A Zigzag Scanning Ordering of Four-Dimensional Walsh Basis for Single-Pixel Imaging

There is a fast imaging method to obtain high-quality reconstruction results, which is named Hadamard transform single-pixel imaging. It is known that the object is sampled and reconstructed through forward and inverse transformation respectively. However, the imaging effect is not ideal in the case of incomplete sampling, because the distribution of the key coefficients of Hadamard transform is not centralized. In this study, we proposed a single-pixel imaging of four-dimensional Walsh vector transform scheme based on zigzag scanning order. Key coefficients are available preferentially because of the four-dimensional Walsh vector transform with the characteristics of energy concentration. Based on the numerical simulations and experimental results, this method can produce clear reconstruction images, even if the number of sampling accounts for 20% of the complete sampling. In our work, the possibility of minimizing sampling times was provided without prior knowledge, which may play an important role in real-time video imaging.