  Single-pixel cameras are effective solution for imaging outside the visible
spectrum where traditional CMOS/CCD cameras have challenges. 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 using 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 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 measure 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.
