Classification and reconstruction of images in the problem single-pixel imaging using classical and quantum neural networks

Single-pixel cameras can be an excellent solution for light ranges outside the visible spectrum, combined with machine learning, they can analyze images quickly enough for practical applications. In the future of the development of quantum technologies, quantum computers can further speed up the solution of such problems. In this work we simulated a single-pixel detection experiment using Hadamard basis patterns, where images from the MNIST handwritten digit dataset were used as objects. There were selected 64 measurements with maximum variance (6\% of the number of pixels in the image). We created algorithms for classifying and reconstruction images based on these measurements using classical fully connected neural networks and parameterized quantum circuits. Classical and quantum classifiers showed accuracies of 96\% and 95\% respectively after 6 training epochs, which is quite competitive result. Image reconstruction was also demonstrated using classical and quantum neural networks after 10 training epochs, the structural similarity index values were 0.76 and 0.25, respectively, which indicates that the problem in such a formulation turned out to be too difficult for quantum neural networks in such a configuration for now.