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 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.

翻译：噪声消除或对消在成像和声学领域具有广泛应用。在日常应用中，降噪甚至可能包含有悖于真实数据的生成性处理。然而对于科学应用而言，降噪必须准确复现真实数据。本文展示了如何通过深度卷积神经网络实现数据降噪，使微弱信号以定量精度显现。我们以晶体材料的X射线衍射为研究对象，证实了由电荷有序化引起的微弱信号（在含噪数据中难以分辨）在降噪后数据中变得清晰可见且准确可测。这一突破得益于采用实测低噪声与高噪声数据对深度神经网络进行监督训练，使网络习得噪声的统计特性。研究证明，使用人工噪声无法获得如此量级精度的结果。我们的方法为噪声滤波提供了一种实用策略，可应用于具有挑战性的数据采集场景。