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arXiv 2024年

作者： Xu, Renjie Wei, Tong Wei, Yimin Xie, Pengpeng Center for Intelligent Multidimensional Data Analysis Hong Kong Science Park Shatin Hong Kong Institute of Science and Technology for Brain-Inspired Intelligence Fudan University Shanghai200433 China School of Mathematical Sciences Shanghai Key Laboratory of Contemporary Applied Mathematics Fudan University Shanghai200433 China School of Mathematical Sciences Ocean University of China Qingdao266100 China

Matrix decompositions in dual number representations have played an important role in fields such as kinematics and computer graphics in recent years. In this paper, we present a QR decomposition algorithm for dual number matrices, specifically geared towards its application in traveling wave identification, utilizing the concept of proper orthogonal decomposition. When dealing with large-scale problems, we present explicit solutions for the QR, thin QR, and randomized QR decompositions of dual number matrices, along with their respective algorithms with column pivoting. The QR decomposition of dual matrices is an accurate first-order perturbation, with the Q-factor satisfying rigorous perturbation bounds, leading to enhanced orthogonality. In numerical experiments, we discuss the suitability of different QR algorithms when confronted with various large-scale dual matrices, providing their respective domains of applicability. Subsequently, we employed the QR decomposition of dual matrices to compute the DMPGI, thereby attaining results of higher precision. Moreover, we apply the QR decomposition in the context of traveling wave identification, employing the notion of proper orthogonal decomposition to perform a validation analysis of large-scale functional magnetic resonance imaging (fMRI) data for brain functional circuits. Our approach significantly improves the identification of two types of wave signals compared to previous research, providing empirical evidence for cognitive neuroscience theories. Copyright © 2024, The Authors. All rights reserved.

关键词： Brain

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Unsupervised Domain Adaptation for Low-dose CT Reconstruction via Bayesian Uncertainty Alignment

arXiv

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arXiv 2023年

作者： Chen, Kecheng Liu, Jie Wan, Renjie Lee, Victor Ho-Fun Vardhanabhuti, Varut Yan, Hong Li, Haoliang The Department of Electrical Engineering The Center for Intelligent Multidimensional Data Analysis City University of Hong Kong Hong Kong The Department of Computer Science Hong Kong Baptist University Hong Kong The Department of Clinical Oncology School of Clinical Medicine LKS Faculty of Medicine The University of Hong Kong Hong Kong The Department of Diagnostic Radiology School of Clinical Medicine LKS Faculty of Medicine The University of Hong Kong Hong Kong

Low-dose computed tomography (LDCT) image reconstruction techniques can reduce patient radiation exposure while maintaining acceptable imaging quality. Deep learning is widely used in this problem, but the performance of testing data (a.k.a. target domain) is often degraded in clinical scenarios due to the variations that were not encountered in training data (a.k.a. source domain). Unsupervised domain adaptation (UDA) of LDCT reconstruction has been proposed to solve this problem through distribution alignment. However, existing UDA methods fail to explore the usage of uncertainty quantification, which is crucial for reliable intelligent medical systems in clinical scenarios with unexpected variations. Moreover, existing direct alignment for different patients would lead to content mismatch issues. To address these issues, we propose to leverage a probabilistic reconstruction framework to conduct a joint discrepancy minimization between source and target domains in both the latent and image spaces. In the latent space, we devise a Bayesian uncertainty alignment to reduce the epistemic gap between the two domains. This approach reduces the uncertainty level of target domain data, making it more likely to render well-reconstructed results on target domains. In the image space, we propose a sharpness-aware distribution alignment to achieve a match of second-order information, which can ensure that the reconstructed images from the target domain have similar sharpness to normal-dose CT images from the source domain. Experimental results on two simulated datasets and one clinical low-dose imaging dataset show that our proposed method outperforms other methods in quantitative and visualized performance. © 2023, CC BY.

关键词： Uncertainty analysis

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