired intensity. Moreover, we incorporate compressed sensing algorithms within the framework of HG-SI, integrating moment-based sampling strategies to optimize imaging capability under sparse measurements.

Both simulations and experiments confirm the superior imaging quality and computation efficiency of our proposed Hermite–Gaussian single-pixel imaging (HG-SI), especially at low measurement levels. Our research underscores the effectiveness of HG modulation in SPI reconstruction, enabling high-quality outcomes via compressed sampling. Our method entails no additional setups or constraints compared to other SPI modes, making it applicable to a wide range of SPI scenarios. This advancement propels the investigation of optical field modulation modes within SPI and holds promise in offering a universal solution for weak-intensity and non-visible light microscopy.