Despite offering high sensitivity, a high signal-to-noise ratio, and a broad spectral range, single-pixel imaging (SPI) is limited by low measurement efficiency and long data-acquisition times. To address this, we propose a wavelength-multiplexed, spatially incoherent diffractive optical processor combined with a compact/shallow digital artificial neural network (ANN) to implement compressive SPI. Specifically, we model the bucket detection process in conventional SPI as a linear intensity transformation with spatially and spectrally varying point-spread functions. This transformation matrix is treated as a learnable parameter and jointly optimized with a shallow digital ANN composed of 2 hidden nonlinear layers. The wavelength-multiplexed diffractive processor is then configured via data-free optimization to approximate this pre-trained transformation matrix; after this optimization, the diffractive processor remains static/fixed. Upon multi-wavelength illumination and diffractive modulation, the target spatial information of the input object is spectrally encoded. A single-pixel detector captures the output spectral power at each illumination band, which is then rapidly decoded by the jointly trained digital ANN to reconstruct the input image. In addition to our numerical analyses demonstrating the feasibility of this approach, we experimentally validated its proof-of-concept using an array of light-emitting diodes (LEDs). Overall, this work demonstrates a computational imaging framework for compressive SPI that can be useful in applications such as biomedical imaging, autonomous devices, and remote sensing.

翻译：尽管单像素成像（SPI）具有高灵敏度、高信噪比和宽光谱范围等优势，但其测量效率低且数据采集时间长。为解决这一问题，我们提出一种波长复用、空间非相干的衍射光学处理器，结合紧凑/浅层数字人工神经网络（ANN），以实现压缩式SPI。具体而言，我们将传统SPI中的桶探测过程建模为具有空间和光谱变化点扩散函数的线性强度变换。该变换矩阵被视为可学习参数，并与包含2个隐藏非线性层的浅层数字ANN联合优化。随后，通过无数据优化配置波长复用衍射处理器，以逼近该预训练变换矩阵；优化完成后，衍射处理器保持静态/固定。在多波长照明和衍射调制下，输入物体的目标空间信息被光谱编码。单像素探测器捕获每个照明波段输出的光谱功率，然后由联合训练的数字ANN快速解码以重建输入图像。除数值分析证明该方法的可行性外，我们使用发光二极管（LED）阵列进行了概念验证实验。总体而言，本研究提出了一种适用于压缩SPI的计算成像框架，可应用于生物医学成像、自主设备和遥感等领域。