Deep learning denoising unlocks quantitative insights in operando materials microscopy

TL;DR

The paper addresses noise-limited quantitative insights in operando materials microscopy by introducing a modality-agnostic framework that embeds unsupervised deep denoising into microscopy workflows. It validates the approach with PDE-constrained optimization to faithfully recover physics, exemplified by recovering $D(c)$ and $μ_h(c)$ in simulated Cahn–Hilliard dynamics, and demonstrates practical gains across STXM for LiFePO$_4$, optical microscopy for graphite electrodes, and neutron radiography for lithium transport. The results reveal nanoscale chemical/structural heterogeneity, enable automated particle segmentation and phase classification, and substantially reduce variability in differential imaging, collectively expanding the reach of previously noise-limited techniques. An open-source Python package for video denoising is released to facilitate community adoption and accelerate cross-modal quantitative operando analyses.

Abstract

Operando microscopy provides direct insight into the dynamic chemical and physical processes that govern functional materials, yet measurement noise limits the effective resolution and undermines quantitative analysis. Here, we present a general framework for integrating unsupervised deep learning-based denoising into quantitative microscopy workflows across modalities and length scales. Using simulated data, we demonstrate that deep denoising preserves physical fidelity, introduces minimal bias, and reduces uncertainty in model learning with partial differential equation (PDE)-constrained optimization. Applied to experiments, denoising reveals nanoscale chemical and structural heterogeneity in scanning transmission X-ray microscopy (STXM) of lithium iron phosphate (LFP), enables automated particle segmentation and phase classification in optical microscopy of graphite electrodes, and reduces noise-induced variability by nearly 80% in neutron radiography to resolve heterogeneous lithium transport. Collectively, these results establish deep denoising as a powerful, modality-agnostic enhancement that advances quantitative operando imaging and extends the reach of previously noise-limited techniques.

Figures (19)

• Figure 1: Deep learning–based denoising integrated into microscopy workflows enables quantitative analysis across diverse imaging modalities and length scales.a Unsupervised denoising algorithms predict smoothed data from a partially-masked input source. Video denoising with umvd uses a temporal masking scheme aiyetigbo_unsupervised_2024 to predict individual frames, and image denoising with n2v uses a spatial masking scheme krull_noise2void_2019 to predict single images. Denoising models are trained by minimizing the error between predicted outputs and unmasked noisy inputs. b Data from a prototypical pattern-forming system is simulated via the Cahn-Hilliard equation and subsequently corrupted with noise and denoised. Deep denoising is validated using PDE-constrained optimization to recover the ground truth physics from denoised data. c At the nanoscale, Lithium iron phosphate nanoparticles are imaged using STXM lim_origin_2016deng_correlative_2021. Raw absorbance measurements denoised with N2V reveal clearer intraparticle heterogeneity in spatiotemporal analysis of lithium composition. d Mesocale optical microscopy visualizes phase-transformation-induced color changes within a graphite electrode in-situ. Denoising enables large-scale data processing by producing robust segmentation and phase quantification across hundreds of particles. e At the macroscopic scale, operando neutron radiography captures lithium transport across full electrodes within a working cell gober_high_2025. Denoising reduces variability in differential imaging, enabling reliable interpretation of reversible and irreversible transport pathways.
• Figure 2: Denoising workflow increases signal to noise ratio of simulated dataset and recovers the ground truth physical properties with reduced variance.a Across three standard noise distributions and a mixed composite case, video denoising (UMVD) achieves visually accurate reconstructions of the ground truth, while image denoising (N2V) provides notable improvements in image quality under continuous noise conditions, such as Gaussian and Poisson. b UMVD and N2V significantly increase the PSNR of the noisy images, with stronger performance in UMVD. Similar improvements are observed for the structural similarity index metric (Fig. \ref{['fig:chr_ssim']}). c Across all noise distributions, UMVD reliably recovers the ground truth $\mu_h(c)$ and diffusivity $D(c)$ with substantially reduced uncertainty, while N2V recovers the ground truth in all but the impulse noise case. A small discrepancy persisted near $c=0$ for $D(c)$, where insensitivity to $D(c)$ introduced higher uncertainty for all noise conditions zhao_learning_2020. A detailed comparison of final optimization error and results for additional noise intensity levels are provided in Supplementary Information section \ref{['subsec:SI_CHR']}. Shaded regions indicate one standard deviation obtained by bootstrapping.
• Figure 3: Visualization of intraparticle heterogeneity revealed by image denoising in compositional analysis of LFP using STXM.a Denoising enhances nanoscale spatial variations in ex situ STXM for both X-ray absorbance and lithium composition in biphasic particles, validated against high-resolution X-ray spectro-ptychography. Noise suppression clarifies intraparticle heterogeneity, bringing STXM measurements into closer agreement with ptychography. X-ray absorbance measurements were collected at 706eV and 711eV. Ptychography measurements were resized and aligned to match the STXM images. b PSNR and SSIM of raw (gray) and denoised (purple) images, computed relative to ptychography and shown as box-and-whisker plots. Both metrics confirm that denoising improves image quality in terms of both error and perceptual fidelity. Boxes show the interquartile range (IQR), center lines at the median, and whiskers 1.5$\times$ IQR (n=18 scans, 5 particles). cOperando characterization of LFP after denoising reveals sharper internal phase boundaries and temporally persistent heterogeneity across multiple cycling conditions. Horizontal scan noise is visually suppressed and phase-separated domains within the denoised particle remain consistent with the raw data and with previous experimental and computational analyses lim_origin_2016zhao_learning_2023 The C-rate, where $C/n$ stipulates the cell will fully (dis)charge to the theoretical capacity in n hours, is labeled below each half-cycle. Scale bar: 500 nm; Ex-situ: 40 nm/pixel; In-situ: 50 nm/pixel.
• Figure 4: Video denoising enables electrode-scale particle segmentation and phase classification in optical microscopy of a graphite electrode.a Raw frames of graphite during C/60 lithiation experiment. Graphite undergoes phase transitions from stage III (blue) to stage II (red) to stage I (gold). Images exhibit cloudiness and short scale temporal fluctuations (Supplementary Video 2). b Denoised frames enhance particle contrast, reducing haziness and improving particle-background separation. c Partic.le segmentations from raw and denoised videos compared with expert manual annotation; denoised results closely match manual expert segmentation. Overlayed gray regions denote expert segmentation. d Algorithmic phase classification of masked particles from denoised images with full spatial resolution. Classifications qualitatively match the corresponding observations in both raw and denoised images. e Automated denoising workflow enables tracking population-level statistics with particle-level resolution. Population density is plotted at the corresponding frames as a function of the particle-averaged state of charge, $\bar{c}$, and characteristic particle size $V/A$. Scale bar: 10 $\mu$m.
• Figure 5: Reduced variability enables mechanistic insight into macroscopic heterogeneity in operando neutron radiography.a Schematic of the analyzed graphite-NMC test cell with thick electrodes and a solvent-free anode preparation. b Distribution of dynamic variability, defined as the local spatiotemporal standard deviation (3 × 3 × 3 window). Denoising lowers the mean from 0.0247 (raw) to 0.005 (denoised), nearly an 80% reduction. c Coulombic efficiency versus cycle number with C-rates indicated. The first cycle displays markedly lower efficiency, before stabilizing in later cycles. d Change in attenuation coefficient reveals uniform anode filling during charge, indicated by the flat distribution across the anode, whereas discharge is heterogeneous, indicated by sharp localized peaks confined to a small active region (dashed green lines). Full 2D maps and corresponding 1D depth averages are shown: the raw data (gray) exhibits high variability with broad error bars, whereas the denoised data (purple) suppresses fluctuations and highlights non-uniform discharge that leaves a zone of inactive lithium near the current collector. Shaded regions denote one standard deviation in the in-plane (x-axis) attenuation. e Active area fraction for both electrodes across half-cycles. The first charge cycle shows high anode activity, whereas later cycles exhibit reduced and asymmetric utilization between charge and discharge, consistent with lithium sequestration. By the fourth cycle, activity is confined to a localized region near the separator, as shown in the inscribed visualization. f Change in lithium attenuation relative to the end of the first charge cycle, shown for both raw and denoised radiographs with corresponding 1D averages. Denoising reduces variability and reveals a clear progression of lithium sequestration near the current collector, with a smooth gradient across the anode. Scale bar: 1 mm.