A novel data-driven reconstruction algorithm for quantum image sensors (QIS) is proposed. Observations are efficiently decoded by modeling the reconstruction structure as a two-layer neural network, where optimal coefficients are obtained via error backpropagation. Our model encapsulates the structure of state-of-the-art algorithms, yet it presents a faster alternative which adapts to input examples without a priori statistical information. Simulations on natural and synthetic datasets show accurate reconstructions consistent with the state of the art, while requiring 5 times less computational cost.