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<p class="title is-5 mathjax"> Distillation-Driven Diffusion Model for Multi-Scale MRI Super-Resolution: Make 1.5T MRI Great Again </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/eess?searchtype=author&query=Wang%2C+Z">Zhe Wang</a>, <a href="/search/eess?searchtype=author&query=Ru%2C+Y">Yuhua Ru</a>, <a href="/search/eess?searchtype=author&query=Bauer%2C+F">Fabian Bauer</a>, <a href="/search/eess?searchtype=author&query=Chetouani%2C+A">Aladine Chetouani</a>, <a href="/search/eess?searchtype=author&query=Chen%2C+F">Fang Chen</a>, <a href="/search/eess?searchtype=author&query=Zhang%2C+L">Liping Zhang</a>, <a href="/search/eess?searchtype=author&query=Hans%2C+D">Didier Hans</a>, <a href="/search/eess?searchtype=author&query=Jennane%2C+R">Rachid Jennane</a>, <a href="/search/eess?searchtype=author&query=Jarraya%2C+M">Mohamed Jarraya</a>, <a href="/search/eess?searchtype=author&query=Chen%2C+Y+H">Yung Hsin Chen</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2501.18736v1-abstract-short" style="display: inline;"> Magnetic Resonance Imaging (MRI) offers critical insights into microstructural details, however, the spatial resolution of standard 1.5T imaging systems is often limited. In contrast, 7T MRI provides significantly enhanced spatial resolution, enabling finer visualization of anatomical structures. Though this, the high cost and limited availability of 7T MRI hinder its widespread use in clinical se… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.18736v1-abstract-full').style.display = 'inline'; document.getElementById('2501.18736v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2501.18736v1-abstract-full" style="display: none;"> Magnetic Resonance Imaging (MRI) offers critical insights into microstructural details, however, the spatial resolution of standard 1.5T imaging systems is often limited. In contrast, 7T MRI provides significantly enhanced spatial resolution, enabling finer visualization of anatomical structures. Though this, the high cost and limited availability of 7T MRI hinder its widespread use in clinical settings. To address this challenge, a novel Super-Resolution (SR) model is proposed to generate 7T-like MRI from standard 1.5T MRI scans. Our approach leverages a diffusion-based architecture, incorporating gradient nonlinearity correction and bias field correction data from 7T imaging as guidance. Moreover, to improve deployability, a progressive distillation strategy is introduced. Specifically, the student model refines the 7T SR task with steps, leveraging feature maps from the inference phase of the teacher model as guidance, aiming to allow the student model to achieve progressively 7T SR performance with a smaller, deployable model size. Experimental results demonstrate that our baseline teacher model achieves state-of-the-art SR performance. The student model, while lightweight, sacrifices minimal performance. Furthermore, the student model is capable of accepting MRI inputs at varying resolutions without the need for retraining, significantly further enhancing deployment flexibility. The clinical relevance of our proposed method is validated using clinical data from Massachusetts General Hospital. Our code is available at https://github.com/ZWang78/SR. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.18736v1-abstract-full').style.display = 'none'; document.getElementById('2501.18736v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2410.06997">arXiv:2410.06997</a> <span> [<a href="https://arxiv.org/pdf/2410.06997">pdf</a>, <a href="https://arxiv.org/format/2410.06997">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Image and Video Processing">eess.IV</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computer Vision and Pattern Recognition">cs.CV</span> </div> </div> <p class="title is-5 mathjax"> Feasibility Study of a Diffusion-Based Model for Cross-Modal Generation of Knee MRI from X-ray: Integrating Radiographic Feature Information </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/eess?searchtype=author&query=Wang%2C+Z">Zhe Wang</a>, <a href="/search/eess?searchtype=author&query=Chen%2C+Y+H">Yung Hsin Chen</a>, <a href="/search/eess?searchtype=author&query=Chetouani%2C+A">Aladine Chetouani</a>, <a href="/search/eess?searchtype=author&query=Bauer%2C+F">Fabian Bauer</a>, <a href="/search/eess?searchtype=author&query=Ru%2C+Y">Yuhua Ru</a>, <a href="/search/eess?searchtype=author&query=Chen%2C+F">Fang Chen</a>, <a href="/search/eess?searchtype=author&query=Zhang%2C+L">Liping Zhang</a>, <a href="/search/eess?searchtype=author&query=Jennane%2C+R">Rachid Jennane</a>, <a href="/search/eess?searchtype=author&query=Jarraya%2C+M">Mohamed Jarraya</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2410.06997v3-abstract-short" style="display: inline;"> Knee osteoarthritis (KOA) is a prevalent musculoskeletal disorder, often diagnosed using X-rays due to its cost-effectiveness. While Magnetic Resonance Imaging (MRI) provides superior soft tissue visualization and serves as a valuable supplementary diagnostic tool, its high cost and limited accessibility significantly restrict its widespread use. To explore the feasibility of bridging this imaging… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.06997v3-abstract-full').style.display = 'inline'; document.getElementById('2410.06997v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2410.06997v3-abstract-full" style="display: none;"> Knee osteoarthritis (KOA) is a prevalent musculoskeletal disorder, often diagnosed using X-rays due to its cost-effectiveness. While Magnetic Resonance Imaging (MRI) provides superior soft tissue visualization and serves as a valuable supplementary diagnostic tool, its high cost and limited accessibility significantly restrict its widespread use. To explore the feasibility of bridging this imaging gap, we conducted a feasibility study leveraging a diffusion-based model that uses an X-ray image as conditional input, alongside target depth and additional patient-specific feature information, to generate corresponding MRI sequences. Our findings demonstrate that the MRI volumes generated by our approach is visually closer to real MRI scans. Moreover, increasing inference steps enhances the continuity and smoothness of the synthesized MRI sequences. Through ablation studies, we further validate that integrating supplementary patient-specific information, beyond what X-rays alone can provide, enhances the accuracy and clinical relevance of the generated MRI, which underscores the potential of leveraging external patient-specific information to improve the MRI generation. This study is available at https://zwang78.github.io/. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.06997v3-abstract-full').style.display = 'none'; document.getElementById('2410.06997v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 December, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2408.00891">arXiv:2408.00891</a> <span> [<a href="https://arxiv.org/pdf/2408.00891">pdf</a>, <a href="https://arxiv.org/format/2408.00891">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Image and Video Processing">eess.IV</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computer Vision and Pattern Recognition">cs.CV</span> </div> </div> <p class="title is-5 mathjax"> Temporal Evolution of Knee Osteoarthritis: A Diffusion-based Morphing Model for X-ray Medical Image Synthesis </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/eess?searchtype=author&query=Wang%2C+Z">Zhe Wang</a>, <a href="/search/eess?searchtype=author&query=Chetouani%2C+A">Aladine Chetouani</a>, <a href="/search/eess?searchtype=author&query=Jennane%2C+R">Rachid Jennane</a>, <a href="/search/eess?searchtype=author&query=Ru%2C+Y">Yuhua Ru</a>, <a href="/search/eess?searchtype=author&query=Issa%2C+W">Wasim Issa</a>, <a href="/search/eess?searchtype=author&query=Jarraya%2C+M">Mohamed Jarraya</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2408.00891v1-abstract-short" style="display: inline;"> Knee Osteoarthritis (KOA) is a common musculoskeletal disorder that significantly affects the mobility of older adults. In the medical domain, images containing temporal data are frequently utilized to study temporal dynamics and statistically monitor disease progression. While deep learning-based generative models for natural images have been widely researched, there are comparatively few methods… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.00891v1-abstract-full').style.display = 'inline'; document.getElementById('2408.00891v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2408.00891v1-abstract-full" style="display: none;"> Knee Osteoarthritis (KOA) is a common musculoskeletal disorder that significantly affects the mobility of older adults. In the medical domain, images containing temporal data are frequently utilized to study temporal dynamics and statistically monitor disease progression. While deep learning-based generative models for natural images have been widely researched, there are comparatively few methods available for synthesizing temporal knee X-rays. In this work, we introduce a novel deep-learning model designed to synthesize intermediate X-ray images between a specific patient's healthy knee and severe KOA stages. During the testing phase, based on a healthy knee X-ray, the proposed model can produce a continuous and effective sequence of KOA X-ray images with varying degrees of severity. Specifically, we introduce a Diffusion-based Morphing Model by modifying the Denoising Diffusion Probabilistic Model. Our approach integrates diffusion and morphing modules, enabling the model to capture spatial morphing details between source and target knee X-ray images and synthesize intermediate frames along a geodesic path. A hybrid loss consisting of diffusion loss, morphing loss, and supervision loss was employed. We demonstrate that our proposed approach achieves the highest temporal frame synthesis performance, effectively augmenting data for classification models and simulating the progression of KOA. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.00891v1-abstract-full').style.display = 'none'; document.getElementById('2408.00891v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 August, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2304.08364">arXiv:2304.08364</a> <span> [<a href="https://arxiv.org/pdf/2304.08364">pdf</a>, <a href="https://arxiv.org/format/2304.08364">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Image and Video Processing">eess.IV</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computer Vision and Pattern Recognition">cs.CV</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.eswa.2024.124614">10.1016/j.eswa.2024.124614 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Transformer with Selective Shuffled Position Embedding and Key-Patch Exchange Strategy for Early Detection of Knee Osteoarthritis </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/eess?searchtype=author&query=Wang%2C+Z">Zhe Wang</a>, <a href="/search/eess?searchtype=author&query=Chetouani%2C+A">Aladine Chetouani</a>, <a href="/search/eess?searchtype=author&query=Jarraya%2C+M">Mohamed Jarraya</a>, <a href="/search/eess?searchtype=author&query=Hans%2C+D">Didier Hans</a>, <a href="/search/eess?searchtype=author&query=Jennane%2C+R">Rachid Jennane</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2304.08364v2-abstract-short" style="display: inline;"> Knee OsteoArthritis (KOA) is a widespread musculoskeletal disorder that can severely impact the mobility of older individuals. Insufficient medical data presents a significant obstacle for effectively training models due to the high cost associated with data labelling. Currently, deep learning-based models extensively utilize data augmentation techniques to improve their generalization ability and… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2304.08364v2-abstract-full').style.display = 'inline'; document.getElementById('2304.08364v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2304.08364v2-abstract-full" style="display: none;"> Knee OsteoArthritis (KOA) is a widespread musculoskeletal disorder that can severely impact the mobility of older individuals. Insufficient medical data presents a significant obstacle for effectively training models due to the high cost associated with data labelling. Currently, deep learning-based models extensively utilize data augmentation techniques to improve their generalization ability and alleviate overfitting. However, conventional data augmentation techniques are primarily based on the original data and fail to introduce substantial diversity to the dataset. In this paper, we propose a novel approach based on the Vision Transformer (ViT) model with original Selective Shuffled Position Embedding (SSPE) and key-patch exchange strategies to obtain different input sequences as a method of data augmentation for early detection of KOA (KL-0 vs KL-2). More specifically, we fix and shuffle the position embedding of key and non-key patches, respectively. Then, for the target image, we randomly select other candidate images from the training set to exchange their key patches and thus obtain different input sequences. Finally, a hybrid loss function is developed by incorporating multiple loss functions for different types of the sequences. According to the experimental results, the generated data are considered valid as they lead to a notable improvement in the model's classification performance. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2304.08364v2-abstract-full').style.display = 'none'; document.getElementById('2304.08364v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 April, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2303.13203">arXiv:2303.13203</a> <span> [<a href="https://arxiv.org/pdf/2303.13203">pdf</a>, <a href="https://arxiv.org/format/2303.13203">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Image and Video Processing">eess.IV</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computer Vision and Pattern Recognition">cs.CV</span> </div> </div> <p class="title is-5 mathjax"> Confidence-Driven Deep Learning Framework for Early Detection of Knee Osteoarthritis </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/eess?searchtype=author&query=Wang%2C+Z">Zhe Wang</a>, <a href="/search/eess?searchtype=author&query=Chetouani%2C+A">Aladine Chetouani</a>, <a href="/search/eess?searchtype=author&query=Chen%2C+Y+H">Yung Hsin Chen</a>, <a href="/search/eess?searchtype=author&query=Ru%2C+Y">Yuhua Ru</a>, <a href="/search/eess?searchtype=author&query=Chen%2C+F">Fang Chen</a>, <a href="/search/eess?searchtype=author&query=Jarraya%2C+M">Mohamed Jarraya</a>, <a href="/search/eess?searchtype=author&query=Bauer%2C+F">Fabian Bauer</a>, <a href="/search/eess?searchtype=author&query=Zhang%2C+L">Liping Zhang</a>, <a href="/search/eess?searchtype=author&query=Hans%2C+D">Didier Hans</a>, <a href="/search/eess?searchtype=author&query=Jennane%2C+R">Rachid Jennane</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2303.13203v2-abstract-short" style="display: inline;"> Knee Osteoarthritis (KOA) is a prevalent musculoskeletal disorder that severely impacts mobility and quality of life, particularly among older adults. Its diagnosis often relies on subjective assessments using the Kellgren-Lawrence (KL) grading system, leading to variability in clinical evaluations. To address these challenges, we propose a confidence-driven deep learning framework for early KOA d… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.13203v2-abstract-full').style.display = 'inline'; document.getElementById('2303.13203v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2303.13203v2-abstract-full" style="display: none;"> Knee Osteoarthritis (KOA) is a prevalent musculoskeletal disorder that severely impacts mobility and quality of life, particularly among older adults. Its diagnosis often relies on subjective assessments using the Kellgren-Lawrence (KL) grading system, leading to variability in clinical evaluations. To address these challenges, we propose a confidence-driven deep learning framework for early KOA detection, focusing on distinguishing KL-0 and KL-2 stages. The Siamese-based framework integrates a novel multi-level feature extraction architecture with a hybrid loss strategy. Specifically, multi-level Global Average Pooling (GAP) layers are employed to extract features from varying network depths, ensuring comprehensive feature representation, while the hybrid loss strategy partitions training samples into high-, medium-, and low-confidence subsets. Tailored loss functions are applied to improve model robustness and effectively handle uncertainty in annotations. Experimental results on the Osteoarthritis Initiative (OAI) dataset demonstrate that the proposed framework achieves competitive accuracy, sensitivity, and specificity, comparable to those of expert radiologists. Cohen's kappa values (k > 0.85)) confirm substantial agreement, while McNemar's test (p > 0.05) indicates no statistically significant differences between the model and radiologists. Additionally, Confidence distribution analysis reveals that the model emulates radiologists' decision-making patterns. These findings highlight the potential of the proposed approach to serve as an auxiliary diagnostic tool, enhancing early KOA detection and reducing clinical workload. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.13203v2-abstract-full').style.display = 'none'; document.getElementById('2303.13203v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2302.13336">arXiv:2302.13336</a> <span> [<a href="https://arxiv.org/pdf/2302.13336">pdf</a>, <a href="https://arxiv.org/format/2302.13336">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Image and Video Processing">eess.IV</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computer Vision and Pattern Recognition">cs.CV</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> </div> </div> <p class="title is-5 mathjax"> Key-Exchange Convolutional Auto-Encoder for Data Augmentation in Early Knee Osteoarthritis Detection </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/eess?searchtype=author&query=Wang%2C+Z">Zhe Wang</a>, <a href="/search/eess?searchtype=author&query=Chetouani%2C+A">Aladine Chetouani</a>, <a href="/search/eess?searchtype=author&query=Jarraya%2C+M">Mohamed Jarraya</a>, <a href="/search/eess?searchtype=author&query=Chen%2C+Y+H">Yung Hsin Chen</a>, <a href="/search/eess?searchtype=author&query=Ru%2C+Y">Yuhua Ru</a>, <a href="/search/eess?searchtype=author&query=Chen%2C+F">Fang Chen</a>, <a href="/search/eess?searchtype=author&query=Bauer%2C+F">Fabian Bauer</a>, <a href="/search/eess?searchtype=author&query=Zhang%2C+L">Liping Zhang</a>, <a href="/search/eess?searchtype=author&query=Hans%2C+D">Didier Hans</a>, <a href="/search/eess?searchtype=author&query=Jennane%2C+R">Rachid Jennane</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2302.13336v2-abstract-short" style="display: inline;"> Knee Osteoarthritis (KOA) is a common musculoskeletal condition that significantly affects mobility and quality of life, particularly in elderly populations. However, training deep learning models for early KOA classification is often hampered by the limited availability of annotated medical datasets, owing to the high costs and labour-intensive nature of data labelling. Traditional data augmentat… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2302.13336v2-abstract-full').style.display = 'inline'; document.getElementById('2302.13336v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2302.13336v2-abstract-full" style="display: none;"> Knee Osteoarthritis (KOA) is a common musculoskeletal condition that significantly affects mobility and quality of life, particularly in elderly populations. However, training deep learning models for early KOA classification is often hampered by the limited availability of annotated medical datasets, owing to the high costs and labour-intensive nature of data labelling. Traditional data augmentation techniques, while useful, rely on simple transformations and fail to introduce sufficient diversity into the dataset. To address these challenges, we propose the Key-Exchange Convolutional Auto-Encoder (KECAE) as an innovative Artificial Intelligence (AI)-based data augmentation strategy for early KOA classification. Our model employs a convolutional autoencoder with a novel key-exchange mechanism that generates synthetic images by selectively exchanging key pathological features between X-ray images, which not only diversifies the dataset but also ensures the clinical validity of the augmented data. A hybrid loss function is introduced to supervise feature learning and reconstruction, integrating multiple components, including reconstruction, supervision, and feature separation losses. Experimental results demonstrate that the KECAE-generated data significantly improve the performance of KOA classification models, with accuracy gains of up to 1.98% across various standard and state-of-the-art architectures. Furthermore, a clinical validation study involving expert radiologists confirms the anatomical plausibility and diagnostic realism of the synthetic outputs. These findings highlight the potential of KECAE as a robust tool for augmenting medical datasets in early KOA detection. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2302.13336v2-abstract-full').style.display = 'none'; document.getElementById('2302.13336v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 26 February, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2023. </p> </li> </ol> <div class="is-hidden-tablet"> <!-- feedback for mobile only --> <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a> </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" 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