Efficient ordering of the Hadamard basis for single pixel imaging

Single-pixel imaging is a technique that can reconstruct an image of a scene by projecting a series of spatial patterns on an object and capturing the reflected light by a single photodetector. Since the introduction of the compressed sensing method, it has been possible to use random spatial patterns and reduce its number below the Nyquist-Shannon limit to form a good quality image but with lower spatial resolution. On the other hand, Hadamard pattern based methods can reconstruct large images by increasing the acquisition measurement time. Here, we propose an efficient strategy to order the Hadamard basis patterns from higher to lower relevance, and then to reconstruct an image at very low sampling rates of at least 8%. Our proposal is based on the construction of generalized basis vectors in two dimensions and then ordering in zigzag fashion. Simulation and experimental results show that the sampling rate, image quality and computational complexity of our method are competitive to the state of the art methods. (C) 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement