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
applications, 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. This way, the neural network learns about the statistical
properties of the noise. We demonstrate that using artificial noise (such as
Poisson and Gaussian) 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.Comment: 8 pages, 4 figure