Advanced Imaging, Volume. 2, Issue 3, 031003(2025)

Compressive single-pixel imaging with low-order nonlinear neural networks

Huaijian Chen, Xiao Wang, Botao Hu, Aiping Fang, Ruifeng Liu*, Pei Zhang*, and Fuli Li
Author Affiliations
  • Ministry of Education Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi’an Jiaotong University, Xi’an, China
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    Figures & Tables(4)
    Schematic of the experimental setup and reconstruction principle. (a) Schematic diagram of the experimental setup. An incoherent light source illuminates the object, which is then imaged onto the DMD surface with L1. Once modulated by patterns loaded on the DMD, the total intensity of the modulated light field is captured by a single-pixel detector. (b) The first fully connected layer that corresponds to the physical process of SPI. (c) The 1st-order PNN structure is chosen as the reconstruction algorithm of two linear tasks: compressive single-pixel imaging and linear-edge extraction. (d), (e) Simulation results of two linear tasks with a sampling ratio of 6.25%. (f) The 2nd-order PNN is selected as the reconstruction algorithm of two nonlinear tasks: nonlinear-edge extraction and handwritten dataset classification; the symbol * denotes the Hadamard product. (g), (h) Simulation results of two nonlinear tasks with a sampling ratio of 6.25%, and the classification accuracy is 98.03%. L1, lens 1; L2, lens 2; DMD, digital micromirror device.
    Experimental results of three regression tasks. For each task, images in the first row represent the experimental results, and the second-row images are the full-sampling results of Hadamard patterns undergoing respective mathematical processing defined in the Supplement 1. The sampling rate for all tasks is 6.25%. The lower right corner of reconstructed images shows the PSNR and SSIM, respectively.
    Experimental results of classification task. The confusion matrix of handwritten dataset classification has an accuracy rate of 99%.
    Quantitative assessment of the robustness of different-order PNNs with four CSPI tasks and β=6.25%. Three types of random noise are dynamically added to the measurements z (the input of PNN) during the training process, and the respective ranges are 0, 3%, and 6% of the standard deviation of z. (a)–(c) present the simulation results regarding the robustness of three regression tasks, while the corresponding results for the classification task are displayed in (d). The shaded bands represent the reconstruction standard deviations at different noise levels.
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    Huaijian Chen, Xiao Wang, Botao Hu, Aiping Fang, Ruifeng Liu, Pei Zhang, Fuli Li, "Compressive single-pixel imaging with low-order nonlinear neural networks," Adv. Imaging 2, 031003 (2025)

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    Paper Information

    Category: Research Article

    Received: Apr. 7, 2025

    Accepted: May. 29, 2025

    Published Online: Jun. 30, 2025

    The Author Email: Ruifeng Liu (ruifeng.liu@mail.xjtu.edu.cn), Pei Zhang (zhang.pei@mail.xjtu.edu.cn)

    DOI:10.3788/AI.2025.10007

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