Compressed Hermite–Gaussian differential single-pixel imaging

Traditional single-pixel imaging (SPI) encounters challenges such as high sampling redundancy and poor imaging quality, constraining its widespread application. Despite a range of orthogonal modulation modes have 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 acquired intensity. Both simulations and experiments confirm superior imaging quality and computation efficiency of proposed Hermite–Gaussian single-pixel imaging (HG-SI), especially at low-measurement levels. Moreover, we incorporate compressed sensing algorithms within the framework of HG-SI, integrating moments-based sampling strategies to optimize imaging capability under sparse measurements. Our research underscores the effectiveness of HG modulation in SPI reconstruction, enabling high-quality outcomes via compressed sampling. 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.