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

As a novel imaging paradigm, single-pixel imaging (SPI) has shown significant potential across various fields.However, intricate nonlinear reconstruction algorithms, such as compressive sensing or deep neural networks, are crucial to enable real-time imaging.In general, the former incurs substantial reconstruction time, and the latter often results in substantial energy consumption.Optical neural networks (ONNs) offer a promising alternative because of the intrinsic alignment between the sampling of SPI and the fully connected layers in ONNs.Nevertheless, achieving nonlinear reconstruction via ONNs remains a challenging task since the nonlinear activation functions still pose significant difficulties.Here, we propose an all-optical ONN architecture with controllable nonlinear order that mitigates the reliance of ONNs on nonlinear activation functions.Following the scheme of compressive SPI, we demonstrate the fitting capability of the structure by two linear tasks-compressive SPI and linear-edge extraction-and two nonlinear tasksnonlinear-edge extraction and handwritten dataset classification.Experimental results show that this structure has good fitting capabilities for both regression tasks and classification tasks, even with low order.