Learnable foveated sampling and dual-prior reconstruction for single-pixel imaging

Single-pixel imaging (SPI) is a low-cost, high-sensitivity compressed sensing technique with broad application prospects. Most existing deep learning-based SPI reconstruction methods adopt a uniform sampling strategy. They fail to fully exploit the flexibly programmable nature of sampling patterns in SPI. Inspired by the high-resolution perception mechanism of the fovea in biological vision systems, we propose a deep network called FDP_Net. This network jointly optimizes foveated sampling and dual-prior reconstruction. First, we design a learnable foveal sampling module that adaptively performs high-resolution sampling on the image center region and low-resolution aggregated sampling on the periphery. Thus, under a limited total number of measurements, it equivalently increases the sampling rate of the center region. Second, we construct a deep unfolding reconstruction network with dual-prior fusion. It integrates a sparse prior module (SPM) and a denoising prior module (DPM) in a cascade manner. This enables more comprehensive capture of image texture and structure information. In addition, we introduce a center-weighted differential loss function. This loss function guides the network to prioritize the reconstruction quality of the region of interest. Experimental results show that our method achieves significantly better reconstruction accuracy in the image center region than mainstream comparison methods. Finally, we binarize the trained sampling matrix. The proposed method is successfully validated on a real single-photon counting SPI microscopy system.