Classification and reconstruction for single-pixel imaging with classical and quantum neural networks

Single-pixel cameras are an effective solution for imaging outside the visible spectrum, where traditional CMOS/CCD cameras have challenges. When combined with machine learning, they can analyze images quickly enough for practical applications. Solving the problem of high-dimensional single-pixel visualization can potentially be accelerated via quantum machine learning, thereby expanding the range of practical problems. In this work, we simulated a single-pixel imaging experiment using Hadamard basis patterns, where images from the MNIST handwritten digit dataset and FashionMNIST items of clothing 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 reconstructing images based on these measurements using classical fully-connected neural networks and parameterized quantum circuits. Classical and quantum classifiers showed the best accuracies of 96% and 95% for MNIST and 84% and 81% for FashionMNIST, respectively, after 6 training epochs, which is a quite competitive result. In the area of intersection by the number of parameters of the quantum and classical classifiers, the quantum demonstrates results no worse than the classical one, even better by a value of about 1-3%. Image reconstruction was also demonstrated using classical and quantum neural networks after 10 training epochs; the best structural similarity index measure values were 0.76 and 0.26 for MNIST and 0.73 and 0.22 for FashionMNIST, 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.