Single pixel imaging via unsupervised deep compressive sensing with collaborative sparsity in discretized feature space

Single-pixel imaging (SPI) enables the use of advanced detector technologies to provide a potentially low-cost solution for sensing beyond the visible spectrum and has received increasing attentions recently. However, when it comes to sub-Nyquist sampling, the spectrum truncation and spectrum discretization effects significantly challenge the traditional SPI pipeline due to the lack of sufficient sparsity. In this work, a deep compressive sensing (CS) framework is built to conduct image reconstructions in classical SPIs, where a novel compression network is proposed to enable collaborative sparsity in discretized feature space while remaining excellent coherence with the sensing basis as per CS conditions. To alleviate the underlying limitations in an end-to-end supervised training, for example, the network typically needs to be re-trained as the basis patterns, sampling ratios and so on. change, the network is trained in an unsupervised fashion with no sensing physics involved. Validation experiments are performed both numerically and physically by comparing with traditional and cutting-edge SPI reconstruction methods. Particularly, fluorescence imaging is pioneered to preliminarily examine the in vivo biodistributions. Results show that the proposed method maintains comparable image fidelity to a sCMOS camera even at a sampling ratio down to 4%, while remaining the advantages inherent in SPI. The proposed technique maintains the unsupervised and self-contained properties that highly facilitate the downstream applications in the field of compressive imaging.