Single-pixel hyperspectral imaging (HSI) has received a lot of attention in recent years due to its advantages of high sensitivity, wide spectral ranges, low cost, and small sizes. In this article, we perform a single-pixel HSI experiment based on an untrained convolutional neural network (CNN) at an ultralow sampling rate, where the high-quality retrieved images of the target objects can be achieved by every visible wavelength of a light source from 432 nm to 680 nm. Specifically, we integrate the imaging physical model of single-pixel HSI into a randomly initialized CNN, which allows the images to be reconstructed by relying solely on the interaction between the imaging physical process and the neural network without pre-training the neural network.

In this paper, we propose a single-pixel imaging (SPI) method to achieve a higher-resolution image via the Hadamard transform matrix. Unlike traditional SPI schemes, this new method recovers images by correlating single-pixel signals with synchronized transformed patterns of Hadamard bases that are actually projected onto the digital micromirror device. Each transform pattern is obtained through the inverse Fourier transform of the pattern acquired by Gaussian filtering of each Hadamard basis in the frequency domain. The proposed scheme is based on a typical SPI experimental setup and doesn’t add any hardware complexity, enabling the transformation of Hadamard matrices and image reconstruction through data processing alone. Therefore, this approach could be considered as an alternative option for achieving fast SPI in a diffractionlimited imaging system, without the need for additional hardware.