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Yasuhiko Igarashi, [Naoka Nagamura](https://orcid.org/0000-0002-7697-8983), Masahiro Sekine, Hirokazu Fukidome, Hideitsu Hino, Masato Okada

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[Sparse coding-based multiframe superresolution for efficient synchrotron radiation microspectroscopy](https://mdr.nims.go.jp/datasets/144e363b-1e09-45ec-b868-7605b78f0e2d)

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© The Author(s) 2025. Open Access  This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit ​h​t​t​p​:​/​​/​c​r​e​a​​t​i​v​e​c​o​​m​m​o​n​​s​.​o​r​g​​/​l​i​c​e​​n​s​e​s​/​b​​y​-​n​c​​-​n​d​/​4​.​0​/.†Yasuhiko Igarashi and Naoka Nagamura have contributed equally to this work.*Correspondence:Yasuhiko Igarashiigayasu1219@cs.tsukuba.ac.jpNaoka NagamuraNAGAMURA.Naoka@nims.go.jp1Institute of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 3058573, Japan2Photoemission Group, National Institute for Materials Science, 3-13 Sakura, Tsukuba, Ibaraki  3050003, Japan3Graduate School of Advanced Engineering, Tokyo University of Science, 6-3-1 Niijuku, Katsushika, Tokyo 1258585, Japan4Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aobaku, Sendai, Miyagi 9808577, Japan5Department of Advanced Data Science, Research Center for Statistical Machine Learning, The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa,  Tokyo 1908562, Japan6Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5, Kashiwanoha, Kashiwa,  Chiba 2778561, JapanAbstractIn nanostructure extraction, advanced techniques like synchrotron radiation and electron microscopy are often hindered by radiation damage and charging artifacts from long exposure times. This study presents a multiframe superresolution method using sparse coding to enhance synchrotron radiation microspectroscopy images. By reconstructing high-resolution images from multiple low-resolution ones, exposure time is minimized, reducing radiation effects, thermal drift, and sample degradation while preserving spatial resolution. Unlike deep learning-based superresolution methods, which overlook positional misalignment, our approach treats positional shifts as known control parameters, enhancing superresolution accuracy with a small, noisy dataset. Additionally, our sparse coding method learns an optimal dictionary tailored for nanostructure extraction, fine-tuning the SR process to the unique characteristics of the data, even with noise and limited samples. Applied to 3D nanoscale electron spectroscopy for chemical analysis (nano-ESCA) data, our method, utilizing a high-resolution dictionary learned from 3D nano-ESCA datasets, significantly improves image quality, preserving structural details. Unlike state-of-the-art deep learning techniques that require large datasets, our method excels with limited data, making it ideal for real-world scenarios with constrained sample sizes. High-resolution quality can be maintained while reducing the measurement time by over , highlighting the efficiency of our approach. The results underscore the potential of this superresolution technique to not only advance synchrotron radiation microspectroscopy but also to be adapted for other high-resolution imaging modalities, such as electron microscopy. This approach offers enhanced image quality, reduced exposure times, and improved interpretability of scientific data, making it a versatile tool for overcoming the challenges associated with radiation damage and sample degradation in nanoscale imaging.40%Keywords  Sparse coding superresolution, Nanostructure image enhancement, Measurement image analysis, Synchrotron image reconstruction, High-resolution microscopy, Radiation damage reductionSparse coding-based multiframe superresolution for efficient synchrotron radiation microspectroscopyYasuhiko Igarashi1,2*†, Naoka Nagamura2,3,4*†, Masahiro Sekine1, Hirokazu Fukidome4, Hideitsu Hino5 and Masato Okada2,6Igarashi et al. Discover Nano          (2025) 20:102https://doi.org/10.1186/s11671-025-04291-xDiscover NanoR E S E A R C H Open Accesshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/https://doi.org/10.1186/s11671-025-04291-xhttp://crossmark.crossref.org/dialog/?doi=10.1186/s11671-025-04291-x&domain=pdf&date_stamp=2025-7-31  IntroductionTo analyze and extract nanostructures, advanced measurement techniques using syn-chrotron radiation facilities or electron microscopy are commonly employed. These methods are crucial for studying low-dimensional materials, such as atomic layer materi-als and nanowires, which have applications in fields ranging from semiconductor devices to batteries and catalysts [8, 29, 34, 38, 41]. To fully understand the geometric and elec-tronic properties of these materials, it is essential to use measurement techniques that provide high resolution across a broad range from nanometres to micrometres.Photoelectron microscopy is a powerful tool used to study the local electronic states and bonding conditions of materials, particularly for low-dimensional systems [13, 36]. This method can be broadly divided into two types: full-field and scanning photoelec-tron microscopes. Full-field microscopes directly project the image onto a detector using lenses, enabling rapid data acquisition. Scanning microscopes, on the other hand, employ a focused beam to scan across the sample, producing detailed spatial distribu-tions of spectra. While scanning techniques can provide highly accurate spectral data, acquiring high-resolution (HR) images requires scanning in fine steps, which can be a time-consuming process.In this study, we focus on the 3D nanoscale electron spectroscopy for chemical analy-sis (nano-ESCA) system, a versatile scanning photoelectron microscope used in X-ray photoelectron spectroscopy (XPS) imaging [17] (Fig. 1). This system uses high-bright-ness synchrotron X-rays to scan samples and acquire detailed spatial distributions of XPS core-level spectra. Its ability to capture high-resolution and nanoscale images make it ideal for evaluating the performance of our proposed superresolution (SR) method.While high-brightness synchrotron X-rays have reduced the time needed to scan each point [5, 7, 16, 17, 23, 25, 42], they also introduce challenges such as image distortion due to charging, thermal drift, and sample degradation from radiation damage, as shown in the bottom right corner of Fig. 1. These issues are common in scanning microscopes like Raman and scanning electron microscopes. Thus, there is a need for methods that can achieve high resolution and wide coverage while minimizing radiation exposure.Superresolution (SR) technology offers a promising solution to these challenges by generating high-resolution images from multiple low-resolution (LR) measurements, as shown in the bottom right corner of Fig. 1. This method reduces the need for prolongedFig. 1  Research concept: Utilizing machine learning technology to increase the analysis efficiency of analysing inspection data obtained from synchrotron radiation scanning photoelectron microscopy systemsPage 2 of 20Igarashi et al. Discover Nano          (2025) 20:102exposure, thereby mitigating the effects of radiation damage, thermal drift, and sample degradation, all while maintaining the necessary spatial resolution and coverage. SR can be achieved using various techniques, with the simplest being geometrical inter-polation, such as the bicubic method, which relies on pixel value continuity to upscale images. Sparse coding methods [11, 12, 43] represent a more advanced approach, tak-ing advantage of the redundancy in natural image structures. In sparse coding, small image patches are represented as a linear combination of a few basis elements, making it a highly efficient and interpretable technique, especially when dealing with limited data-sets. Sparse coding also allows for the incorporation of known control parameters, such as positional shifts, which is crucial for achieving high-precision SR.In recent years, deep learning-based SR methods [10, 21] have gained popularity due to their ability to automatically extract complex features from large datasets through multiple layers of neural networks. These methods have shown great success in fields such as remote sensing [9, 37], where large amounts of data are available. However, deep learning approaches have notable limitations in scientific imaging tasks, where data may be sparse and noisy. They often struggle to incorporate specific known parameters, like positional shifts, and their black-box nature limits interpretability, making them less suitable for scientific applications where understanding the underlying processes is critical.In this study, we propose a multiframe SR approach for synchrotron radiation micro-spectroscopy images using sparse coding. By reconstructing images from multiple LRIs, our method reduces exposure time while enhancing image quality. This approach addresses key challenges by explicitly accounting for positional shifts as known control parameters, enabling high-precision superresolution even with small and noisy datasets. Additionally, our sparse coding method learns an optimal dictionary tailored for nano-structure extraction, ensuring accurate reconstructions under challenging conditions. Comparative analyses demonstrate that our method outperforms both bicubic interpo-lation and deep learning-based approaches, achieving higher peak signal-to-noise ratio (PSNR) values and more consistent results. Furthermore, our method reduces measure-ment time by over  and has been validated on newly acquired datasets, highlighting its potential for high-resolution imaging in demanding experimental scenarios.40%2  MethodWe first consider a sparse coding SR approach. The proposed algorithm, which is mainly based on [19, 20], consists of dictionary learning and sparse coding for SR.2.1  Dictionary learningTo extract features contained in HRIs of the measured targets, the dictionary is obtained by learning from sufficient training data. For the HRIs, we utilized a dataset of HRIs measured via 3D nano-ESCA, as explained in the next section. For these HRIs, noise removal was performed via a DnCNN [45], and the denoised images were then divided into N patches for dictionary learning. DnCNN, which stands for Denoising Convolu-tional Neural Network, is a deep learning-based model designed for image denoising tasks. It employs convolutional layers to learn and remove noise from corrupted images, outperforming traditional methods.Page 3 of 20Igarashi et al. Discover Nano          (2025) 20:102The HR dictionary   is learned by applying the K-means singular value decomposition (K-SVD) algorithm [1] to the component patches of the denoised HRIs. The K-SVD algorithm is an iterative method used for sparse representation and dic-tionary learning. It extends the k-means clustering approach by applying singular value decomposition (SVD) to update both the dictionary and sparse representations, opti-mizing the representation of data with minimal reconstruction error. For the obtained patch set with a  patch length, the K-SVD algorithm is used to solve the following optimization problem to learn an HR dictionary  :Dh ∈ Rqh×Katom√qhDh ∈ Rqh×KatomDh = argminD,α∥P − Dα∥22 subject to ∀i, ∥αi∥0 ≤ k0,� (1)where   is a matrix in which each patch is a column element,   is a matrix with sparse code  as a column element corresponding to the i-th patch, and  is the maximum number of nonzero elements. The initial dictionary is based on discrete cosine transform (DCT) bases [2] and in the learning process,  is found via the orthogonal matching pursuit (OMP) algorithm. Then,  is fixed, and dictionary  is updated via the K-SVD algorithm.P ∈ Rqh×Kα ∈ RKatom×Kαik0ααD2.2  Superresolution method based on sparse codingSparse coding is a method of reconstructing signals using a dictionary of bases learned from data, which enables highly accurate signal approximation. By sparsely representing the learned bases, this approach can effectively remove noise and artefacts via denois-ing, deburring and SR [11]. This is because the sparse representation captures the most essential features of the data, reducing redundancy and preserving important structural details.We first explain the concept of single-frame SR via sparse coding and then extend this approach to multiframe SR. Let   represent the observed LRI. The goal of SR is to reconstruct an HRI   from , where  . To reduce the computational cost, the SR approach is typically applied to small image regions, known as patches, which are then combined to form the full image. Accordingly, we focus on reconstruct-ing an HRI patch   from a corresponding LR patch  , where  . For each patch, we assume the following degradation process: the HR and LR patches,  and , are related by the observation model  , where G is a degradation opera-tor that includes blurring and downsampling operations and   represents additive noise.Y ∈ RQlX ∈ RQhYQl < Qhx ∈ Rqhy ∈ Rqlql < qhxyy = Gx + εε ∈ RqlWe next consider the degradation operator G. G is generated by  , where H represents the blurring operator and S represents the downsampling operator. We define the blurring operation H as a convolution of the image with an  -pixel Gaussian filter with a standard deviation . The matrix   has elements defined as:  , where i and j are the pixel indices, and the center coordinates are given by   and  . Next, we define a linear downsampling operator S that reduces the resolution by a factor of . The downsampling operator S retains only every -th pixel in both the vertical and horizontal directions. In summary, the blurring operator H is first applied to the HRI,G = SHnblur × nblurσhĤ ∈ Rnblur×nblur[Ĥ]ij =exp(− |i−x0|22σ2h)exp(− |j−y0|22σ2h)∑nbluri,j=1exp(− |i−x0|22σ2h)exp(− |j−y0|22σ2h)x0 = nblur+12y0 = nblur+12srsrPage 4 of 20Igarashi et al. Discover Nano          (2025) 20:102introducing the required blur. The resulting blurred image is then downsampled by the operator S, yielding an LRI basis G.In the sparse coding framework [11, 22, 30], the observed signals are expressed as a linear combination of a few basis vectors, called atoms, selected from a larger set. Let  denote a dictionary consisting of  atoms (  ), and let   be the coefficient vector for the sparse rep-resentation of the patch  . The sparse coding problem can then be formulated as:Dl = [d1, d2, . . . , dKatom ] ∈ Rql×KatomKatomdkk = 1, . . . , Katomα ∈ RKatomy ∈ Rqlminimizeα∥y − Dlα∥22 + η∥α∥1,� (2)where   is the -norm and   is a regularization parameter. With this formulation, the coefficient vector  is sparse, meaning that only a few elements in  are nonzero, allowing  to be well approximated by a small number of atoms. The problem of obtaining  for a fixed dictionary  is referred to as sparse coding.∥α∥1 =∑Kj=1 |αj |ℓ1η > 0ααyαDlWe assume that the HR patch  can be represented as a sparse combination of HR atoms:  . Given this relationship, the LR patch  is approximately related to the HR patch  as follows:xx = Dhαyxy ≃ Gx = GDhα = Dlα,� (3)where  is the LR dictionary generated from  by the degradation process. Each atom in  corresponds to an HR atom in . This leads to the following two-step procedure for single-frame SR: (1) represent the LR patch as a sparse combination of LR atoms, and (2) use the combination coefficients to reconstruct the corresponding HR patch by combining HR atoms, as illustrated in Fig. 2. Before performing single-frame SR, an HR dictionary must be prepared by applying an appropriate dictionary learning algorithm to HR training images.DlDhDlDhNext, we consider multiframe SR with a sparse coding approach as shown in Fig. 2. Suppose that N LRIs   are observed, each being a differentlyYi ∈ RQl , i = 1, . . . , NFig. 2  Overview of the multiframe superresolution (SR) analysis method. This figure illustrates the process of gen-erating an SR image from multiple low-resolution (LR) images (LRIs). The target LRI Y1 is magnified by a factor of three using multiple LRIs Yi . The shift in each LRI, represented by the matrix Wi in 2D space, is estimated or given to accurately align the images. The resulting SR image X is compared with an HR reference image to validate the resolution enhancement achieved with the proposed approachPage 5 of 20Igarashi et al. Discover Nano          (2025) 20:102X ∈ RQhdegraded version of an HRI  . Without loss of generality, assume that  is the target for SR, with the other   LRIs serving as auxiliary images.Y1N − 1We assume that the degradation process for each patch can be modelled as follows: for the target patch , the degradation process is given by Eq. (1). Moreover, for the auxil-iary patches (  ), we assume that  , where  represents the shift and clipping operator corresponding to the i-th LR patch. Once  is estimated, SR based on sparse coding can be performed by stacking the LR dictionaries corresponding to the observations   to form a stacked LR dictionary:y1yii = 2, . . . , Nyi = GWix + εWiWi{yi}Ni=1D̃l =Dl1Dl2...DlN =GDhGW2Dh...GWNDh .� (4)This dictionary is then used to approximate the stacked LR patch  via sparse coding. The HR estimate  is given by:ỹ = [y1 y2 · · · yN ]⊤x̂α̂ = arg minα∥ỹ − D̃lα∥22 + η∥α∥1, x̂ = Dhα̂.� (5)Sparse coding does not demand exact equality,  . Because of this and because of noise and patchwise processing, backprojection [18] is performed to maintain global consistency [19, 40, 43]. In our approach, we perform backprojection on the basis of the consistency between the reconstructed HRI and the SR image by interpolating the LRIs via bicubic interpolation. The synchrotron radiation images used in this study exhibit significant variability in signal intensity across different low-resolution images, with some images showing high intensity in regions where others show the opposite. This level of noise results in instability and inconsistency, which can cause the recon-structed images to be noisy when using the consistency with the target LRIs as a cor-rection factor. To address this issue, we propose a novel approach leveraging the known shift in multiple LRIs. Specifically, we first obtain an SR image by interpolating the LRIs via bicubic interpolation. Then, we shift these SR images according to the known shifts and average them to perform backprojection. This approach, which we define as bicubic stacking, is unique to this study and serves as a bicubic interpolation-based image stack-ing method to enhance the resolution of the LRIs.Dα = xLet  be the SR image obtained through bicubic stacking. To maintain global consis-tency, we perform backprojection by minimizing the discrepancy between the initial SR image  obtained from the SR algorithm and the refined SR image . The minimization problem can be formulated as:ZX0ZminimizeX∥X − X0∥22 + c ∥X − Z∥22 ,� (6)where  is the initial estimate of the HRI obtained from the SR analysis and  is the revised SR image. Here,   is a trade-off parameter. The gradient descent update for the HRI  is given by:  , where   is a step size parameter. Through this iterative process, the SR image  is refined, ensuring that it maintains global consistency with the target LRI while revising the initial estimate  to align more closely with the refined image .X0Zc > 0XXt+1 = Xt − ν [(Xt − X0) + c (Xt − Z)]ν > 0XX0ZPage 6 of 20Igarashi et al. Discover Nano          (2025) 20:102As discussed in the previous paragraph, the major problem of multiframe SR can be reduced to the challenge of accurately estimating the shift and clipping operators . In both sparse coding and deep learning-based multiframe SR tech-niques, the estimation accuracy of positional shifts between frames considerably impacts measurement precision [14, 24, 39].Wi, i = 2, . . . , NIn this study, we assume that the shifts between pixels are known a priori and explore the impact of this assumption on the performance of multiframe SR methods. We com-pare the performance of our multiframe SR method based on sparse coding with two representative state-of-the-art approaches. The first is a method based on sparse cod-ing with shift estimation [20], which is widely used for its interpretability and efficiency in scenarios with limited datasets and known control parameters like positional shifts. The second is a deep learning approach that incorporates shift estimation into its frame-work [37]. This method represents the cutting edge of data-driven techniques, leverag-ing large datasets to automatically extract complex features and achieve high-resolution results. These methods were chosen because they reflect the two dominant approaches to superresolution in the current field: sparse coding, which excels in interpretability and data-limited cases, and deep learning, which performs well when large amounts of data are available. The comparison allows us to evaluate the effectiveness and limitations of each method in achieving HR results. The development of an interpretable HR method, such as the sparse coding approach, is important, and such an approach is anticipated to obtain results that are not only easily understood but also capable of achieving high-accuracy SR. This could further contribute to the derivation of scientific knowledge, par-ticularly when working with relatively small datasets.3  Data acquisition and experimental setup3.1  Training and evaluation datasets for the multiframe superresolution analysis methodIn this study, we utilized 118 HR 3D nano-ESCA datasets, measured between 2011 and 2022, to train dictionary learning models and evaluate the performance of the proposed multiframe SR analysis method. These datasets were obtained using the 3D nano-ESCA system, which incorporates an X-ray focusing system equipped with a Fresnel zone plate and a modified VG Scienta R3000 analyser. The system maintains a high spatial resolu-tion of approximately 100 nm in the in-plane direction, enables depth analysis through angle-resolved detection of photoelectrons, and allows operando measurements by applying an electric field to the sample. This setup has been extensively used for analys-ing various semiconductor device microstructures and energy nanomaterials [3, 26–28, 35]. The HR 3D nano-ESCA datasets cover various materials and technologies, mainly semiconductor devices, graphene, and battery materials.The 3D nano-ESCA system was installed at the University of Tokyo outstation beamline, BL07LSU at SPring-8, and relocated to NanoTerasu in 2023. All the results presented here were obtained with excitation photon energies ranging from 800 eV to 1500 eV. The step sizes between observed points, mostly ranging from  to , mainly include small intervals, with  being the most commonly used step size. These step sizes were applied to ensure evenly spaced measurements across each dataset.0.05µm0.25µm0.1µmThe two-axis piezo scanner is used for precise sample scanning along the x and y direc-tions during SPEM measurements, offering a maximum scan range of100µm × 100µmPage 7 of 20Igarashi et al. Discover Nano          (2025) 20:102with an accuracy of 2nm [17]. Furthermore, the system maintains a high spatial reso-lution of approximately 100nm in the in-plane direction and enables depth analysis through angle-resolved detection of photoelectrons. Therefore, the precision of the piezo scanner is sufficiently high compared to the assumed resolution, and the shift val-ues in the low-resolution images can be regarded as known a priori.The HR 3D nano-ESCA datasets include images of varying sizes, represented by their height and width. The sizes have wide ranges, including small images of   pixels to much larger images of   pixels. Common image dimensions include ,  , and   pixels, reflecting a preference for square images with smaller dimensions. The variety in image sizes suggests that the datasets cover a range of spatial resolutions and possibly different scales of the observed structures. Addition-ally, the dataset includes measurements of the horizontal (X) and vertical (Z) sizes in micrometres (). These sizes vary widely, with common dimensions of approximately  and  . This range indicates that the analysis spans multiple scales and is suitable for examining various features and structures within the samples.21 × 21301 × 301101 × 10181 × 8161 × 61µm10 × 10 µm20 × 20 µm3.2  Experimental setup for microstructured gold patterns and fine surface irregularities in GaN films for the evaluation of the proposed methodIn addition to the HR 3D nano-ESCA datasets, we obtained new data by acquiring LRIs and HRIs of gold (Au) and GaN films by measuring peak intensities in the core-level spectra of Au 4f and C 1s, respectively. Low resolution images were obtained using mea-surements at 500 nm intervals, whereas high resolution images were acquired using measurements at 200 nm intervals. The effectiveness of the proposed method was dem-onstrated by applying it to these new datasets.Specifically, we conducted measurements of finely processed Au patterns on a  substrate for evaluation. Au patterns were fabricated via vacuum deposition after apply-ing standard electron-beam lithography and lift-off techniques. Spectromicroscopic measurements were performed via the 3D nano-ESCA system, which maintains a high spatial resolution of approximately 100 nm.SiO2/SiThe experimental conditions for analysing the microstructured Au patterns involved obtaining spectral mapping images within a   area. For the low resolu-tion images, measurements were performed in 500 nm steps, while for the high resolu-tion images, measurements were conducted in 200 nm steps. Similar measurements of a GaN film with fine surface irregularities were obtained. The SR analysis method was then applied to multiple LRIs to estimate the HR results. Detailed information about the experimental setup and data analysis can be found in the Supporting Information.15 µm × 15 µmFor the evaluation using fine gold patterns as reference materials and GaN films, low-resolution images (LRIs) were acquired via synchrotron radiation measurements by obtaining spectral mapping images with a 500 nm scanning step. To enable super-reso-lution analysis, high-resolution images were subsequently obtained with a 200 nm scan-ning step. However, since performing super-resolution on the 500 nm LRIs with a   upscaling results in a different pixel count compared to that from the 200 nm high-res-olution images, the high-resolution images were processed using bicubic interpolation to match the pixel count of the   upscaled LRIs. This procedure ensured that the accuracy of the super-resolution analysis could be fairly compared.sr = 3sr = 3Page 8 of 20Igarashi et al. Discover Nano          (2025) 20:1023.3  Data preprocessingWe processed 118 HR 3D nano-ESCA datasets to extract  -pixel HRIs and the corresponding  -pixel LRIs. Each HRI was paired with nine   LR patches ( ), resulting in a total of 146 datasets. The extraction process involved normalizing the images and dividing them into patches of specific sizes, with a stride setting of half the patch size to ensure overlapping regions. The generated patches were filtered on the basis of minimum size requirements, and both the HRIs and LRIs were normalized for consistency. The images were then stored for further analysis, ensuring that only reliable pixels were considered, particularly given the variations in weather conditions across different scenes.90 × 9030 × 3030 × 30N = 9To generate LRIs from HR data, we employed a strategic sampling approach. Starting from a defined initial point, such as (, ) in a two-dimensional plane, we sampled the HR data at intervals corresponding to every third pixel to downsample the images by a factor of three. This method effectively reduces the spatial resolution while maintaining representative coverage across the image. Finally, each image was normal-ized to range between 0 and 1 by subtracting the minimum pixel intensity value from each pixel and then dividing by the range. By shifting the starting point for each sample, we prevented overlap between the resulting LRIs, ensuring that nine distinct LRIs were generated from each HRI. Each of these LRIs corresponds to a different region in the original HRI, allowing us to construct a comprehensive dataset that captures variations in the original HR data at a lower resolution.55.0µm44.6µmIn addition to creating these datasets, we prepared data for dictionary learning. Spe-cifically, we extracted   pixel patches from the 118 HR 3D nano-ESCA datasets. To ensure that there was no overlap between patches, the extraction process was care-fully controlled. From this process, we generated   patch datasets, which were then used to create a dictionary of   pixel elements, with  . This dic-tionary is intended to support the dictionary learning models used in the multiframe SR analysis method.54 × 54K = 2506 × 6qh = 6 × 6 = 364  Results and discussionIn this section, we present the validation of our multiframe superresolution (SR) method based on sparse coding, applied to high-resolution 3D nano-ESCA datasets. First, we compare the performance of dictionaries learned from natural images and 3D nano-ESCA data, demonstrating the importance of using a tailored dictionary for accurate image reconstruction. Next, we apply the SR method to low-resolution images, show-ing that it outperforms traditional bicubic interpolation and deep learning approaches in terms of PSNR and SSIM. Finally, we test the method on newly acquired datas-ets of microstructured gold patterns and GaN films, confirming its ability to preserve fine structural details and validating its potential for use in challenging experimental conditions.4.1  Dictionary for high-resolution 3D nano-ESCA datasetsIn this section, we aim to evaluate the effectiveness of dictionary learning for 3D nano-ESCA datasets by comparing dictionaries learned from natural images and those learned from 3D nano-ESCA data. The goal is to determine which type of dictionary is betterPage 9 of 20Igarashi et al. Discover Nano          (2025) 20:102suited for accurate image reconstruction, particularly in the context of high-resolution 3D nano-ESCA images.We applied the dictionary learning method using the OMP algorithm to both datasets. Fig. 3 illustrates the dictionaries learned via the OMP algorithm. The dictionary in Fig. 3a was obtained from natural images, consisting of 512 atoms, each of size   pix-els. In contrast, Fig. 3b shows the dictionary   learned from the HR 3D nano-ESCA dataset. For this 3D nano-ESCA dictionary, a sparsity value of   was used, with   atoms of size   pixels, and the learning process was iterated 500 times.15 × 15Dh ∈ Rqh×Katomk0 = 5Katom = 225qh = 6 × 6The comparison between the two dictionaries reveals key insights into their suitability for different types of image data. Although both the 3D nano-ESCA and natural image dictionaries exhibit similar patterns, the smaller size of the 3D nano-ESCA images poses challenges in accurate reconstruction, particularly when bases with pixel sizes of   or   are used. When a dictionary is learned from   pixel patches of 3D nano-ESCA images, the reconstruction error is more than  higher than that when a dictionary is learned from   pixel patches. This suggests that dictionaries trained based on natural images are not well suited for reconstructing 3D nano-ESCA images, as the fine details inherent in these smaller-scale images cannot be captured when larger pixel bases are used for training.15 × 1518 × 1818 × 1870%6 × 64.2  Multiframe superresolution method for high-resolution 3D nano-ESCA datasetsIn this section, we aim to validate the effectiveness of our proposed multiframe super-resolution (SR) method based on sparse coding, applied to high-resolution (HR) 3D nano-ESCA datasets. The goal is to assess how well the method can reconstruct high-resolution images from low-resolution inputs, considering critical parameters such as positional shifts and image degradation. By applying the method to a series of 146 data-sets created in Sect. 3.3 we quantitatively evaluate the performance of the SR process using metrics such as PSNR and SSIM. We, then, aim to demonstrate that high-qual-ity superresolution images can be achieved with fewer low-resolution inputs, reducing measurement time by over  without sacrificing image quality.40%We generate SR images with a scaling factor of   from   LRIs using the sparse coding approach. We first consider the degradation operator  . In thesr = 3N = 9G = SHFig. 3  Improved reconstruction with a 3D Nano-ESCA dictionary compared to a natural image dictionary a shows a dictionary obtained from natural images with 512 atoms, each of size 15 × 15 pixels. b shows the diction-ary Dh ∈ Rqh×Katom  learned from high-resolution 3D nano-ESCA data, with Katom = 225 atoms of size qh = 6 × 6 pixelsPage 10 of 20Igarashi et al. Discover Nano          (2025) 20:102nblur = 8blurring operation H, we set   and an  -pixel Gaussian filter with a standard deviation of  . The blurred and shifted images are then downsampled by a factor of  . We also set the regularization parameter   in the sparse coding approach defined in Eq. (2). The detailed impacts of the parameters  and  on the multiframe SR results are provided in the Supporting Information. For backprojec-tion, we choose the trade-off parameter  , which controls the influence of the regularization term in the optimization process. The step size parameter , which determines the gradient descent step, is set to  . These settings were selected to ensure stable and efficient convergence during the backprojection process.nblur × nblurσh = 1.2sr = 3η = 0.05ησhc = 1 × 10−1 × 9νν = 1 × 10−4 × 1To quantitatively compare the performance of the SR methods, we use the peak signal-to-noise ratio (PSNR), which is defined as  , where MSE is the mean squared error between the original HRI and the estimated HRI. A higher PSNR value indicates better SR performance. In addition, we use the structural similarity index measure (SSIM), which is defined as  , where x and y are the original HRI and the estimated HRI, respectively.  and   are the mean pixel values,   and   are the variances, and   is the covariance of x and y. The constants  and  are used to stabilize the division with weak denominators and are defined as   and  , where L is the dynamic range of the pixel values. For images normalized to the [0, 1] range,  , and typical values for  and  are 0.01 and 0.03, respectively. A higher SSIM value indicates better SR performance.PSNR[dB] = 10 log1012MSESSIM(x, y) = (2µxµy+c1)(2σxy+c2)(µ2x+µ2y+c1)(σ2x+σ2y+c2)µxµyσ2xσ2yσxyc1c2c1 = (k1L)2c2 = (k2L)2L = 1k1k2The SR results for the 23rd dataset, which consist of images of a single-layer graphene field-effect transistor (FET), demonstrate the effectiveness of the proposed method. Fig. 4a shows one of the LRIs from the set of   images. Fig. 4b represents the true HRI after noise removal via the DnCNN [45], which serves as a reference for evaluating the SR methods. The PSNR and SSIM values between this denoised HRI (Fig. 4b) and the SR images with a scaling factor of   are used as the evaluation metrics.N = 9sr = 3With the bicubic interpolation approach, as shown in Fig. 4c, a PSNR of 18.70 and an SSIM of 0.40 are obtained, indicating moderate performance in preserving structural details. We next consider the results of the bicubic stacking method, which is referred to as Z in 2.2 and used as a backprojection approach. While this method is effective in preserving the structural similarity, it struggles with accurately reproducing image con-trast, leading to a reduction in the PSNR value. As shown in Fig. 4d, higher SSIM values (0.58) tend to be achieved with the bicubic stacking method, indicating better structural similarity. Nevertheless, the method struggles with accurate contrast estimation, which results in a lower PSNR of 17.11. The deep learning-based SR method (RAMS), which is specifically trained based on HR satellite images, achieves a PSNR of 16.28 and an SSIM of 0.44, as shown in Fig. 4e. This lower PSNR value suggests that despite the slightly bet-ter structural similarity achieved with this approach, this method struggles with noise and fine detail preservation, likely due to a mismatch between the training data and the unique features of the graphene FET.The proposed method, as shown in Fig. 4f, excels in accurately reproducing the edge structures of the denoised HRIs, demonstrated by its high SSIM of 0.56 and PSNR of 21.05. These values highlight the method’s effectiveness, which stems from three key fac-tors. The first key factor is the use of sparse coding with a   pixel dictionary learned from HR 3D nano-ESCA datasets. Second, unlike methods that apply backprojec-tion to noisy LRIs [19, 40, 43], this approach uses the accumulated bicubic image for6 × 6Page 11 of 20Igarashi et al. Discover Nano          (2025) 20:102backprojection, thereby preserving image quality. Third, the accurate use of shift vari-ations in the LRIs, which are critical control parameters in the measurement process, ensures precise alignment and reconstruction, further enhancing the overall structural integrity and details captured in the SR image.On the other hand, Fig. 4e and g present results that are more similar to those of the bicubic interpolation approach. This similarity arises from the influence of backprojec-tion on the LRI, a common technique used in previous multiframe SR studies [19, 40, 43]. In Fig. 4e, although the shifts are given, the use of a dictionary trained based on natural images leads to the retention of unnatural edge artefacts in the image before backprojection. Moreover, the results in Fig. 4g, which were obtained using the same dictionary as in Fig. 4f, suffer from inadequate shift estimation, causing the edge struc-tures to deteriorate, thereby compromising the overall image quality.The PSNR and SSIM values presented in Table 1 represent the mean values calculated across the 146 LRI and HRI dataset pairs. The proposed method, Sparse Coding SR (3D nano-ESCA Dictionary, Shift Given), achieved the highest mean PSNR of 22.94 dB and the highest mean SSIM of 0.69, along with the smallest standard deviations of 2.80 and 0.11, respectively. These results demonstrate that the proposed method not only pro-duces images with superior quality, closely matching the denoised HR data, but also presents consistent performance across datasets.In comparison, the bicubic stacking method, although it achieves a relatively high SSIM of 0.62, has a lower PSNR of 18.59 dB. This finding indicates that while the bicubic stacking method is effective in preserving structural similarity, it struggles with accu-rately reproducing image contrast, leading to a reduction in the PSNR value. On the other hand, the proposed sparse coding SR method obtains good PSNR and SSIM val-ues, outperforming other approaches, including the traditional bicubic interpolation and deep learning-based SR (RAMS) methods [37]. This highlights the effectiveness of using a dictionary specifically learned from 3D nano-ESCA data and incorporating accurateFig. 4  Superresolution (SR) results for the 23rd dataset among the 146 datasets analysed. The images are of a single-layer graphene field-effect transistor (FET). a One of the low-resolution images (LRIs) from the set of N = 9 images. b True high-resolution image (HRI) after noise removal via the DnCNN [45]. The PSNR and SSIM values between these denoised HRIs and the SR images with a scaling factor of sr = 3 were used for evaluation. c Bicu-bic interpolation result from a single LRI. d Bicubic stacking interpolation result from multiple LRIs. e Multiframe SR result when a deep neural network trained on HR satellite images was used [37]. f Multiframe SR using sparse coding with a dictionary of 15 × 15 pixels learned from natural images, with given shifts W. g Multiframe SR using sparse coding with a 6 × 6 pixel dictionary learned from HR 3D nano-ESCA datasets, with given shifts W. h Similar to g, but with shifts W estimated via the method in [20]Page 12 of 20Igarashi et al. Discover Nano          (2025) 20:102shift information during the SR process, leading to both high structural similarity and accurate image contrast.Previous studies have shown that methods based on natural image dictionaries often struggle to accurately reconstruct fine structures in nanoscale imaging due to the mis-match between the training data and the target data [19, 20, 40, 43]. Our approach addresses this issue by tailoring the dictionary specifically to the 3D nano-ESCA data, which results in better reconstruction performance, as evidenced by the higher PSNR and SSIM values. Furthermore, the incorporation of precise shift information during the SR process enhances the alignment and reconstruction accuracy, a factor that has been overlooked or inadequately addressed in previous SR methods [37]. This advancement in SR methodology contributes to improving image quality in the field of synchrotron radiation microscopy, and it has the potential to be applied to other imaging systems that require high precision with limited datasets.As the number of LRIs increases from 1 to 9, the sparse coding SR method (3D nano-ESCA Dictionary, Shift Given) consistently achieves the highest PSNR and SSIM values across all scenarios (Fig. 5). For dataset 23, as shown in Supplementary Information, a PSNR of 22.85 and an SSIM of 0.69 are achieved with approximately 5 images, compa-rable to the results obtained with 9 images. This suggests that high image quality can be achieved while reducing the measurement time by more than . In contrast, the other methods achieve minimal improvements in the PSNR and SSIM values as the num-ber of LRIs increases, underscoring the limitations of these approaches. The consistent superiority of the proposed method highlights its efficiency in maintaining high image quality with fewer images. This approach offers enhanced image quality, reduced expo-sure times, and improved interpretability of scientific data, making it a versatile tool for overcoming the challenges associated with radiation damage and sample degradation in nanoscale imaging.40%One key strategy to further improve estimation accuracy is to incorporate additional prior knowledge about the sample. In the present work, our goal was to develop a broadly applicable approach that could be used for various nanomaterials, such as sin-gle-layer graphene field-effect transistors (FETs) or surface-scratched gallium nitride (GaN) films, in the context of 3D-nano ESCA. Consequently, our learned dictionary was designed to be general rather than specialized for a specific pattern. However, as reported by [6], when the nanoparticle pattern or other structural features of interest are known in advance, learning a dedicated dictionary that reflects this prior knowledge can significantly enhance the reconstruction quality.The integration of more specific prior information is a promising direction for improving the robustness of super-resolution methods in high-noise environments. Table 1  Mean PSNR and SSIM values across 146 datasets for different SR methods Method PSNR (dB) SSIM Bicubic 21.08 ± 3.62 0.53 ± 0.18 Bicubic stacking 18.59 ± 3.55 0.62 ± 0.10 Deep learning superresolution (RAMS) 16.63 ± 3.94 0.51 ± 0.12 Sparse coding superresolution (3D-nano ESCA Dictionary, Shift Estimation) 21.11 ± 3.39 0.55 ± 0.16 Sparse coding superresolution (3D-nano ESCA Dictionary, Shift Given) 22.94 ± 2.80 0.69 ± 0.11 Sparse coding superresolution (Natural image dictionary, Shift Given) 20.81 ± 3.32 0.54 ± 0.14 Bold values indicate the best (i.e., highest) performance values across all the listed superresolution (SR) methods for each metricPage 13 of 20Igarashi et al. Discover Nano          (2025) 20:102Furthermore, advanced imaging techniques such as electron holography—where elec-tron interference patterns (holograms) are formed by overlapping object and reference waves using an electron biprism—could benefit from similar approaches in extracting high-fidelity signals from noisy datasets. Extending our method to these and other cut-ting-edge measurement techniques remains an important avenue for future research.In this study, we generated super-resolution (SR) images with a fixed scaling factor of  to demonstrate the effectiveness of our proposed method. However, in real appli-cations, the determination of the optimal enhancement factor is a multifaceted issue. First, the experimental sampling conditions, including how multiple low-resolution images are acquired, must be adapted to the desired upsampling factor. Second, the dic-tionary learning framework intrinsically couples the high-resolution patch size () with the low-resolution patch size () according to the scaling factor. For instance, if  is set to   pixels, then  can be defined as   pixels for a  upsampling or   pixels for a  upsampling. This coupling limits the upsampling factor to integer values (or their reciprocals). Although one might consider using larger patch sizes to enable more flexible scaling factors, the relatively small size of the original images and the inherent multi-scale characteristics of materials images pose practical challenges in dictionary learning [11]. Such constraints may represent a disadvantage of dictionary-based SR compared to interpolation-based methods like bicubic interpolation.sr = 3qhqlqh6 × 6ql3 × 32×2 × 23×Nevertheless, for advanced materials analysis—where large training datasets are typi-cally unavailable—the ability to learn a meaningful dictionary from a limited number of images is a significant advantage. Future research will focus on developing multi-scale and adaptive dictionary learning strategies to relax these constraints, potentially allow-ing for more flexible upsampling factors while maintaining high reconstruction quality.In the current work, high-resolution images are used to learn a dictionary with effec-tive patch sizes that typically span dimensions from approximately   to , thereby covering multiple scales of the sample features. Based on these patch sizes, a fixed scaling factor of   is adopted. This scaling factor not only determines10 × 10µm20 × 20µmsr = 3Fig. 5  The variation in the PSNR as the number of low-resolution images increases from 1 to 9 in the multiframe SR analysis. The sparse coding SR method (3D nano-ESCA Dictionary, Shift Given) consistently achieves the highest PSNR values across all the scenarios. In this figure, to improve the visibility of the plotted data, a small offset was applied to the error bars, preventing overlap and ensuring a clearer distinction between different methodsPage 14 of 20Igarashi et al. Discover Nano          (2025) 20:102the resolution enhancement but also implicitly defines the acquisition parameters for the low-resolution images, including their size and the number of frames recorded.While this approach offers a systematic way to obtain low-resolution frames from high-resolution data, it also suggests that by adjusting the high-resolution image selec-tion or modifying the dictionary parameters, the scaling factor could be tuned to opti-mize the reconstruction quality. Exploring such adaptive strategies for determining the ideal scaling factor is a promising direction for future work.4.3  Multiframe superresolution method for microstructured gold patterns and fine surface irregularities on GaN filmsTo further validate the superiority of the proposed method, we applied our SR analysis approach to newly acquired datasets, including 9 LRIs and HRIs of microstructures and surface irregularities on GaN films. Using this set of 9 LRIs, we performed multiframe SR with a scaling factor of  , following the same protocol described previously. This allowed us to assess the effectiveness of the method across various datasets, ensuring consistent performance in preserving structural details. The results for a 1000 nm gold (Au) wire arranged in a cross pattern, shown in Fig. 6, highlight the effectiveness of vari-ous reconstruction methods. The sparse coding approach using the 3D nano-ESCA dic-tionary with provided shifts (Fig. 6e) effectively preserves the sharp edges of the gold wire, crucial for accurate characterization. This method consistently outperforms both the bicubic interpolation approach (Fig. 6c), which produces a more blurred image, and the sparse coding method with estimated shifts (Fig. 6f ), which shows only mar-ginal improvement. The clear advantage of incorporating shift information and using asr = 3Fig. 6  Superresolution analysis results for a 1000 nm gold (Au) wire arranged in a cross pattern. a Low-resolution image (LRI). b Denoised high-resolution image (HRI) used as the ground truth. c Bicubic interpolation result, with a PSNR of 18.09 and an SSIM of 0.32. d Sparse coding-based superresolution result using a dictionary learned from natural images with provided shifts, yielding a PSNR of 19.92 and an SSIM of 0.39. e Sparse coding-based super-resolution result using the 3D nano-ESCA dictionary with provided shifts, achieving the highest PSNR of 20.78 and an SSIM of 0.55. f Sparse coding-based superresolution approach with estimated shifts [20], resulting in a PSNR of 18.70 and an SSIM of 0.33Page 15 of 20Igarashi et al. Discover Nano          (2025) 20:102specialized dictionary is evident in the higher structural similarity and contrast achieved by our approach.The in-plane resolution of the imaging system was estimated using a standard proce-dure based on intensity profile analysis. For each selected row, the profile was split at its maximum intensity, and rising and falling sigmoid functions were fitted to the left and right portions, respectively. The resolution was calculated as  , and con-verted into physical units using the known pixel size. As shown in Fig. S5 and the corre-sponding table in the Supplementary File, the proposed Sparse Coding Superresolution (3D-nano ESCA Dictionary, Shift Given) method consistently achieves a resolution of 0.1396 µm (std = 0.0213 µm), which is significantly better than the resolution obtained from the denoised high-resolution image (0.2061 µm). The Sparse Coding Superresolu-tion method (using the 3D-nano ESCA Dictionary with Shift Given) robustly achieves a resolution of  with a margin of , effectively matching the system’s in-plane resolution of approximately 100nm even under significant noise conditions. Fur-ther details are provided in the Supplementary File.R = 2 ln(3)|slope|0.1396µm0.0213µmThese results emphasize the importance of using a specialized dictionary and accurate shift information for high-quality image reconstruction, confirming the superiority of the proposed method in preserving the true structure of the Au wire.The SR analysis results for fine structures on a GaN film, as shown in Fig. 7, dem-onstrate the varying effectiveness of different reconstruction methods. The LRI in Fig. 7a serves as a reference for comparison. When upscaled via bicubic interpolation (Fig. 7c), the result shows a PSNR of 20.00 and an SSIM of 0.49. However, despite this rela-tively high PSNR value, the interpolation method fails to accurately reconstruct the fineFig. 7  Superresolution analysis results for a SiC structure. a Low-resolution image (LRI). b Denoised high-resolution image (HRI) used as the ground truth. c Bicubic interpolation approach, with a PSNR of 20.00 and an SSIM of 0.49. d Sparse coding-based superresolution approach using a dictionary learned from natural images with provided shifts, yielding a PSNR of 20.00 and an SSIM of 0.51. e Sparse coding-based superresolution approach using the 3D nano-ESCA dictionary with provided shifts, achieving a PSNR of 19.85 and an SSIM of 0.55. Despite the slightly lower PSNR, this method better reconstructs key features of the HRI. f Sparse coding-based superresolution ap-proach with estimated shifts [20], resulting in a PSNR of 20.64 and an SSIM of 0.53Page 16 of 20Igarashi et al. Discover Nano          (2025) 20:102structural details, particularly in the central line region, which is a key feature in the denoised HRI shown in Fig. 7b.When the sparse coding-based SR approach with a dictionary learned from natural images is used (Fig. 7d), a PSNR of 20.00 and an SSIM of 0.51 are achieved, indicating some improvement in edge detail preservation. However, the image still retains unnatu-ral edge artefacts, and the true structure is not accurately reconstructed. In contrast, the sparse coding method using the 3D nano-ESCA dictionary with provided shifts (Fig. 7e) produces a PSNR of 19.85 and an SSIM of 0.55. Although the PSNR is slightly lower than that of the bicubic interpolation approach, this method more accurately reconstructs the central line and other subtle features of the HRI, making it a better overall repre-sentation of the true image. The ability of the sparse coding method to preserve these fine details, especially in the challenging regions like the central line, demonstrates its superiority over traditional interpolation methods. This shows that even when numeri-cal metrics like PSNR are comparable, the quality of the structural details preserved by the sparse coding method is significantly better, highlighting its robustness and preci-sion in applications requiring high fidelity, such as nanoscale imaging. Moreover, when shifts are estimated rather than provided (Fig. 7f ), the PSNR improves to 20.64, and the SSIM is 0.53, which is slightly greater than that of the bicubic interpolation approach. Despite this improvement in numerical metrics, the method still struggles to fully repli-cate the central line structure, particularly in regions of high complexity. This indicates that while the estimated shifts improve alignment, they are not sufficient to capture the subtle details present in the high-resolution image, which underscores the importance of using accurate shift information. Thus, the use of provided shifts in the sparse coding approach remains crucial for the superior reconstruction of fine structures.To further investigate the variability observed in Fig. 7, we analyzed the performance of bicubic interpolation across multiple frames. As shown in Supplementary Fig. S5, bicubic interpolation was applied to nine LRI frames and the corresponding PSNR and SSIM values are presented. These results reveal that, while high metric values can occa-sionally be observed due to noise, our proposed method more consistently captures the true signal.In this study, our analysis method is presented under the assumption that the actuator operates with precision far exceeding the resolution. However, in cases where the actua-tor’s precision is not as high relative to the resolution, it would be beneficial to simulta-neously estimate the shift values during the analysis. The convolution of noise in each dataset suggests that the estimation of shift values can become unstable. To counteract this, extending the measurement time of the low-resolution images to improve the S/N ratio is crucial for stabilizing the shift estimation. Extending our method to image analy-sis in other advanced measurement techniques remains a promising direction for future research.Although our current results demonstrate a  reduction in radiation dose, we believe that further reductions are achievable. The primary challenge in pushing this number further down lies in accurately estimating which components of the acquired data represent the true signal versus noise. As discussed earlier, the incorporation of prior knowledge into the reconstruction process can significantly improve this signal/noise discrimination. Furthermore, a more refined modeling of the measurement sys-tem—including a detailed analysis of the noise characteristics (e.g., distinguishing40%Page 17 of 20Igarashi et al. Discover Nano          (2025) 20:102between Poisson and Gaussian noise)—is critical. Such an approach would allow for a more robust estimation of the underlying signal, even under lower dose conditions. These enhancements in noise modeling and the integration of additional prior informa-tion are promising avenues for future work, potentially enabling even greater reductions in radiation dose while maintaining, or even improving, image quality.While the proposed sparse coding SR method demonstrates excellent performance in reconstructing high-resolution images from low-resolution inputs, there are certain limitations to its generalizability. One notable limitation is the reliance on a dictionary that is specifically trained for a given dataset or scale [11]. When the scale of the imag-ing data changes significantly, such as when analyzing structures at vastly different spa-tial resolutions, the dictionary must be retrained to accommodate the new data. This requirement limits the method’s ability to be applied universally across datasets without prior retraining, thus affecting its scalability and computational efficiency.When deciding between deep learning [9, 10, 21, 37] and sparse coding [11, 12, 19, 20, 43] for superresolution, the nature of the dataset plays a critical role. Deep learning, par-ticularly convolutional neural networks (CNNs), works best with large datasets. In such cases, transfer learning or fine-tuning on pre-trained models can effectively adapt them to new tasks [4, 15, 31, 44, 46]. However, deep learning methods require significant data and computational resources, which may not be feasible for smaller, specialized datasets like those in nanoscale imaging. Sparse coding, on the other hand, is advantageous when working with smaller, noisier datasets or when interpretability is essential. It allows the incorporation of domain-specific knowledge into the dictionary learning process, mak-ing it more adaptable to unique datasets. While multi-scale dictionaries extend sparse coding to broader scales [32, 33], retraining is often required for different datasets, lim-iting its scalability. Choosing between these methods depends on the dataset’s scale, complexity, and noise. For well-represented datasets, deep learning with transfer learn-ing may be ideal, while sparse coding is better suited for specialized, limited datasets. Future research could explore hybrid approaches, combining deep learning for prepro-cessing with sparse coding for fine-tuned reconstruction, balancing generalization and precision.5  ConclusionThis study presents a multiframe superresolution (SR) method based on sparse coding for enhancing synchrotron radiation microspectroscopy images, significantly reducing exposure times and mitigating issues such as radiation damage and thermal drift. By leveraging positional shifts as known control parameters and utilizing a high-resolution dictionary tailored to 3D nano-ESCA data, our method achieves high-resolution recon-structions with minimal data, outperforming traditional methods like bicubic interpola-tion and even deep learning-based approaches under limited dataset conditions.The broader applicability of this technique, particularly in fields where exposure con-straints and data limitations are common, highlights its potential for advancing high-resolution imaging beyond synchrotron radiation microspectroscopy. Future work could explore the integration of this method into other imaging modalities, such as elec-tron microscopy or Raman spectroscopy, where similar challenges exist. Additionally, further refinement of the dictionary learning process could enhance SR performance,Page 18 of 20Igarashi et al. Discover Nano          (2025) 20:102particularly in highly noisy environments, making the approach even more versatile across different applications.Supplementary InformationThe online version contains supplementary material available at https://doi.org/10.1186/s11671-025-04291-x.Supplementary file 1 (pdf 3067 KB)AcknowledgementsThis work was supported by KAKENHI Grant-in-Aid for Scientific Research (24K02995, 21H04696, 24K01243) from the Japan Society for the Promotion of Science (JSPS), CREST: JPMJCR1761, JPMJCR21O1, JPMJCR2235 and PRESTO: JPMJPR17N2, JPMJPR17N2, JPMJPR20T7 from the Japan Science and Technology Agency (JST), and the Innovative Science and Technology Initiative for Security of ATLA Japan (JPJ004596). A part of this study was financially supported by Beyond 5 G Research and Development Project (05901). We thank Yasunori Tateno and Tsuyoshi Kouchi of Sumitomo Electric Industries, Ltd., for their assistance with sample preparation. Experimental measurements were performed with a 3D nano-ESCA system installed at the University of Tokyo outstation beamline, BL07LSU at SPring-8 (2022A7444, 2021B7435, 2021B7433, 2021A7422, 2021A7421, 2019B7466, 2019A7451, 2018B7580), which has since been relocated to NanoTerasu.Author contributionsY.I. and N.N. contributed equally to this work. Y.I. led the data analysis with support from M.S. N.N. was responsible for acquiring the new measurement data, including those of GaN and Au, as well as conducting previous 3D-nano ESCA measurements. Both Y.I. and N.N. jointly determined the research direction and wrote the manuscript. H.F. provided the GaN and Au samples for the new measurements. H.H. and M.O. offered programs related to sparse super-resolution and provided valuable insights on machine learning techniques. All authors reviewed the manuscript and contributed to its completion.FundingThis research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.Availability of data and materialsData is available from the corresponding author upon reasonable request.DeclarationsEthics approval and consent to participateNot applicable.Consent for publicationAll authors have reviewed and approved the final version of the manuscript and consent to its publication.Competing interestsThe authors declare no Conflict of interest.Received: 11 September 2024 / Accepted: 20 June 2025References1.  Aharon M, Elad M, Bruckstein A. K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans Signal Process. 2006;54(11):4311–22.2.  Ahmed N, Natarajan T, Rao KR. Discrete cosine transform. IEEE Trans Comput. 1974;100(1):90–3.3.  Akada K, Sudayama T, Asakura D, et al. 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Discover Nano          (2025) 20:102http://arxiv.org/abs/1503.02531 Sparse coding-based multiframe superresolution for efficient synchrotron radiation microspectroscopy Abstract 1 Introduction 2 Method 2.1 Dictionary learning 2.2 Superresolution method based on sparse coding 3 Data acquisition and experimental setup 3.1 Training and evaluation datasets for the multiframe superresolution analysis method 3.2 Experimental setup for microstructured gold patterns and fine surface irregularities in GaN films for the evaluation of the proposed method 3.3 Data preprocessing 4 Results and discussion 4.1 Dictionary for high-resolution 3D nano-ESCA datasets 4.2 Multiframe superresolution method for high-resolution 3D nano-ESCA datasets 4.3 Multiframe superresolution method for microstructured gold patterns and fine surface irregularities on GaN films 5 Conclusion References