Objective Single- pixel imaging is an indirect imaging technique that uses only one detector element instead of an array of imaging sensors to acquire images. Compared to traditional methods, it offers better detection efficiency in scenarios with limited resources or specific environmental conditions. However, the sampling speed and image quality of current single- pixel imaging methods are insufficient for practical applications. To address this, improvements in sampling methods are needed to reduce time costs while obtaining high- quality images-specifically, optimizing the calibration and sampling strategy to enhance the speed of single- pixel imaging. Many research institutes and universities, both domestically and internationally, have investigated single- pixel imaging sampling and achieved significant results. After continuous innovation and optimization of the sampling method, the sampling rate has decreased under the same signal-to-noise ratio, and the sampling time has been markedly reduced. However, previous research has neglected the processing of non- essential coefficients. When focusing on sampling important regional information, concentrating solely on important coefficients can lead to sampling lag for local information within those regions. Prioritizing the sampling of important coefficients first, followed by non- essential coefficients, can help restore the important regions more completely. Based on this, we propose a new method to tackle these shortcomings and reduce the number of samples required for imaging while ensuring image quality. Methods The two-dimensional reflectance spatial distribution function of the target object is first converted into wavelet coefficients using the Haar wavelet transform, which reveals its energy distribution at different frequencies and scales. Initially, based on the information available about the measured target, each scale is assigned an orthorhombic diagonal diameter and subsequent sampling is performed within this orthorhombic area. In the pre-subsampling step, the number of subsamples is set for wavelet coefficients at each scale: the number of sampling points for low- scale coefficients (1st to 4th levels) is either minimal or sampled fully, while the number of high- scale coefficients (5th level and above) is reduced. Finally, random subsampling of the target object is performed. The wavelet coefficients collected through subsampling are first arranged according to the absolute values of their magnitudes, and the corresponding subsampling points are determined to guide subsequent sampling. Next, the remaining wavelet coefficients are sorted in terms of their sampling order. For each scale from the first to the eighth level, the subsampling coefficients are arranged by the absolute value, and sampling points are expanded accordingly. Repeated sampling points are skipped, and the remaining points are sampled to complete the process. All points are then sorted and organized to create a new sampling order for further sampling. In this paper, the peak signal-to-noise ratio (PSNR) of the reconstructed image using the proposed algorithmic sampling method is compared to that of the reconstructed image with standard sampling. The difference in PSNR values is used as the evaluation index. Results and Discussions The comparison of reconstructed PSNR differences shows that the proposed method significantly outperforms the orthogonal sampling one with the same number of samples (Figs. 5 and 8). The detail comparison figures for landscape and people images (Figs. 7 and 11) further illustrate that, with the same number of samples, the proposed method excels in image reconstruction, particularly in preserving detail. This method requires fewer samples to achieve reconstruction, which maintains the main features and structure of the original image while providing a clearer and more natural effect at the detail level. Consequently, it reduces the computational and storage resources needed and allows for more valuable data acquisition within the same timeframe. Our method notably boosts data acquisition efficiency, enabling effective and accurate data collection even with limited resources. Conclusions Single- pixel imaging can accurately reconstruct an image with a small amount of sampling data. We put forward a subsampling fast single- pixel imaging method based on sample reordering. It guides the subsequent sampling order by wavelet subsampling and devises an ordering strategy from the results of random subsampling at each image scale in the previous stage. Theoretical analysis and simulations show that, with the same number of samples, the proposed method considerably improves the signal-to-noise ratio and strengthens imaging efficiency. However, the method is highly dependent on pre-subsampling, which requires continual optimization. Future research should focus on mitigating the effects of pre-subsampling and exploring additional optimization strategies to strengthen the robustness and applicability of the method in real imaging scenarios.
