Super Sub-Nyquist Single-Pixel Imaging by Total Variation Ascending Ordering of the Hadamard Basis

Single pixel imaging (SPI) captures images without array detectors or raster scanning. When combined with compressive sensing techniques it enables novel solutions for high-speed optical imaging and spectroscopy. However, when it comes to the real-time capture and analysis of a fast event, the challenge is the inherent trade-off between frame rate and image resolution. Due to the lack of sufficient sparsity and the intrinsic iterative process, conventional compressed sensing techniques have limited improvement in capturing natural scenes and displaying the images in real time. In this work, we demonstrate a novel alternative compressive imaging approach employing an efficient and easy-implementation sampling scheme based on reordering the deterministic Hadamard basis through their total variation. By this means, the number of measurements and acquisition are reduced significantly without needing complex minimization algorithms. We can recover a 128 × 128 image with a sampling ratio of 5% at the signal peak signal-to-noise ratio (PSNR) of 23.8 dB, achieving super sub-Nyquist sampling SPI. Compared to other widely used sampling e.g. standard Hadamard protocols and Gaussian matrix methods, this approach results in a significant improvement both in the compression ratio and image reconstruction quality, enabling SPI for high frame rate imaging or video applications.