Efficient construction and comparison of Hadamard orderings for single-pixel imaging at large frame size

The Hadamard basis is widely used for single-pixel imaging due to its orthogonal and binary properties. To achieve rapid and efficient imaging, subsampling is commonly performed, which relies on the construction of various optimized matrix orderings. However, the complex construction and substantial memory consumption limit applications at large frame sizes. In this paper, a novel method is proposed for constructing Hadamard basis orderings based on the Gray code sequence, bypassing the need to generate huge complete Hadamard basis. A significant efficiency boost is achieved with a 1000-fold reduction in the time required to construct optimized orderings compared to existing methods. Furthermore, we conducted comprehensive comparisons of the performance of different orderings under large frame sizes through both simulations and experimental validations. Our approach not only simplifies the use of optimized orderings but also significantly improves sampling and reconstruction efficiency, especially for frame sizes of 256 × 256 and higher.