Single-pixel compressive imaging via single photon counting

Single-pixel compressive imaging reconstructs a target scene with many pixels by using a single-pixel detector to measure the power variations as small sequences of sampling patterns are applied. While it boasts remarkable capabilities, its practical applications remain a challenge in the photon-starved regime where signal-to-noise is low. To address this challenge, we propose to combine quantum parametric mode sorting (QPMS) and deep neural networks (DNN) to overcome low signal-to-noise for faithful image construction. We benchmark our approach in a telecom-LiDAR system against that using direct photon counting detection. Our results show that with only 25 sampling patterns (corresponding compression ratio ~0.043%), QPMS plus DNN give structural similarity index measure and peak signal-to-noise ratio on average above 22 dB and 0.9, respectively, much higher than those with direct detection (DD). The details of our targets from QPMS are more clearly compared with from DD. Notably, such high performance is sustained even in the presence of 500 times stronger in-band background noise, while DD fails. The high efficiency and robust noise rejection promise potential applications in various fields, especially in photon-starving scenarios.