Weak-signal extraction enabled by deep-neural-network denoising of diffraction data

TL;DR

This work tackles denoising of noisy X-ray diffraction data to reveal weak signals such as charge-density-wave order without distorting ground truth. It trains two CNNs (VDSR and IRUNet) on paired experimental low-count and high-count frames and compares performance to networks trained on artificial Poisson noise, showing experimental-noise training yields substantially more accurate recovery. The denoising improves the signal-to-residual-background ratio (SRBR), often matching or surpassing high-count data, and demonstrates generalization to other scattering modalities like RIXS. The approach offers a practical route to faster data acquisition and broader exploration of experimental parameter spaces while maintaining quantitative fidelity.

Abstract

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.

Figures (10)

• Figure 1: Example of denoising X-ray diffraction (XRD) data using a deep convolutional neural network (CNN). (a) Real experimental low-count frame (exposure time 1 second) is used as an input to a deep CNN (b) -- trained to remove the noise. (c) The denoised output reveals a charge-density-wave signal (CDW, marked in red), barely visible in the raw low-count data. (d) The real experimental high-count frame (exposure time 20 seconds) is shown for comparison. (e) A stack of denoised X-ray intensity frames as in (c). Arrows indicate the projected reciprocal coordinates $Q=(h,k,\ell)$. (f-h) One-dimensional projected scans through $Q \approx (0.23,0,8.5)$ along the $h$, $k$ and $\ell$ reciprocal space axes, in units of reciprocal lattice units (r.l.u.). For every projected scan, a background subtraction has been performed -- see main text. Gaussian fits for high-count and denoised output profiles are indicated by red solid lines. The data points depicted in the denoised output profile are computed as the mean value over five training runs of the IRUNet neural network with different initial conditions. Error bars for low- and high-count are shown under the assumption of counting statistics. Error bars for the denoised output are shown as the standard deviation over the mentioned training runs. The clock symbols indicate relative counting time and the network symbol indicates the denoised low-count produced by the neural network.
• Figure 2: Comparison of experimental and simulated noise statistics. (a) Schematic of the experimental X-ray diffraction setup. Long exposure time leads to a high-count (HC) frame (b) while short exposure time leads to a low-count (LC) frame (c). Adding Poisson noise to experimental high-count frame (b) leads to a simulated low-count frame (d). (e) Intensity distribution of the high-count frame (b) with fitted Poisson and skewed Voigt profiles. (f) Intensity distribution of the experimental and simulated low-count frame in (c,d) with fitted Poisson profile. (g,h) Zoom of white dashed rectangular region in (b,c) encircling the charge-density-wave reflection. (i,j) Zoom of white dashed rectangular region in (c,d) after denoising using the IRUNet network trained on the respective noise distributions.
• Figure 3: Enhancement of signal-to-residual-background ratio (SRBR) using CNN denoising via the IRUNet network trained on experimental data. Multiple frames containing charge-density-wave signals are analyzed along the reciprocal $(h,k,\ell)$ direction in a similar fashion as in Figure \ref{['fig:denoising_schematic']}(f-h). The signal-to-residual-background ratio of the charge-density-wave reflection in the high-count frame is plotted against the signal-to-residual-background ratio of the low-count frame and its denoised version. We observe that the denoising of the low-count frames improves the signal-to-residual-background ratio and, in many cases, even leads to better results than the high-count data.
• Figure 4: Resonant inelastic X-ray scattering (RIXS) spectra recorded on SrTiO$_3$. (a-c) RIXS spectra with counting statistics of 1, 4 and 40 times 3 minutes (top row). Left panels display counting intensities with detector channel versus energy loss. The right panels show the (horizontally) projected RIXS spectra. The panels in the bottom row are the corresponding denoised neural-network outputs of the top row. Three inelastic peaks are highlighted by arrows in (c).
• Figure 5: Impact of different loss functions on the denoised neural-network output. (a) Low-count frame. (b) Denoised low-count frame in (a) using different loss functions during the training of the network. A combination of mean absolute error and multiscale structural similarity (MAE + MS-SSIM) shows the best denoising performance. (c) High-count frame for comparison.