Single-pixel imaging technology is a novel imaging technique based on the theory of compressive sensing. It has the ability to achieve high-quality image reconstruction while reducing the complexity and cost of imaging systems. It offers the advantages of wide spectral response, high sensitivity, and strong robustness, and reveals potential to be applied in the fields of medical imaging, non-destructive testing, and aerospace remote sensing. During the process of modulating structured light for single-pixel imaging, it is necessary to pre-design modulation masks. Among them, deterministic Hadamard masks have received widespread attention due to their excellent binary properties and ease of experimental implementation. To improve imaging speed and quality, many researchers have focused on sorting Hadamard masks in order to obtain reliable reconstructed images under the condition of undersampling.
Previous common methods for sorting Hadamard masks relied on the analysis of the characteristics of each mask, which was a complicated and inefficient process. Furthermore, as the order of Hadamard masks increased, the computational complexity of the mask sequences also increased dramatically. Directly sampling in the frequency domain is another mask sorting method that is much faster than analyzing masks' features. However, the sampling paths of this method are usually specific simple shapes, such as circular, square, and zigzag. In addition, by comparing the spectra of previous sorting methods, it was found that existing orders can be approximated by sampling from low to high frequencies. Such a sampling path can reconstruct more reliable images at low sampling rates. However, the absence of high-frequency components can lead to indistinguishable details, blurred edges, and ringing effect. Therefore, using the direct frequency-domain sampling to obtain mask sorting can reduce the complexity of order generation and improve sampling efficiency. The key issue is how to design an efficient, reasonable, and detail-enhancing sampling strategy.
The research group led by Prof. Qing Zhao and Assoc. Prof. Xu-Ri Yao from Beijing Institute of Technology presented an effective Hadamard sampling strategy. The core of this method is to obtain the energy distribution of Hadamard spectra for high-frequency and low-frequency information and balance their weights using a probability function to enhance image details, which is called the Hadamard SPI sampling strategy based on XY order and probability function (XY+PF). The research results are published in Chinese Optics Letters, Volume 21, No. 7, 2023 (Yan Cai, Shijian Li, Wei Zhang, Hao Wu, Xu-ri Yao, and Qing Zhao. A detail-enhanced sampling strategy in Hadamard single-pixel imaging[J]. Chinese Optics Letters, 2023, 21(7): 071101).
Fig.1 Hadamard pattern-selection strategy. (a) &(b) The sampling path of energy order and XY order. (c) Probability function graph at different sampling ratios. (d) Sampling diagram in the Hadamard spectral domain for our method (XY+PF).
The XY order exhibits good performance and an extremely short generation time which can generate a Hadamard patterns order of size 256 × 256 in only 0.445 s. An exponential function is used subsequently as the probability function to sample the XY order to obtain the required Hadamard patterns. This method avoids the complex process of analyzing each pattern and achieves a global pattern selection. Simulation and experimental results show that this method has the advantages of low complexity and high generation speed, and it improves the resolution of important details and edge structures based on reliable image reconstruction.
In future work, this sorting method can be applied in scenarios where the mask size needs to be continuously changed or when the computational hardware resources are limited. It can generate Hadamard orders within an extremely short time, thus improving imaging efficiency. Additionally, it may be essential to study the characteristics of Hadamard spectral energy distribution, which has potential applications in adaptive selecting the proportion of high-frequency or low-frequency information from a reconstructed image. This provides a feasible path for further research on improving and optimizing Hadamard mask sorting methods.
