Super-resolved quantum ghost imaging

Quantum ghost imaging offers many advantages over classical imaging, including low photon fluxes and non-degenerate object and image wavelengths for imaging light sensitive structures, but suffers from slow image reconstruction speeds. Image reconstruction times depend on the resolution of the required image which scale quadratically with the image resolution. Here, we propose a super-resolved imaging approach based on neural networks where we reconstruct a low resolution image, which we denoise and super-resolve to a high resolution image. To test the approach, we implemented both a generative adversarial network as well as a super-resolving autoencoder in conjunction with an experimental quantum ghost imaging setup, demonstrating its efficacy across a range of object and imaging projective mask types. We achieved super-resolving enhancement of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4\times$$\end{document}4× the measured resolution with a fidelity close to 90\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}% at an acquisition time of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^2$$\end{document}2 measurements, required for a complete N \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times$$\end{document}× N pixel image solution. This significant resolution enhancement is a step closer to a common ghost imaging goal, to reconstruct images with the highest resolution and the shortest possible acquisition time.


JUPYTER NOTEBOOK code for the Generative Adversarial network model
Our Generative Adversarial Network (GAN) is termed such as it is the name of a type of neural network and was implemented using the implementation model detailed in Ref. [1]. We used the simulated MNIST ghost images (called x_train) as well as the original MNIST images (called X_train) to train the network. We detail the model architecture below.

JUPYTER NOTEBOOK code for the Autoencoder network model
Here we detail the model architecture implemented for the autoencoder network which reesolves the low resolution image to a higher resolution with more pixels. In neural network terms this type of network is termed a Super-Resolving Autoencoder network.
[ ]: # import all the dependencies required from keras.datasets import mnist import numpy as np from keras import layers from keras.layers import Input, Dense, Dropout from keras.models import Model import matplotlib.pyplot as plt from PIL import Image from keras.callbacks import ReduceLROnPlateau from keras import utils from keras.datasets import mnist from keras import backend as K import cv2 encoding_dim = 32 # specify number of pixels in the unsampled and upsampled images LR = 12 # low resolution HR = 32 # high resolution

MATLAB code for generating random masks
We created random masks that were used in the experiment. These masks were read and displayed on the spatial light modulator using LabVIEW. The MALAB code is detailed below.

LabVIEW virtual instrument to control the ghost imaging experiment
In Fig. 1 we show the block diagram of the LabVIEW virtual instrument (VI) we created and used for data acquisition during our ghost imaging experiment. We show the VI architecture used during data acquisition. LabVIEW is a graphical programming language; a typical LabVIEW VI would look something like what is shown in Fig. 1. This VI allows for real-time image 10/12 reconstruction during data acquisition. The virtual instrument reads in the masks created in MATLAB and displays them on the spatial light modulator. The National Instruments (NI) coincidence counter is connected to the PC and LabVIEW is once again used to acquire the signal from the NI counter. Figure 1. LabVIEW ghost imaging virtual instrument implemented for image acquisition and used to reconstruct ghost images in real-time.