Optical sensing and metrology are vital across various applications, from biomedical and environmental monitoring to manufacturing and autonomous driving. While traditional systems are often bulky and expensive, single-pixel compressive sensing offers a cost-effective, mechanically flexible alternative with advantages in size, weight, and power. Its applications extend to terahertz and short-wave infrared imaging, optical microscopy, imaging through scattering media, and three-dimensional sensing. Active optical compressive sensing employs an encoded laser beam to illuminate the target, capturing the back-reflected signal with a single-pixel detector. Encoding patterns, such as random or structured patterns (Fourier transform bases, Hadamard matrices), undersample the target's optical properties for image reconstruction and recognition. Artificial intelligence (AI) and machine learning enhance image quality by processing compressed data using deep learning and recurrent neural networks. However, single-photon compressive sensing faces challenges from background noise (ambient environment, detector dark counts, Poissonian fluctuations of signal photon numbers). For instance, satellite LiDAR systems struggle in daylight due to overwhelming sunlight. Mid and near-infrared (IR) upconversion imaging and detection research aims to enhance sensitivity compared to direct IR detection (using thermal sensors which suffer from limited sensitivity and high noise, often requiring cryogenic cooling). Visible detectors offer lower noise and better sensitivity without cryogenic cooling. Frequency upconversion has been demonstrated for various photon-starving imaging scenarios. This paper presents an experiment combining single-pixel compressive sensing, single-photon detection, and machine learning for image classification, focusing on understanding and mitigating quantum noise effects.

The existing literature extensively covers single-pixel compressive sensing and its applications across various imaging modalities. Numerous studies explore different encoding schemes, such as the use of Hadamard matrices and Fourier transform bases, to optimize the compression and reconstruction process. Furthermore, the integration of machine learning techniques, particularly deep learning algorithms, has shown significant improvements in image reconstruction quality. However, the literature lacks comprehensive studies on the impact of noise, specifically photon-counting noise, on the performance of single-pixel compressive sensing systems in low-light conditions. While there are papers discussing noise reduction techniques in general imaging systems, the unique challenges posed by single-photon detection and the specific noise sources associated with this technology require dedicated investigation. This study bridges this gap by focusing on the noise mitigation strategies relevant to single-photon compressive sensing.

The experimental setup consists of a femtosecond mode-locked laser (~1550 nm) generating probe and pump pulses (6 ps), a digital micromirror device (DMD) displaying Walsh 2D patterns, a spatial light modulator (SLM) showing MNIST digit images, and two single-photon counting systems: an avalanche photodiode (InGaAs SPD) for direct detection (DD) and an upconversion photon detector based on QPMS. The probe beam is encoded by the DMD and SLM, and then split. One path is directly detected (DD), while the other is combined with a pump pulse and sent through a PPLN module for QPMS detection, which upconverts the signal photons to a more favorable wavelength. Amplified spontaneous emission (ASE) noise is introduced to simulate ambient noise. A deep neural network (DNN) with seven layers (including input, five hidden, and output layers) is used for image classification. The DNN uses rectified linear unit (ReLU) activation functions in hidden layers and a log-softmax function between the second-to-last and last layers. Data is acquired by varying the integration time of single-photon detectors to study quantum noise effects. For each digit, 300 photon counts for 300 Walsh 2D patterns are acquired. 75% of the data is used for training and 25% for testing. The experiment measures and compares the classification accuracy of DD and QPMS under various conditions, including different integration times, probe powers, and ASE noise levels. The signal-to-noise ratio (SNR) is calculated as 10log10[(Noff - Ndark)/(Non - Noff)], where Noff is the photon count without ASE, Ndark is the photon count with the probe off, and Non is the photon count with ASE noise. The dark counts of both detection channels are also measured. The NEDC is calculated as detector dark count divided by total detection efficiency. Robustness is tested by training on one ASE noise level and testing on another.

The experimental results show a significant accuracy drop for direct detection (DD) when the mean photon numbers per digit pattern fall below 300. With 600 µs integration time and ~14 nW probe power, DD achieves 82.8% accuracy (398.6 average photon counts per mask), increasing to 90% with 800 µs integration time (551.2 average photon counts). However, reducing probe power to ~8.5 nW (391.5 average photon counts) lowers accuracy to 80.4%. At ~4 nW (299.7 average photon counts), accuracy plummets to 31.6%. QPMS shows significantly higher accuracy (98% with 200 µs integration time and ~14 nW probe power, 485.8 average photon counts) due to lower dark counts (0.29 per 10 µs for DD vs 0.21 per 10 µs for QPMS). QPMS achieves 97.2% accuracy with 300 masks and 93.2% with 100 masks at 119.7 average photon counts per mask, saturating at ~99.2% for higher counts. With ASE noise, DD accuracy drops sharply (22% at 0 dB SNR, 51.6% at 3 dB SNR) whereas QPMS maintains high accuracy (above 98% even when the signal is 100 times weaker than the noise, 94% accuracy even when the signal is 500 times weaker than the noise at -27dB SNR). QPMS’ superior performance is due to noise rejection (over 99.9% noise rejection) and lower noise equivalent dark counts (NEDC: 281 for DD, 71 for QPMS). Training on one ASE noise level and testing on a different level also shows high accuracy (at least 98%).

The findings directly address the research question of improving the noise resilience of single-pixel compressive sensing in low-light conditions. The significant performance difference between direct detection and QPMS highlights the effectiveness of the proposed approach. The high accuracy achieved by QPMS, even in the presence of overwhelming background noise, demonstrates its potential for real-world applications where ambient light and other noise sources are prevalent. The results validate the importance of mode-selective upconversion for single-photon sensing, offering a pathway to highly sensitive and robust optical sensing systems. The improved performance is attributable to both higher detection efficiency and significantly lower dark counts. The ability of the system to maintain high classification accuracy with varying levels of ASE noise underlines its robustness and potential for practical implementation.

This work demonstrates a significant advancement in noise-resilient single-pixel compressive sensing using QPMS. The achieved high classification accuracy in the presence of substantial background noise demonstrates the practicality of this approach for various applications. Future research could explore different encoding patterns, more advanced machine learning architectures, and the integration of this technique into diverse single-photon sensing systems. Investigating the potential benefits of the high timing resolution of QPMS in further enhancing the classification accuracy warrants further study.

The current study uses MNIST handwritten digits, which might not fully represent the complexity of real-world scenes. The experimental setup relies on specific equipment available in the lab, and alternative configurations might yield different results. The QPMS implementation has a limited detection range, which could be further improved with better components. Further investigation is needed to explore the full extent of the temporal resolution’s contribution to the improved accuracy.