# aquaDenoising: AI-enhancement of in situ liquid phase STEM video for automated quantification of nanoparticles growth

Adrien Moncomble, Damien Alloyeau, Maxime Moreaud, Abdelali Khelfa, Guillaume Wang, Nathaly Ortiz-Peña, Hakim Amara, Riccardo Gatti, Romain Moreau, Christian Ricolleau, et al.

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## ► To cite this version:

Adrien Moncomble, Damien Alloyeau, Maxime Moreaud, Abdelali Khelfa, Guillaume Wang, et al. "aquaDenoising: AI-enhancement of in situ liquid phase STEM video for automated quantification of nanoparticles growth." Ultramicroscopy, In press, 271, pp.114121. 10.1016/j.ultramic.2025.114121. hal-04966490v3

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# aquaDenoising: AI-enhancement of in situ liquid phase STEM video for automated quantification of nanoparticles growth

Adrien Moncomble<sup>a,†</sup>, Damien Alloyeau<sup>a,†,*</sup>, Maxime Moreaud<sup>b</sup>, Abdelali Khelfa<sup>a</sup>, Guillaume Wang<sup>a</sup>, Nathaly Ortiz-Peña<sup>a</sup>, Hakim Amara<sup>a,c</sup>, Riccardo Gatti<sup>c</sup>, Romain Moreau<sup>c</sup>, Christian Ricolleau<sup>a</sup>, Jaysen Nelayah<sup>a,†,*</sup>

## ARTICLE INFO

**Keywords:**

Liquid phase STEM

Nanoparticles growth

Kinematic simulation

Deep learning

Gold nanoparticles

## ABSTRACT

Automatic processing and full analysis of *in situ* liquid phase scanning transmission electron microscopy (LP-STEM) acquisitions are yet to be achievable with available techniques. This is particularly true for the extraction of information related to the nucleation and growth of nanoparticles (NPs) in liquid as several parasitic processes degrade the signal of interest. These degradations hinder the use of classical or state-of-the-art techniques making the understanding of NPs formation difficult to access. In this context, we propose aquaDenoising, a novel simulation-based deep neural framework to address the challenges of denoising LP-STEM images and videos. Trained on synthetic pairs of clean and noisy images obtained from kinematic-model-based simulations, we show that our model is able to achieve a fifteen-fold improvement in the signal-to-noise ratio of videos of gold NPs growing in water. The enhanced data unleash unprecedented possibilities for automatic segmentation and extraction of structures at different scales, from assemblies of objects down to the individual NPs with the same precision as manual segmentation performed by experts, but with higher throughput. The present denoising method can be easily adapted to other nanomaterials imaged in liquid media. All the codes developed in the present work are open and freely available.

## 1. Introduction

Liquid phase transmission electron microscopy (LP-TEM) in liquid cells has become a state-of-the-art technique for unlocking the secrets of nanomaterial formation in solution. This *in situ* technique allows to visualise the nucleation and growth processes at different scales ranging from colloidal assemblies, containing several hundred nanostructures, to single nanoparticles (NPs), allowing their surface dynamics to be monitored with atomic resolution. This versatility opens up a unique window to observe the many atomic-scale mechanisms that govern NP size and shape [1-4]. Typically, the nucleation and growth of NPs in the liquid cell are driven, or at least influenced, by the radiolysis of the solvent, and consequently, the reaction dynamics vary with the electron dose rate, providing a way to control and study kinetic effects [5,6]. Combined with the ability to vary the composition and temperature of the reactive media [7], LP-TEM has allowed the investigation of strategies used in colloidal chemistry to control the habit of nanocrystals such as the seed-mediated synthesis [8,9], diffusion-limited growth [10,11], face-blocking methods [12,13], kinetically-controlled formation [14,

[15] and selective etching [16,17]. High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM), also known as Z-contrast imaging, allows for direct visualisation of the atomic and chemical structures of nanomaterials, both under vacuum and in liquid and gas environments [7,18-20]. This technique offers several advantages for the study of metal NPs in solutions: a better resolution and contrast when imaging high Z nanomaterials in thick liquid layers [21], the possibility of combining Z-contrast imaging with local element identification by energy dispersive X-ray spectroscopy [22], a clear image of the top membrane of the liquid cell, near which nucleation and growth processes preferentially occur, and the straightforward relationship between the electron dose rate ($d_e$) and image magnification. Nevertheless, the processing and analysis of liquid phase STEM (LP-STEM) videos remain a bottleneck that significantly slow down the retrieval of quantitative results on colloid dynamics. Image segmentation is a routine task in (S)TEM data analysis that requires automated procedures when processing large image datasets. Conventional segmentation methods, based on handcrafted parameters, to

<footnote><sup>a</sup> Université Paris Cité, Laboratoire Matériaux et Phénomènes Quantiques, CNRS, F-75013 Paris, France</footnote>

<footnote><sup>b</sup> IFP Energies nouvelles, Rond-point de l'échangeur de Solaize BP 3 69360 Solaize, France</footnote>

<footnote><sup>c</sup> Université Paris-Saclay, ONERA, CNRS, Laboratoire d'étude des microstructures (LEM), F-92322 Châtillon, France</footnote>

<footnote>* Corresponding authors.
E-mail addresses: damien.alloyeau@u-paris.fr (D. Alloyeau), jaysen.nelayah@u-paris.fr (J. Nelayah).</footnote>
<figure><img src="image_5.png" /><figcaption>**Fig. 1.** Geometry and contributions to the HAADF contrast of *in situ* STEM liquid experiments. (a) Schematic of a liquid cell microscopy in STEM configuration. (b) Flower-like gold NPs in water. The arrows indicate to the different contributions to the overall contrast of the STEM image. (1) Spatially varying background intensity due to the bulging of the SiN membranes of the liquid cell. (2) Intensity from an in-focus NP imaged on the upper SiN window. (3) Diffuse intensity from an out-of-focus NP imaged on the lower window. (4) Detection white noise. (c–e) Time series of HAADF-STEM images showing the radiolysis-driven growth of gold NPs in water. The time evolution (in seconds) is shown in yellow.</figcaption></figure>

delineate the NPs from the image background involve two steps: (i) the use of image filtering strategies to improve the signal-to-noise ratio (SNR) of the NPs (Supplementary Material section 1.1) (ii) followed by image binarisation using intensity thresholding algorithms. However, as shown in Fig. 1, LP-STEM cinematography of NP formation presents several contributions to the overall HAADF-STEM contrast that make conventional segmentation methods cumbersome.

First, the SNR of NPs in a filled liquid cell is usually very low. It is generally between 1 and 2 when heavy metal NPs are imaged through the two 50 nm thick SiN membranes and the few hundred nanometres of liquid layer tightly sandwiched between them. Increasing $d_e$ to improve the SNR is not a relevant strategy as it inevitably affects the growth dynamics and the final shape of the NPs. In a general manner, $d_e$ must be considered as a parameter that can be used to tune the dynamics of chemical reactions, or it must remain below the threshold at which radiolysis effects are detected. Secondly, the noise level in LP-STEM images is not uniform due to the spatially varying liquid layer thickness resulting from the bowing of the SiN windows towards the microscope vacuum. The wider the field of view, the greater the non-uniformity. Worse still, the noise content and level across pixels fluctuates continuously and in a completely uncorrelated manner over time as a result of the contrast from NPs growing on the bottom SiN membrane. Because these NPs are way out of focus, they are imaged as randomly distributed localised blurs that distort the intensities of the HAADF-STEM images. Finally, as the size, shape, and SNR of the nanomaterials also evolve over time, the filtering and

thresholding strategies and the corresponding parameters need to be adapted locally in the image and for each frame of the videos. As a result, the automated processing of LP-STEM videos acquired at different magnifications and probe currents is very challenging and the entire data analysis workflow is consequently labour intensive, prone to operator bias and limited in throughput.

The application of deep learning to the acquisition and analysis of (S)TEM data is a rapidly growing field that is pushing further the limits of imaging, diffraction, and spectroscopy techniques available on microscopes by developing automated procedures for microscope alignment, data acquisition, atomic structure or nanoscale morphology analysis and classification, image or spectrum denoising, image segmentation and three-dimensional reconstruction, among others [23–25]. The large datasets generated by the monitoring of dynamic processes and the artefacts induced by the application of external stimuli place *in situ* TEM at the heart of this revolution in data acquisition and analysis [24]. More specifically, the use of convolutional neural networks (CNN), in particular encoder–decoder architectures such as the U-Net architecture [26], has emerged as a robust method for the semantic segmentation of time-series TEM images capturing the dynamics of NP assembly under environmental conditions. Such deep learning (DL) approach has been successfully applied to study the structural dynamics of metal catalysts under gas environments [27,28]. However, a dataset of simulated noiseless and noisy images is required to train CNN architectures. Since the noise is specific to the imaging conditions, each *in situ* TEM experiment requires specifically trained
CNN. For LP-TEM, Yao et al. have recently developed a customised automated analysis framework, based on a U-Net neural network, to segment LP-TEM images of metal NPs in solution. By achieving a high tolerance to low SNR, spatial heterogeneity in particle intensity and particle overlap, they successfully studied the motion, etching, and self-assembly of inorganic NPs in solution [29]. However, although HAADF-STEM is widely used to study the nucleation and growth of metal NPs in liquid, the development of DL approaches to process the specific noise content and level and features of in situ LP HAADF-STEM images, which is a prerequisite for robust segmentation of such data, is still lacking.

Here, we propose a new approach based on a CNN for state-of-the-art, robust and automatic denoising of LP HAADF-STEM videos. Trained on simulated pairs of noisy and noise-free HAADF-STEM images, our model is able to achieve a fifteen-fold improvement in the SNR of Au NPs growing in solution and an effective minimisation of image blurring due to out-of-focus NPs. The model has been applied to the study of Au NP growth processes, demonstrating that image denoising subsequently enables the accurate and automated segmentation of LP-STEM videos with extraction of quantitative information on growth kinetics at both the ensemble and single particle levels.

## 2. Data and network design

Denoising of time series LP HAADF-STEM images using neural networks relies on the definition of two crucial components: (i) a representative image database, and (ii) a specific neural network architecture. The combination of these two elements results in efficient and reliable neural networks capable of denoising experimental noisy images. In this work, we started by defining and optimising the simulations of realistic images. Then, we used them for the training of several neural networks to test and compare their performances for denoising experimental LP HAADF-STEM acquisitions.

### 2.1. Training database generation

#### 2.1.1. Synthetic samples modelling

In a deep learning project, the training dataset must contain a large set of initial data and their associated expected results. In the present denoising task, the initial data are the noisy images and the expected results are noise-free images of the same objects. The acquisition of experimental LP STEM noisy images is straightforward but it is impossible to get access to the associated noise-free images. To overcome this limitation, our approach was to create synthetic datasets with the same characteristics as the experimental images. Denoising performance is correlated with the ability to achieve a good signal/noise decomposition. Therefore, the training datasets must be representative of the experimental images, including a realistic intensity distribution even though the latter do not include all the physical processes contributing to the contrast (Fig. 1b). Thus, the simulations performed in this work do not take into account the full dynamic of the transmission and scattering of the electrons, which is computationally demanding. Instead, we generated training datasets containing pairs of synthetic noisy and corresponding noise-free reference HAADF-STEM images using a kinematic scattering method [30,31]. Within this approach, the training datasets are faster to construct and result in a fully realistic representation of the objects to be imaged. This provides a more reliable denoising prediction than we would get with fewer images generated by taking into account the dynamic of the scattering processes.

The first requirement for such simulations is the construction of 3D models of the nano-objects observed in the 2D experimental images. In the present work, as we are interested in the growth of gold nanocubes and nanorods, we have built a library of the main morphologies and sizes observed experimentally (Fig. 2a). As high resolution cannot be achieved with our experimental setup in LP STEM, it is not necessary

to represent the NPs at atomic resolution. All NP geometries were thus represented as convex solids, defined by the 3D position of their vertices and their faces. Through scaling, rotation and translation, we have composed a wide set of geometries size and orientation. The physical size of the NPs does not matter for the denoising, only the size they occupy on the projected image. As a result, if two particles of different sizes occupy the same area of the image at different magnifications and both are not atomically resolved, then they can be denoised by the same trained neural network. In terms of particle shapes, it is not necessary to perfectly define all the zoology of the nano-objects in the experimental sample, but only their main features. For instance, to denoise flower-like particles, training on images containing cubes, octahedra, and icosahedra was sufficient (see Fig. S2a-c in Supplementary Material section 1.3). However, if the sample now contains rods, a neural network trained on the same shapes will not work. As none of the shapes in the training data are elongated, the rods will be understood and denoised as a superposition of small round particles (Fig. S2d-f). In the following, the training datasets consisted of NPs of different sizes, belonging to the five shape categories presented in Fig. 2a, cubes, octahedra, icosahedra, truncated octahedra and pentagonal rods.

#### 2.1.2. LP STEM images simulations

Noise-free kinematic HAADF-STEM images (equivalent to unsupported monometallic NPs in vacuum) were simulated according to Eq. (1), which relates the pixel intensity to the corresponding projected mass thickness:

$$I(X) = \sum_{X'} \frac{Z^\alpha t(X')}{2\pi \sigma^2} e^{-\frac{(x-x')^2}{2\sigma^2}} \quad (1)$$

where $X = (x, y)$ is the probe position and $X' = (x', y')$ are the positions in the 2D local thickness map $t(X')$. $Z$ is the atomic number and $\alpha$ is a power exponent that accounts for the scattering of the primary electron beam into the HAADF detector and $\sigma$ is the radius of the electron probe.

2D thickness maps, $t$, of the objects in the image were evaluated from the 3D models as described in Fig. 2a (see Fig. S1 in Supplementary Material section 1.2.1). At 200 kV and with an inner HAADF collection angle of 68 mrad, the value of $\alpha$ was evaluated according to [32]. The probe size $\sigma$ was taken to be equal to the STEM resolution of the double-aberration corrected JEOL ARM 200F microscope used in this work. The values of all simulations are listed in Table 1. An example of resulting simulated images are shown in Fig. 2b.

For the simulation of the kinematic noisy HAADF-STEM images, all the characteristics of in situ liquid microscopy imaging described in Fig. 1 are taken into account and added to the images: (i) the broadening of the electron beam due to its interaction with the liquid cell membranes and the liquid environment, (ii) the presence of out-of-focus NPs which appear as diffuse intensity superimposed to the in focus NP intensity and (iii) white noise due to variations in the detection efficiency of the HAADF detector. Total noise content in the images is the sum of these two last contributions with the signal of interest being the in focus NPs. In this work, CNN are trained not only to identify and to remove all the noise but also to correct for the beam broadening so as to enhance the quality of the signal in the videos. For kinematic-based HAADF-STEM simulation mimicking liquid conditions, the intensity at each position is thus defined in Eq. (2):

$$I(X) = \sum_{X'} \frac{Z^\alpha t_f(X')}{2\pi \sigma_f^2} e^{-\frac{(x-x')^2}{2\sigma_f^2}} + \sum_{X''} \frac{Z^\alpha t_o(X'')}{2\pi \sigma_o^2} e^{-\frac{(x-x'')^2}{2\sigma_o^2}} + \mathcal{N}(0, \sigma_n^2) \quad (2)$$

Similar to Eq. (1), $X$ is the probe position, $X'$ are the positions in the 2D local thickness map $t_f(X')$ of the in-focus particles and $X''$ are the positions in the 2D local thickness map $t_o(X')$ of out-of-focus particles. Random noise is added as white noise $\mathcal{N}(0, \sigma_n^2)$, following a
<figure><img src="image_6.png" /><figcaption>**Fig. 2.** Simulation of HAADF-STEM images in different media of Au NP models. (a) Examples of NP models with different morphologies. The blue NP is an icosahedron, the green is an octahedron, the purple is a cube, the red is a truncated octahedron, and the orange is a pentagonal rod. (b) Simulation of an assembly of NPs in vacuum and (c) in liquid conditions according to the setup in Fig. 1.</figcaption></figure>

<caption>**Table 1**</caption>

Values of the parameters for the simulations of HAADF-STEM images in vacuum and in liquid according to Eqs. (1) and (2) respectively.

<table><thead><tr><td>Simulations parameters</td><td>Value</td></tr></thead><tbody><tr><td>α</td><td>1.65</td></tr><tr><td>σ</td><td>0.08 nm</td></tr><tr><td>σ<sub>f</sub></td><td>1 nm</td></tr><tr><td>σ<sub>o</sub></td><td>25 nm</td></tr></tbody></table>

Gaussian distribution. The standard deviation $σ_n$ depends on the target SNR of the images to be denoised as described in section 1.2.2 of the supplementary material.

For gold NPs in a liquid cell with a spacer of 150 nm, De Jonge calculated the density of scattered electrons to evaluate the probe diameter and found a $σ_f$ of 1 nm [33]. When the probe reaches the plane of the out-of-focus particles, $σ_o$ is roughly estimated to be 25 nm in diameter from the analysis of the intensities of the out-of-focus objects in the experimental images (Table 1). Due to the presence of liquid and of the interaction with the electron beam, NPs can only be acquired experimentally if they are fixed to one of the SiN membranes. Therefore, only two beam distributions, $σ_f$ and $σ_o$, are needed, one for each possible image plane on which NPs can rest. As a result, images with all these *in situ* liquid features can be computed (Fig. 2c).

## 2.2. Neural networks architectures

Denoising was performed using PDHM-net, a densified U-Net like architecture (Supplementary Material section 1.4.1). PDHM-net is an optimised version of the UNet++ CNN algorithm developed in 2018 by Zhou et al. [34]. It has been shown to outperform other architectures in the denoising task. PDHM-net is a convolutional encoder-decoder network with denser intermediate connections. This network learns high- and low-level image features using 3 × 3 convolution, batch normalisation, ReLU activation, followed by max-pooling sub-sampling operations, and then reconstructs the output from upsampling

by depth-to-space subpixel convolution layers [35]. The spatial representativeness of the image details is preserved by the highly accurate upscaling and by reducing the gradient vanishing through the dense paths available between the different depth layers and between the encoder and decoder parts. In the present work, the performances of PDHM-net were evaluated against those of a standard U-Net architecture [26], Noise2Void (N2V) [36] and a classical set of Gaussian filters (Supplementary Material section 2.1).

To train the networks, a dataset of 50 synthetic 2048 × 2048 pixel square image pairs, containing uniformly distributed NPs, is first simulated according to equations (1) and (2). Using a stochastic patch procedure of size 128 × 128, each image was then decomposed into 512 randomly extracted patches and normalised between 0 and 1 [37]. In total, the dataset thus consists of 25 600 pairs of *in situ* liquid and vacuum simulated images with 18 432 pairs for training, 4608 pairs for the validation and 2560 pairs for the final tests. The unsupervised N2V model only takes liquid noisy images as an input, while PDHM-net and U-Net architectures require the associated vacuum reference images.

To effectively train PDHM-net and U-Net, we propose an image-to-image training method using a two-component loss function constructed on two performance indicators (i) the Structural SIMilarity index (SSIM) [38] and (ii) the Symmetric Mean Absolute Percentage Error (SMAPE) between denoised and ground truth clean patches. The SSIM function measures the similarity between the features of the two images, whereas the SMAPE function reflects the difference between the intensity of the predicted images and the noiseless target. The loss function was defined as a ratio of 0.84 SSIM and 0.16 SMAPE (Supplementary Material section 1.4.2). To evaluate the accuracy of the models, we compute the SSIM and the peak signal-to-noise ratio (PSNR) on the reconstructed images. PSNR and SMAPE both quantify the same feature of the image reconstruction, the pixel-by-pixel difference between the expected and predicted images. In the following, PSNR is used as it is easier to interpret and is a more standard metric for the denoising tasks.

The denoising process for a noisy image follows a similar approach to the preparation of the images in the training dataset. First, the image
<figure><img src="image_7.png" /><figcaption>**Fig. 3.** Evaluation of the different denoising techniques on a simulated image of gold NPs. (a) Initial noisy image simulated to match the typical noise and background levels found in SiN liquid cells with Eq. (2). Red arrows indicate the contribution of out-of-focus NPs in the noisy image. (b) Noise-free image simulated without noise using Eq. (1). (c) Comparison of the profile of a cube nanoparticle between the raw ground-truth signal in dashed black, the denoising result obtained with PDHM-net in blue and U-Net in yellow. Denoising results with (d) Gaussian filters, (e) Noise2Void, (f) PDHM-net, (g) U-Net.</figcaption></figure>

is normalised to values between 0 and 1. It is then divided into a series of 128 × 128 patches. This step is slightly different from training because training uses a wider range of intensities to help the model distinguish between signal and noise. For denoising, however, it is important to maintain consistent relative intensities between patches, so normalisation is performed first. Each patch is then passed through the neural network, which predicts the corresponding denoised patches. Finally, the full image is reconstructed by averaging the overlapping intensities of multiple patches, following the same sequence used to create the patches [37].

Image simulations, model training and evaluation were performed on a single desktop with an Intel® Core™ I7-9700 CPU, an NVIDIA Quadro P2200 graphic card, and 30 Gb of RAM. All reported execution times were measured on this machine. Simulations and deep learning denoising algorithms are implemented using Python 3.9 and Tensorflow 2.10.1 [39]. All the code presented is open and available on GitHub [40]. The N2V source code is freely available [36]. The convergence time of U-Net was 2 h with an SSIM of 95.7% on the validation dataset. For the PDHM-net, the convergence time extends to 6 h with a final SSIM of 95.5%. N2V took 8 h to converge with an SSIM of only 14.6%. Once trained, image denoising is faster to compute. For an image of 1024 × 1024 pixels, image denoising takes 2.5 s with PDHM-net, 0.5 s with U-Net and 6 s with N2V.

# 3. Results and discussion

## 3.1. Denoising synthetic images

First, we evaluate and compare the denoising performance of the three networks on the synthetic HAADF-STEM images from the test dataset, together with the classical Gaussian filters. Starting from the noisy images (Fig. 3a), all methods are applied to extract the signal shown in the ground truth images (Fig. 3b) from the different noise sources. Of all the methods, the Gaussian filters show the worst results, as the images remain a noisy and grainy appearance, although the contrast between the particles and the background is improved (Fig. 3d). The denoising obtained with the N2V network removes the random noise of the simulated readout noise (Fig. 3e). However, the contributions of the out-of-focus NPs are still present. Finally, both PDHM-net and U-Net show similar results, where all noise sources are

<caption>**Table 2**</caption>

Table comparing the different methods evaluated with the SSIM and PSNR on the same synthetic images. For both metrics, the higher the score, the better the method. The best scores are in bold.

<table><thead><tr><td>Methods</td><td>SSIM</td><td>PSNR (dB)</td></tr></thead><tbody><tr><td>Gaussian filters</td><td>0.173</td><td>21.3</td></tr><tr><td>Noise2Void [36]</td><td>0.178</td><td>21.5</td></tr><tr><td>U-Net [26]</td><td><b>0.957 ± 0.004</b></td><td><b>30.2 ± 0.6</b></td></tr><tr><td>PDHM-net</td><td><b>0.960 ± 0.004</b></td><td><b>30.2 ± 0.7</b></td></tr></tbody></table>

efficiently removed (Fig. 3f-g). Out-of-focus NPs are no longer present and the contour of the NPs is well defined, with PDHM-net being qualitatively sharper than U-Net (Fig. 3c). This difference is mainly due to the additional connections between the layers and the optimised upsampling layers, which help in the final reconstruction of the images.

Since the ground truth reference images are known, SSIM and PSNR scores are calculated to quantitatively compare the different approaches (Table 2).

Both PDHM-net and U-Net outperform the Gaussian filters and N2V for the two metrics and have a similarity of about 96% with the references. These results confirm the applicability of the developed approach to experimental images, since the synthetic images include all the contributions in the experiment.

## 3.2. Denoising experimental images

A comparative analysis is ultimately performed on experimental datasets of growing Au NPs acquired by LP-STEM. Experimental details of the *in situ* NP growth experiments are described in [41]. Briefly, the sample solution consists of 1 mM of gold(III) chloride trihydrate (HAuCl₄) purchased from Sigma Aldrich Inc. diluted in Milli-Q water. All *in situ* liquid STEM videos to be denoised were acquired on a double-corrected cold FEG JEOL ARM 200F operating at 200 kV using heating liquid cells commercialised by Protochips with 150 nm spacers. The STEM HAADF signals were collected on a detector with a 30 mrad convergence semi-angle and 68-280 mrad collection angle. Nucleation and growth of Au NPs are driven by electron beam controlled water radiolysis. The growth rate and the final shape of the NPs are governed by the electron dose rate and the temperature, which is here set at 25 °C [7]. The STEM-HAADF time series are captured with the
<figure><img src="image_8.png" /><figcaption>**Fig. 4.** Evaluation of the different denoising techniques on an experimental image of gold NPs. (a) Initial noisy experimental image in liquid conditions. Denoising results with (b) Gaussian filters, (c) Noise2Void, (d) PDHM-net, (e) U-Net. (f) Comparison of the profile of a cube nanoparticle between the denoising result obtained with PDHM-net in blue and U-Net in yellow.</figcaption></figure>

acquisition software Gatan DigitalMicrograph at 1 frame/s in the HD Video mode in the .avi format. The time-series show NP dynamic feature across ranges of sizes (20 to 100 nm) and shapes (mostly cubes and rods) as they grow on a fluctuating background, all captured at nanometre resolution.

Using the same four methods as for the synthetic images, the video frames were denoised (Fig. 4). After denoising, the experimental images show the same features as the simulated images. Gaussian filters show residual noise (Fig. 4b). N2V removes the random noise but cannot remove the contribution of out-of-focus NPs (Fig. 4c). PDHM-net and U-Net work well (Fig. 4d–e), although PDHM-net is slightly sharper than U-Net (Fig. 4f).

SSIM and PSNR cannot be measured without reference noiseless images. As a result, we first quantify the performance of each image based on the SNR of the images (Supplementary Material section 1.1, Table 3). PDHM-net denoised images have the best SNR, with a fifteen-fold increase in SNR on the experimental noisy images. To go further, the performance of each method is also evaluated based on the automatic segmentation of the corresponding denoised image using the state-of-the-art software *ilastik*. The latter is a semi-automatic image segmentation machine learning algorithm capable of classifying pixels in images based on a small subset of pixels given by the user [42]. As ground truth for the segmentation of the image, a reference manual segmentation of one of the frames of the video is mandatory. It is compared with the segmentation of all the methods to calculate their SSIM and their intersection over union (IOU) scores [43]. At the same time, it is also compared with the manual segmentation obtained by four additional experts to assess the variability in manual segmentation (Table 3). On the basis of denoising, PDHM-net is the most performant method as it shows the best SNR, SSIM and IOU. Compared to the manual results of the experts, PDHM-net is in the same range as the fluctuating human interpretation of the images, while being much faster. The manual segmentation of a single image of 512 × 512 pixels takes about 30 min, while the denoising and segmentation takes a few seconds. In the rest of this work, we will mainly focus on the results extracted from images denoised with PDHM-net.

<caption>**Table 3**</caption>

Table comparing the different methods using the SNR to evaluate the denoising capabilities and the SSIM and IOU to evaluate the segmentation of the experimental images. For all metrics, the higher the scores, the better the method. The best scores are in bold. For SNR and the segmentation, the distinction between particles and background is made manually directly on the noisy images.

<table><thead><tr><th>Methods</th><th>SNR</th><th>Segmentation SSIM</th><th>Segmentation IOU</th></tr></thead><tbody><tr><td>Experimental noisy images</td><td>1.614</td><td>0.575</td><td>0.699</td></tr><tr><td>Gaussian filters</td><td>2.556</td><td>0.558</td><td>0.688</td></tr><tr><td>Noise2Void [36]</td><td>2.529</td><td>0.580</td><td>0.703</td></tr><tr><td>U-Net [26]</td><td>23.04</td><td>0.587 ± 0.004</td><td>0.744 ± 0.003</td></tr><tr><td>PDHM-net</td><td><b>25.36</b></td><td><b>0.632 ± 0.005</b></td><td><b>0.769 ± 0.002</b></td></tr><tr><td>Manual segmentation</td><td>-</td><td>0.645 ± 0.017</td><td>0.719 ± 0.009</td></tr></tbody></table>

In Fig. 5c, we compare the profile of the original image and its denoised version by PDHM-net. We can see that the standard deviation of the noise is reduced from about 0.14 to 0.02. The contrast is greatly improved as the mean intensity of the background in the denoised images is close to zero. It is due to the full removal of all noise contribution and, in particular, the contrast contribution of the support. Finally, the position of the peaks is unchanged, showing that denoising does not degrade the signal of interest.

This demonstrates the strength of our proposed denoising method. All objects are correctly extracted from the noise and the relative intensity of the peaks is qualitatively accurate. A quantitative evaluation of the intensities is not possible due to the lack of noise-free experimental reference of the signal. Since the training of the neural network was done on simulated images taking into account all the contributions from the experimental images, we can confidently attest that the performance on experimental images is equal to that on simulated images, even if the score may be slightly lower.

### 3.3. Quantitative study of growth of gold nanoparticles

From the PDHM-net denoised LP-STEM videos, the study of the dynamical evolution of the NPs is facilitated by the removal of the
<figure><img src="image_9.png" /><figcaption>**Fig. 5.** Comparison of the profile in one frame of an experimental video of Au NPs growth. (a) Frame from the original video and (b) the same frame denoised with PDHM-net. (c) Comparison of the intensity profiles from the original and the denoised frames measured along the line drawn in each image with corresponding colours.</figcaption></figure>

noise. The growth and the shape changes of the particles are visually and precisely detectable. In order to automatically quantify the growth of gold NPs, a segmentation step is necessary as it makes the boundary and the contour of the particles accessible. We focus on the video S1 from the supplementary materials and study the percentage coverage of the field of view by NPs as a function of the time (Fig. 6a-c). Thanks to the automatic segmentation of the PDHM-net denoised individual frames, the diameter of the NPs can be measured. Since none of the particles are perfect spheres, the mean diameter, defined as the average of the orthogonal major and minor diameters, is measured for each time step (Fig. 6d). Over time, NPs become larger and cover more and more of the field of view (Fig. 6e). The overall mean diameter increases at a steady rate of about 1 nm per second, but the diameter distribution of the NPs becomes more spread out. This can be explained by the different geometries of the NPs in the sample.

To emphasise the efficiency of the segmentation of denoised videos, we apply it to the resolution of a general particle characterisation task. In Fig. 7, manual segmentation performed by an expert and automatic segmentations obtained with *ilastik* are compared to extract the size distribution of NPs. Two size populations are identified, one with a mean diameter of around 40 nm and the other one around 60 nm (Fig. 7a). In the segmentations obtained directly from the experimental

noisy image and from N2V, neither of these populations can be clearly identified (Fig. 7b-c). Both show a relatively uniform distribution that includes false particles smaller than 10 nm in diameter. These false NPs result from residual noise in the images. In comparison, the size distribution obtained by the segmentation of the PDHM-net denoised image is closer to the reference manually obtained size distribution (Fig. 7d). This is the result of the better removal of the noise contribution from the image.

Going one step further, we can even consider individual particles. Using the *Trackmate* plugin from *ImageJ*, it is possible to track single particles frame by frame across the video [44,45]. In the video published online or in the supplementary material (Video S2), nanocubes and nanorods were tracked to quantitatively evaluate the growth rate in both populations [46]. The growth of cubes tends to be isotropic, while that of the rods is anisotropic. Within the approximation that the height of a nanocube is equal to the length of its sides and that the nanorod has a circular section, it is possible to estimate the 3D morphology of both geometries from the 2D projection. The volume evolution over time is shown in Fig. 8. Both particles grow at almost the same rate of about 6 · 10³ nm³ per second in the initial phase of the particle growth. The growth rate reaches a plateau, indicating that the active surfaces are screened by surrounding particles. This plateau always occurs earlier
<figure><img src="image_10.png" /><figcaption>**Fig. 6.** Analysis of the gold NPs growth from video denoised with PDHM-net. (a–c) Frames of the analysed video. The time evolution (in seconds) is indicated in yellow. (d) Evolution of the distribution of the mean diameter of NPs for different time steps. There is a shift in the mean of the distributions of 0.98 nm/s over time. (e) Evolution of the coverage of the field of view with nanoparticles as a function of time. An uncertainty of 2.5% is used to account for the errors of the automatic segmentation.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Fig. 7.** Size distribution of NPs in an experimental image using different techniques. (a) Manual selection of the particles. Automatic segmentation of (b) the raw noisy experimental image, (c) the image denoised by Noise2Void and (d) the image denoised by PDHM-net. (e) Original image from which the size distributions were obtained.</figcaption></figure>

for rods (10 s or less in the video) than for cubes (40 s or more). Assuming a uniform initial distribution of the NPs, since nanorods grow in a particular direction, they will come in closer proximity to other particles in a shorter time than isotropically growing nanocubes.

## 4. Conclusion

In this work, we present a method based on DL to denoise *in situ* LP HAADF-STEM images and videos. First, the training dataset is generated by using kinematic simulations of HAADF-STEM images with and without noise. Once a dataset is generated from these simulations and the images are transformed, a neural network can be trained. Comparing several classical and state-of-the-art methodologies, PDHM-net works the best for the denoising of synthetic and experimental images. This DL denoising network was applied to videos of gold NPs to get a better view and understanding of the growth mechanism. For the

first time, we are able to automatically extract quantitative information on the evolution of the particles over time and at different scales, from the particles assemblies to the single particles with the same quality as the manual segmentation performed by experts. This open access and freely available method will pave the way for more statistically accurate studies. Instead of a small set of hand-picked NPs, we now have access to all the NPs visible in any LP HAADF-STEM images and videos.

To go beyond the study of gold NPs, this approach can be adapted to other materials, especially those that are sensitive to the electron beam. LP-STEM is a growing field but the characterisation of the various dynamic phenomena of interest is mostly limited by the electron dose and the resulting lack of signal. At the same time, lower dose rate acquisitions and higher frame rate videos are also possible as analysis is no longer a problem. As a result, new data can be obtained that allow a better understanding of the formation mechanisms. With adapted
<figure><img src="image_12.png" /><figcaption>Fig. 8. Evolution of the estimated volume of a single NP as a function of time. Growth of (a) a nanocube and (b) a nanorod.</figcaption></figure>

computational capabilities, this can even be extended to on-the-fly
denoising, providing researchers with an enhanced view of the system
of interest during *in situ* liquid experiments.

CRediT authorship contribution statement

**Adrien Moncomble:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Resources, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Damien Alloyeau:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Maxime Moreaud:** Writing – review & editing, Validation, Software, Methodology, Investigation, Funding acquisition, Conceptualization. **Abdelali Khelfa:** Writing – review & editing, Resources, Formal analysis, Data curation. **Guillaume Wang:** Writing – review & editing, Resources, Methodology, Funding acquisition, Data curation. **Nathaly Ortiz-Peña:** Writing – review & editing, Resources, Funding acquisition, Data curation. **Hakim Amara:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Riccardo Gatti:** Writing – review & editing, Validation, Software, Resources, Methodology, Funding acquisition. **Romain Moreau:** Writing – review & editing, Software, Investigation, Data curation. **Christian Ricolleau:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.
**Jaysen Nelayah:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.

Declaration of competing interest

The authors declare the following financial interests/personal rela-
tionships which may be considered as potential competing interests:
Christian Ricolleau reports financial support was provided by French
National Research Agency. If there are other authors, they declare
that they have no known competing financial interests or personal
relationships that could have appeared to influence the work reported
in this paper.

Acknowledgements

The authors acknowledge the French National Research Agency
under the ARTEMIA project (ANR-21-CE42-0012) for their financial
support.

**Appendix A. Supplementary data**

Supplementary material related to this article can be found online
at https://doi.org/10.1016/j.ultramic.2025.114121.

Data availability

Data will be made available on request.

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