Robust Spectral Anomaly Detection in EELS Spectral Images via 3D Convolutional Variational Autoencoders

Abstract

A 3D Convolutional Variational Autoencoder (3D‐CVAE) is introduced for automated anomaly detection in electron energy‐loss spectroscopy spectrum imaging (EELS‐SI) data. This approach leverages the full 3D structure of EELS‐SI data to detect subtle spectral anomalies while preserving both spatial and spectral correlations across the datacube. By employing cross‐entropy loss and training on bulk spectra, the model learns to reconstruct bulk features characteristic of the defect‐free material. In exploring methods for anomaly detection, both the 3D‐CVAE approach and principal component analysis (PCA) are evaluated, testing their performance using Fe L‐edge ΔE peak shifts designed to simulate material defects. These results show that 3D‐CVAE achieves superior anomaly detection and maintains consistent performance across various shift magnitudes. The method demonstrates clear bimodal separation between bulk and anomalous spectra, enabling reliable classification. Further analysis verifies that lower‐dimensional representations are robust to anomalies in the data. While performance advantages over PCA diminish with decreasing anomaly concentration, our method maintains high reconstruction quality even in challenging, noise‐dominated spectral regions. This approach provides a robust framework for unsupervised automated detection of spectral anomalies in EELS‐SI data, particularly valuable for analyzing complex material systems.

Automated anomaly detection is demonstrated for electron energy‐loss spectrum imaging in an atomic‐resolution scanning transmission electron microscope using an unsupervised learning approach. A 3D convolutional variational autoencoder is introduced and tested on the iron L‐edge spectra taken from a single‐crystal BiFeO₃ sample. This approach is benchmarked against Principal Component Analysis and high reconstruction quality is demonstrated even in challenging, noise‐dominated spectral regions.

1. Introduction

High‐resolution transmission electron microscopy has emerged as the predominant technique for material characterization across diverse systems, including 2D materials,^{[ 1 ]}superconductors,^{[ 2 ]} semiconductors,^{[ 3 ]} and catalysts.^{[ 4 ]} A particularly powerful approach to materials characterization is the combination of scanning transmission electron microscopy (STEM)^{[ 5 ]} with electron energy‐loss spectroscopy (EELS),^{[ 6 ]} which can measure the local density of states up to single atomic‐column resolutions.^{[ 7 ]} This approach is often referred to as EELS spectrum imaging (EELS‐SI),^{[ 8 ]} and the resulting 3‐dimensional data cubes contain a detailed map of elemental composition, electronic structure, and bonding at the atomic scale, which is critical for understanding the fundamental properties of condensed matter systems. 

Core‐loss EELS, which stems from the transition of highly‐localized states, such as the 1s or 2p states into unoccupied orbitals above the Fermi level (E _F ), often exhibit a detailed fine structure of a particular edge, for example, the oxygen K‐edge or a transition metal L‐edge, near the edge onset, which reflects the density of unoccupied states near E _F .^{[ 6 ]} Subtle changes in this near‐edge fine structure are due to changes in the local crystal structure, changes in orbital or spin ordering, valence state changes or the presence of defects/vacancies. These insights are invaluable for exploring phenomena, such as superconductivity,^{[ 9 ]} magnetism,^{[ 10 ]} and topological states of matter.^{[ 11 ]} Furthermore, atomic‐column resolved EELS is particularly impactful in analyzing interfaces, grain boundaries,^{[ 12 ]} and low‐dimensional materials,^{[ 13 ]} where local electronic and chemical environments dictate macroscopic material properties. By bridging the gap between atomic‐scale phenomena and bulk material behavior, this technique plays a crucial role in advancing the design of quantum materials, catalysts, and energy devices.

Existing EELS‐SI data analysis methods predominantly rely on manual inspection or dimensionality reduction techniques, such as Principal Component Analysis (PCA). While effective at noise reduction and extracting statistically significant features, PCA's linear nature limits its ability to capture physically significant, intricate spectral details. Its variance‐based decomposition often relegates subtle spectral features to low variance components, which are commonly discarded as noise. Furthermore, PCA, being constrained to linear combinations of input features, cannot accurately represent non‐linear relationships in the data, potentially overlooking complex spectral patterns crucial for anomaly detection.

Machine learning (ML) has emerged as a significant tool across scientific disciplines, offering new approaches for analyzing complex datasets.^{[ 14} , ¹⁵ , ^{16 ]} In electron microscopy, conventional ML techniques have enhanced data analysis, enabling robust methods for denoising images and identifying atoms/patterns in STEM/scanning tunneling microscopy (STM)/atomic force microscopy (AFM) data.^{[ 17} , ¹⁸ , ^{19 ]} The increasing accessibility of high‐performance computing has accelerated the adoption of more complex, data‐intensive methods, particularly deep learning (DL) models like autoencoders, which have gained prominence in physics applications. Autoencoders, hourglass‐shaped feed‐forward neural networks, compress input data through an encoder, then reconstruct it from a low‐dimensional representation, preserving salient features while finding a succinct data representation.^{[ 20 ]}

Variational Autoencoders (VAEs)^{[ 21 ]} combine variational inference and autoencoders to create deep generative models trainable in an unsupervised fashion. VAEs excel at learning compact, non‐linear representations of high‐dimensional data. They achieve this by regularizing the latent space so that nearby points encode semantically similar information. This regularization is accomplished by modeling the latent space as a product of Gaussian distributions and minimizing the Kullback–Leibler (KL) divergence between the estimated and true underlying distributions.^{[ 21 ]} The KL divergence is minimized when the estimated distribution matches the true underlying distribution, allowing the VAE to learn a smooth, continuous latent space that captures meaningful data features.

Unlike conventional autoencoders, which may learn discontinuous or arbitrary latent representations, VAEs' regularized latent space improves the quality of both learned features and the learned relationships between them. This characteristic makes VAEs more resistant to learning undesirable features such as noise signatures or subtle shifts in the training set ‐ issues that often reduce the semantic meaning of latent encodings in conventional autoencoders ‐ thereby enhancing VAEs' generalizability to new data.

In physics, VAEs have shown the ability to learn physically relevant representations. For example, in molecular systems, VAEs have been applied to represent free energy surfaces (FES), enabling improved sampling of high‐dimensional spaces and prediction of properties like isothermal compressibility or nuclear magnetic resonance (NMR) spin‐spin J couplings.^{[ 22 ]} They have also been used for dimensionality reduction, such as identifying slowly varying collective variables in peptide folding, which is crucial for developing Markov state models of conformational changes.^{[ 22 ]}

In materials science, VAEs and related autoencoder architectures have been applied to extract meaningful features from various scientific images, including spatial‐spectral characteristics from hyperspectral images using 3D convolutional autoencoders^{[ 23 ]} and structural patterns from STEM/STM images using shift‐invariant VAEs.^{[ 24 ]} The latent space variables often correlate with key physical properties such as atomic positions, lattice periodicities, or electronic states, providing insights into the underlying physics. VAEs have demonstrated the capability to separate individual structural building blocks from relevant order parameter fields that change slowly on the length scale of the atomic lattice, enabling efficient exploration of complex configurational spaces.^{[ 24 ]}

Recent studies have applied ML to EELS data, creating models for predicting individual spectra from structural images based on the idea that local structures and functional phenomena are correlated through a small number of latent mechanisms.^{[ 25 ]} Denoising autoencoders have been explored as an alternative to PCA, matching and outperforming PCA reconstructions.^{[ 26 ]} However, most approaches have primarily addressed individual EELS spectra, leaving the full potential of 3D EELS‐SI data unexplored.

VAEs have demonstrated effectiveness in anomaly detection across various domains. In civil engineering, they have been applied to detect temporal and spatial anomalies in dam monitoring data.^{[ 27 ]} In computer vision, VAEs have been used to detect and localize anomalous events in surveillance videos using only bulk samples for training.^{[ 28 ]} In medical imaging, 3D VAEs have shown promise in detecting schizophrenia from brain MRI data.^{[ 29 ]}

Our previous work focused on developing an approach using Convolutional VAEs (CVAEs) to detect and classify point defects and other structural anomalies in atomic‐resolution STEM images.^{[ 30} , ^{31 ]} We successfully validated this method on STEM images of SrTiO ₃ and more complex structures like FePO ₄ and CdTe. In this approach, a CVAE trained solely on bulk crystal structure images learned the expected atomic positions and intensities. Anomalies were then identified by subtracting the input images from the CVAE's reconstructions.

The present work extends this concept to EELS‐SI data, introducing a novel 3D Convolutional Variational Autoencoder (3D‐CVAE) for discovering intricate spectral anomalies. This unsupervised approach can learn complex, disentangled patterns in EELS‐SI data while requiring relatively small training datasets compared to most supervised neural networks. Importantly, it can be implemented using computing resources widely available to researchers in the field, without requiring high‐performance supercomputers.

To enhance scalability and applicability, our model operates directly on EELS‐SI data, eliminating the need for additional feature engineering or comprehensive prior knowledge of the material system. This element‐agnostic approach allows the model to learn underlying spectral patterns for any element, given sufficient training examples.

For our experiments, we employed an EELS–SI datacube acquired on a Nion UltraSTEM 100 operated in STEM mode at 60 keV (convergence semi‐angle 30 mrad, camera length 1 m). Spectra were recorded with a Gatan EELS detector (collection semi‐angle 48 mrad, dispersion 0.30 eV channel⁻¹, dwell time 20 ms) and cover the Fe L _{2, 3} and O K edges, starting from an energy offset of 420 eV. The datacube contains 192 × 192 spatial pixels and L = 2048 energy channels, yielding a total of 36 864 spectra from epitaxial BiFeO₃ thin films grown on SrTiO₃. We train the 3D‐CVAE on overlapping 24 × 24 × L blocks extracted from this bulk dataset and evaluate performance by reconstructing spectra with artificially injected ΔE peak shifts. Our results demonstrate that the 3D‐CVAE‐based method outperforms traditional PCA in both spectral reconstruction and anomaly detection, successfully identifying subtle spectral changes associated with defect structures and interface phenomena, surpassing the capabilities of conventional analysis methods.

2. Experimental Section

The 3D‐CVAE employs 3D convolutional layers to simultaneously capture spectral features and their spatial relationships within the EELS‐SI data cube. Translational invariance is achieved through strided convolutions^{[ 32 ]} across all three dimensions, ensuring consistent feature detection regardless of the exact position of spectral features. This architecture is capable of processing the full 3D structure of the data while maintaining spatial relationships.

During training, the 3D‐CVAE approximates the underlying data distribution by modeling it as a multivariate Gaussian distribution in a continuous latent space. In practice, the network learns to estimate the parameter space that generates this approximate distribution, with a KL divergence term ensuring smoothness and preventing overfitting. The model encodes each spectrum as parameters (mean and variance) of this distribution in the latent space, where similar spectra cluster together based on their shared structural characteristics. During inference, when presented with an anomalous image, the VAE's encoder maps it into this learned latent space.^{[ 21 ]} The subsequent reconstruction by the decoder is based on this mapping, effectively filtering out features that deviate from the learned data distribution. This process can be understood as a form of probabilistic dimensionality reduction followed by a generative reconstruction, where the model's learned prior acts as a constraint that guides the reconstruction toward the bulk structure of the training data. Consequently, the reconstructed image tends to exclude or attenuate elements that fall outside the learned distribution. The discrepancy between the original input and its reconstruction can then serve as a quantitative measure of anomaly, making VAEs an effective tool for both detecting and localizing anomalies in complex, high‐dimensional data such as EELS SI datacube.

We present a novel DL method for EELS data by reformulating the reconstruction problem through Cross‐Entropy (CE) Loss. While existing DL approaches to spectral data typically employ Mean Squared Error (MSE)^{[ 26 ]} or Evidence Lower Bound (ELBO)^{[ 21 ]} objectives that treat spectral intensities as continuous values, our formulation recognizes the discrete nature of electron energy loss events. Each spectrum in EELS represents a distribution of discrete electron counting events across energy channels. By utilizing CE Loss instead of MSE or ELBO, we treat each energy channel as a distinct class, where the normalized spectrum intensities represent the probabilities of electron energy loss events. This formulation aligns more closely with the probabilistic nature of the data and improves the model's ability to capture and reconstruct critical spectral features. The total loss function used for training combines the CE Loss term with a KL divergence term, as follows:

$$\begin{array}{c}\hfill L_{\text{total}}(\mathbf{x},\widehat{\mathbf{x}})=\underset{\text{Cross-Entropy Loss}}{\underbrace{{\sum }_{i=1}^N{L}_{\text{CE}}({\mathbf{y}}_i,{\widehat{\mathbf{y}}}_i)}}+\beta ·L_{\text{KL}}\end{array}$$ (1)

Where x represents 3D input shard of the SI datacube, and $\widehat{\mathbf{x}}$ represents the reconstructed shard produced by the decoder. The total number of spectra in a shard is denoted by N, which is obtained by flattening the spatial dimensions (x, y) of the SI datacube. The parameter β^{[ 33 ]} is a weighting factor that controls the trade‐off between the reconstruction accuracy (governed by the CE Loss) and the regularization of the latent space (enforced by the KL divergence term). The CE Loss quantifies the discrepancy between the original spectra and their reconstructions. For an individual spectrum, the CE Loss is defined as:

$$\begin{array}{c}\hfill L_{\text{CE}}(\mathbf{y},\widehat{\mathbf{y}})=-\sum _{e=1}^E\left\{y_e·\log [\text{softmax}({\widehat{y}}_e)]\right\}\end{array}$$ (2)

where $\mathbf{y}={\{y_e\}}_{e=1}^E$ represents the normalized intensities of the original spectrum and $\widehat{\mathbf{y}}={\{{\widehat{y}}_e\}}_{e=1}^E$ represents the reconstructed normalized intensities. The number of energy channels in each spectrum is denoted by E. The softmax function, $\text{softmax}({\widehat{y}}_e)$, normalizes the reconstructed intensities to ensure that they are treated as probabilities, with values that sum to 1 across all energy channels. This formulation treats each energy channel as a distinct class, where the original normalized intensities y _e represent the probability of observing an electron energy loss event in channel e. By optimizing this loss, the model reconstructs the spectra in a way that matches the probabilistic distribution of the original input data. In addition to the reconstruction loss, the KL divergence term regularizes the organization of the latent space, ensuring that it is smooth and aligned with a prior Gaussian distribution. The KL divergence is defined as:

$$\begin{array}{c}\hfill L_{\text{KL}}=-\frac{1}{2}\sum _{j=1}^J\left[1+\log ({\sigma }_j^2)-{\mu }_j^2-{\sigma }_j^2\right]\end{array}$$ (3)

Here, J is the dimensionality of the latent space. The terms µ _j and ${\sigma }_j$ are the mean and variance of the approximate posterior distribution for the j‐th latent dimension, respectively. This term encourages the latent representations to be close to the standard Gaussian prior, promoting a compact and well‐organized latent space. The parameter β in the total loss function governs the balance between the strength of this regularization and the fidelity of spectral reconstructions. Higher values of β^{[ 33 ]} enforce stricter regularization at the cost of reconstruction accuracy, while lower values prioritize precise reconstructions of the input spectra.^{[ 21 ]} Through hyperparameter tuning, we determined β = 1.2 to provide the optimal balance between latent space organization and reconstruction quality for this specific dataset.

3. Results

To validate our approach, we inject synthetic anomalies in the form of Fe L‐edge ΔE peak shift anomalies in spatially clustered patterns, simulating realistic defect structures. The Fe L‐edge was specifically chosen for this proof of concept due to its characteristically high Signal‐to‐Noise Ratio (SNR).

The injected anomalies consist of an energy shift ΔE, chosen to represent realistic defect‐induced changes in electronic structure. Figure  1 demonstrates an example of such an anomaly, showing the original Fe L‐edge spectrum (black) compared to the anomaly‐injected spectrum (red), highlighting the characteristic ΔE peak shift our model aims to detect. To evaluate detection performance, we compare our VAE‐based approach against PCA reconstructions. The analysis pipeline processes the anomaly‐injected datacube through both methods. For the VAE analysis, we segment the data cube into 24 × 24 × L voxel blocks (where L represents the spectral dimension), process these through the network, and recombine them to preserve the original dimensions. For quantitative comparison, we calculate the Pearson Correlation Coefficient (PCC) between original and reconstructed spectra within the Fe L‐edge energy window (690–730 eV) for both methods.

Figure 1.

Example of an injected peak shift anomaly in EELS spectra. The original Fe L‐edge spectrum (black) compared to an artificially introduced ΔE = 2.5 eV peak shift (red segment).

The PCC^{[ 34 ]} metric measures the linear correlation between two variables, ranging from −1 to 1, and is given by:

$${\rho }_{x,y}=\frac{{\sum }_{e=1}^E(x_e-\overline{x})(y_e-\overline{y})}{\sqrt{{\sum }_{e=1}^E{(x_e-\overline{x})}^2}·\sqrt{{\sum }_{e=1}^E{(y_e-\overline{y})}^2}}$$ (4)

In this context, the spectrum is treated as a pair of multivariate data vectors, x = (x ₁, x ₂, …, x _E ) and y = (y ₁, y ₂, …, y _E ), where E denotes the total number of energy channels. The variables x _e and y _e represent the intensities at the e‐th energy channel for the respective spectra. The mean intensities of the spectra are given by $\overline{x}=\frac{1}{E}{\sum }_{e=1}^E{x}_e$ and $\overline{y}=\frac{1}{E}{\sum }_{e=1}^E{y}_e$, which capture the average intensity across all energy channels in each spectrum.

Figure  2 provides a comprehensive visualization of both methods' performance, highlighting the true positive areas detected by the VAE. To quantitatively identify anomalies, we analyze the distribution of PCC scores across all pixels. As shown in Figure 2, the VAE‐generated error maps provide a clearer visualization of localized errors, while the corresponding PCC distributions (Figure  3 ) exhibit distinct bimodality, effectively separating bulk and anomalous pixels. In contrast, while PCA‐generated error maps show lower mean PCC values for anomalous regions, the distribution lacks clear separation between bulk and anomalous populations, making reliable classification challenging.

Figure 2.

Comparison of the original EELS‐SI datacube, VAE and PCA reconstructions, and their anomaly detection performance. a) Sum–along–energy map of the original 192 × 192 × Z datacube. b) Split reconstruction showing VAE (left) and PCA (4 components, right) results as z–direction intensity sums. c) VAE reconstruction error heatmap (Pearson Correlation Coefficients between original and reconstructed spectra), and d) PCA reconstruction error heatmap. In both (c) and (d), green circles indicate successfully detected anomalies (Otsu thresholding), while red circles mark undetected anomalous regions. Lower PCC values (lighter colors) denote greater deviation from the original spectra.

Figure 3.

Distribution of pixels across Pearson Correlation Coefficient (PCC) values for VAE (top) and PCA with 4 components (bottom). Each histogram shows the distribution of bulk and anomalous pixels on a logarithmic scale. PCC values range from 0.2 to 1.0, where 1.0 indicates perfect correlation between original and reconstructed spectra. The VAE shows clear bimodal separation between bulk and anomalous distributions, enabling reliable anomaly detection, while PCA distributions remain overlapped.

Figure 2 provides a comprehensive visualization of both methods' performance, highlighting the anomaly areas clearly detected by the VAE but not easily visible when utilizing PCA. Still, to systematically identify these areas, we need a quantitative approach. To achieve this, we analyze the distribution of PCC scores between the original spectra and their reconstructions from both VAE and PCA approaches, calculated for each spectrum within the data cube. Looking at the results in Figure 2, we can see that PCC distributions for VAE‐generated spectral predictions exhibit distinct bimodality, effectively separating bulk and anomalous pixels. Furthermore, VAE shows superior reconstruction quality, with a higher PCC score means for bulk pixels compared to PCA. The VAE‐reconstructed anomalous populations show significantly lower correlation means compared to their bulk counterparts, while PCA‐reconstructed anomalous spectra have correlation values much closer to their bulk data mean. This, combined with PCA's lack of clear separation between bulk and anomalous populations, makes reliable classification challenging when using PCA.

To classify anomalies automatically, we implement Otsu's method,^{[ 35 ]} an algorithm that optimally separates the PCC histogram into two classes by maximizing between‐class variance. To minimize false positives in anomaly‐free data, we incorporate a unimodality check of the PCC distribution. For the EELS SI datacube shown in Figures 2 and 3, our VAE approach demonstrated reliable classification accuracy: out of 36,864 total spectra, only 6 anomalous spectra were misclassified as bulk material.

To verify the robustness of our method, we performed a comparative statistical analysis between our VAE approach and PCA using different numbers of principal components (3, 4, and 5) across various ΔE shift magnitudes. (Figure  4 ). Performance was evaluated using F1‐scores,^{[ 15} , ^{36 ]} a harmonic mean of precision and recall that balances detection accuracy by accounting for both undetected anomalies (false negatives) and misclassified bulk pixels (false positives). The results demonstrate that our VAE approach maintains consistently high F1‐scores across different ΔE shift magnitudes, achieving both high precision and recall. In contrast, PCA performance shows a fundamental trade‐off: using three components provides the best anomaly detection among PCA variants but exhibits periodic performance fluctuations based on shift‐basis vector alignment. Adding more components improves spectral reconstruction fidelity but degrades anomaly detection capability, a limitation most apparent when examining subtle spectral features such as the O K edge.

Figure 4.

Performance comparison across different magnitudes of ΔE peak shifts. F1‐scores for VAE (red) and PCA with 3 (blue), 4 (orange), and 5 (green) components. VAE maintains consistently high F1‐scores across all shift magnitudes, while PCA exhibits periodic fluctuations in performance. PCA with 3 components shows the best performance among PCA variants, though its effectiveness varies with shift magnitude.

Further analysis reveals that PCA performance is optimal when anomalies are small in number and sparsely distributed, while our VAE approach maintains consistent performance even beyond physically realistic anomaly concentrations. Although peak shifts beyond ΔE = 4 eV exceed typical physical scenarios, we extended our analysis to larger ΔE shifts to demonstrate that PCA's trend of improving performance from ΔE = 0 eV to ΔE = 4 eV does not persist beyond this threshold and to show periodic nature of PCA performance. To gain insight into the network's internal representations, we analyzed the latent space encodings of 64 pairs of EELS‐SI sub‐images, where each pair consisted of a bulk datacube shard and its anomaly‐injected counterpart. Analysis of cosine similarity between the 48‐dimensional encodings (corresponding to our model's latent space dimensionality) reveals that the encoder consistently places paired images in close proximity within the latent space, as shown by the high correlation values along the diagonal in Figure  5 . This proximity is crucial for our anomaly detection approach, as it demonstrates that the encoder recognizes anomalous and bulk spectra as fundamentally the same data point, leading to reconstructions that effectively filter out the anomalous features. This behavior confirms that our encoder successfully learns to represent the underlying bulk spectral features while being robust to anomalous variations.

Figure 5.

Visualization of latent space relationships through cosine similarity between 48‐dimensional encodings of EELS‐SI sub‐image pairs. Each point compares an unmodified image (Y axis) with its anomaly‐injected counterpart (X axis). The diagonal values close to 1 demonstrate that the encoder places paired images in nearly identical positions in the latent space, confirming that our model successfully recognizes anomalous spectra as variants of their bulk counterparts.

4. Conclusion

We have demonstrated a novel approach for automated anomaly detection in EELS‐SI data using a 3D Convolutional Variational Autoencoder. Our method reliably outperforms traditional PCA‐based approaches across various ΔE shift magnitudes while preserving spectral‐detail fidelity, though this performance gap narrows with decreasing anomaly concentration. Analysis of the latent‐space representations reveals that the model develops effective encoding strategies that adapt to local spectral features, enabling robust anomaly detection without compromising reconstruction quality. While manual analysis confirms that our VAE approach maintains high reconstruction quality and feature preservation in lower‐SNR regions such as the O K edge, challenges remain regarding the development of quantitative metrics that can reliably assess reconstruction performance in these noise‐dominated spectral regions. Future work will therefore focus on establishing robust evaluation metrics that can better capture the demonstrated capabilities of our method, particularly for subtle spectral features where traditional correlation‐comparison metrics become unreliable due to noise. In future work, we plan to broaden our benchmark suite to include state‐of‐the‐art 3D generative‐adversarial detectors—such as PatchGAN and StyleGAN variants—so that the relative merits of variational versus adversarial latent regularisation can be quantified under identical protocols. We also plan to couple our encoder with diffusion‐based generative priors,^{[ 37 ]} which may further enhance the recovery of fine spectral details in low‐SNR edges. In addition, we will investigate transfer learning across chemically distinct materials to determine the minimum bulk data required for robust performance and explore integration of the detector into an active‐learning STEM workflow for real‐time identification of rare events. These models are effective at learning complex noise patterns and can efficiently generate high‐quality samples, which could potentially improve the recovery of fine spectral features in low‐SNR regions.^{[ 38} , ³⁹ , ⁴⁰ , ⁴¹ , ⁴² , ⁴³ , ⁴⁴ , ^{45 ]}

Conflict of Interest

The authors declare no conflict of interest.

Author Contributions

S.S. designed and implemented the 3DCVAE model and the codebase, performed the primary data analysis, and drafted the manuscript, R.A.W.A. assisted with data analysis, J.P.B. conceptualized the project, provided implementation guidance, and advised on core technical decisions, and R.F.K. supervised the project and edited the manuscript.

Supporting information

Supporting Information

Sultanov S., Ayyubi R. A. W., Buban J. P., and Klie R. F., “Robust Spectral Anomaly Detection in EELS Spectral Images via 3D Convolutional Variational Autoencoders.” Small 21, no. 33 (2025): 21, 2503019. 10.1002/smll.202503019

Data Availability Statement

The code and experimental data used in this study are publicly available in the GitHub repository at https://github.com/seyfal/3DCVAE. This repository includes both the implementation of the 3DCVAE model and the EELS SI datacube used in all experiments, which can be found in the data folder.