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Sensors

Robust Entangled-Photon Ghost Imaging with Compressive Sensing

Jun Li, Wenyu Gao, Jiachuan Qian, Qinghua Guo, Jiangtao Xi, Christian H. Ritz

Published Jan 7, 2019• 16 citations
Publisher

Abstract

This work experimentally demonstrates that the imaging quality of quantum ghost imaging (GI) with entangled photons can be significantly improved by properly handling the errors caused by the imperfection of optical devices. We also consider compressive GI to reduce the number of measurements and thereby the data acquisition time. The image reconstruction is formulated as a sparse total least square problem which is solved with an iterative algorithm. Our experiments show that, compared with existing methods, the new method can achieve a significant performance gain in terms of mean square error and peak signal⁻noise ratio.

DOI
10.3390/s19010192

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This work experimentally demonstrates that the imaging quality of quantum ghost imaging (GI) with entangled photons can be significantly improved by properly handling the errors caused by the imperfection of optical devices. We also consider compressive GI to reduce the number of measurements and thereby the data acquisition time. The image reconstruction is formulated as a sparse total least square problem which is solved with an iterative algorithm. Our experiments show that, compared with existing methods, the new method can achieve a significant performance gain in terms of mean square error and peak signal⁻noise ratio.
We have experimentally demonstrated high-resolution compressive ghost imaging at the single-photon level using entangled photons produced by a spontaneous parametric down-conversion source and using single-pixel detectors. For a given mean-squared error, the number of photons needed to reconstruct a two-dimensional image is found to be much smaller than that in quantum ghost imaging experiments employing a raster scan. This procedure not only shortens the data acquisition time, but also suggests a more economical use of photons for low-light-level and quantum image formation.
Demonstrating the utility of quantum algorithms is a long-standing challenge, where quantum machine learning becomes one of the most promising candidates that can be resorted to. In this study, we investigate a quantum neural compressive-sensing algorithm for ghost imaging to showcase its utility. The algorithm utilizes the variational quantum circuits to reparameterize the inverse problem of ghost imaging and uses the inductive bias of the physical forward model to perform optimization. To validate the algorithm's effectiveness, we conduct optical ghost-imaging experiments, capturing signals from objects at different physical sampling rates and detection signal-to-noise ratios. The experimental results show that our proposed algorithm surpasses conventional methods in both visual appearance and quantitative metrics, achieving state-of-the-art performance. Of note, we observe that the quantum neural network, guided by prior knowledge of physics, effectively overcomes the challenge of barren plateau in the optimization process. The proposed algorithm demonstrates robustness against various quantum noise levels, making it suitable for near-term quantum devices. Our study leverages a physical inductive-bias-guided variational quantum algorithm, underscoring the potential of quantum computation in tackling a broad range of optimization and inverse problems.
We demonstrate a compressive normalized ghost imaging system with entangled photons employing complementary compressive imaging (CCI) technique. The quantum ghost image reconstruction was achieved with 19.53% sampling ratio of raster scanning and average 0.78 photons/pixel of each measurement. Using the special +1/-1 type sensing matrix and appropriate optimal algorithm, the photon utilization efficiency, and robustness of the imaging system is enhanced significantly. Our results reveal the great potential of CCI technique applied in quantum imaging and other quantum optics field such as quantum characterizing and quantum state tomography to use the information loaded in each photon with high efficiency.
Using the entangled photons generated by the spontaneous parametric down conversion as a light source, we demonstrate the first quantum ghost imaging system with a modified compressive sensing technique based on the spatial correlation of sensing matrix (SCCS). The ghost image is achieved at 16.27% sampling ratio of raster scanning and 0.65 photons/pixel at each measurement on average. Our results show that image quality and photon-utilization efficiency are remarkably enhanced in comparison with the traditional compressive imaging technique, due to the sensing matrix and noise-free measurement vector rebuilt by SCCS technique. It suggests the great potential of SCCS technique applied in quantum imaging and other quantum optics fields, such as quantum charactering and quantum state tomography to use the information loaded in each photon with high efficiency.
Ghost imaging allows one to obtain information on an object from the spatial correlation function between photons propagating through or reflected from the object and photons of the reference arm. In this case, detection in the object arm is performed over the entire aperture of the beam and, therefore, it does not give information on the object. The reference beam does not interact with the object, but is recorded with a scanning point detector or a CCD array permitting the measurement of the spatial correlation function of photons in two arms. The use of multimode entangled quantum light beams by illuminating the object by one beam and orienting other beams to reference arms makes it possible to obtain simultaneously several ghost images (GIs). Cross correlations of multiplexed GIs (MGIs) are determined by eighth-order field correlation functions. A special algorithm is developed for calculating higher-order correlations of Bose operators. The presence of GI cross correlations is used for improving the quality of the reconstructed object’s image by their processing using the measurement reduction method. An example of the computer simulation of the image reconstruction by MGIs formed in the field of four-frequency entangled quantum states is considered. It is found that in this case the reduced GI has a signal-to-noise ratio several times higher than that of GIs.