  Removal or cancellation of noise has wide-spread applications for imaging and
acoustics. In every-day-life applications, denoising may even include
generative aspects, which are unfaithful to the ground truth. For scientific
use, however, denoising must reproduce the ground truth accurately. Here, we
show how data can be denoised via a deep convolutional neural network such that
weak signals appear with quantitative accuracy. In particular, we study X-ray
diffraction on crystalline materials. We demonstrate that weak signals stemming
from charge ordering, insignificant in the noisy data, become visible and
accurate in the denoised data. This success is enabled by supervised training
of a deep neural network with pairs of measured low- and high-noise data. We
demonstrate that using artificial noise does not yield such quantitatively
accurate results. Our approach thus illustrates a practical strategy for noise
filtering that can be applied to challenging acquisition problems.
