We consider the problem of imaging sparse scenes from a few noisy data using an $l_1$-minimization approach. This problem can be cast as a linear system of the form $A \, ρ=b$, where $A$ is an $N\times K$ measurement matrix. We assume that the dimension of the unknown sparse vector $ρ\in {\mathbb{C}}^K$ is much larger than the dimension of the data vector $b \in {\mathbb{C}}^N$, i.e, $K \gg N$. We provide a theoretical framework that allows us to examine under what conditions the $\ell_1$-minimization problem admits a solution that is close to the exact one in the presence of noise. Our analysis shows that $l_1$-minimization is not robust for imaging with noisy data when high resolution is required. To improve the performance of $l_1$-minimization we propose to solve instead the augmented linear system $ [A \, | \, C] ρ=b$, where the $N \times Σ$ matrix $C$ is a noise collector. It is constructed so as its column vectors provide a frame on which the noise of the data, a vector of dimension $N$, can be well approximated. Theoretically, the dimension $Σ$ of the noise collector should be $e^N$ which would make its use not practical. However, our numerical results illustrate that robust results in the presence of noise can be obtained with a large enough number of columns $Σ\approx 10 K$.
Explicit Abnormality Extraction for Unsupervised Motion Artifact Reduction in Magnetic Resonance Imaging
School of Electrical Engineering and Automation, Wuhan University（武汉大学电气与自动化学院）；University Hospital Heidelberg（海德堡大学医院）；Vitalent Consulting（维塔伦特咨询公司）；College of Science and Engineering, James Cook University（詹姆斯库克大学科学与工程学院）；Uppsala University（乌普萨拉大学）；School of Computer Science, University of Sydney（悉尼大学计算机学院）
ClusMFL: A Cluster-Enhanced Framework for Modality-Incomplete Multimodal Federated Learning in Brain Imaging Analysis
School of Science and Engineering, the Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）理工学院）；Department of Computer Science and Engineering, Lehigh University（利哈伊大学计算机科学与工程系）；Department of Computer Science, Emory University（埃默里大学计算机科学系）
GMENet: Generative Mixture of Experts Network for Multi-Center Glioma Diagnosis with Incomplete Imaging Sequences
School of Biomedical Engineering and Technology Innovation, Fudan University（复旦大学生物医学工程与技术创新学院）；Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University（复旦大学脑启发智能科学技术研究院）；Intelligent Diagnosis and Treatment Laboratory for Brain Diseases, Joint Laboratory of Neurosurgery Department of Huashan Hospital and School of Information Science and Technology, Fudan University（脑病智能诊断与治疗实验室，华山医院神经外科部门联合实验室，复旦大学信息科学学院）
DIGEST: Deeply supervIsed knowledGE tranSfer neTwork learning for brain tumor segmentation with incomplete multi-modal MRI scans
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）；University of Chinese Academy of Sciences（中国科学院大学）；Peng Cheng Laboratory（鹏城实验室）；Guangdong Provincial People’s Hospital（广东省人民医院）；Guangdong Academy of Medical Sciences（广东省医学科学院）
Personalized Topology-Informed Localization of Standard 12-Lead ECG Electrode Placement from Incomplete Cardiac MRIs for Efficient Cardiac Digital Twins
School of Electronics & Computer Science, University of Southampton（南安普顿大学电子与计算机科学学院）；University of Oxford（牛津大学）；National University of Singapore（新加坡国立大学）；School of Biomedical Engineering and Imaging Sciences, Kings College London（伦敦国王学院生物医学工程与影像科学学院）
Learning stochastic object models from medical imaging measurements by use of advanced ambient generative adversarial networks
University of California Santa Barbara（加州大学圣巴巴拉分校）；Washington University in St. Louis（圣路易斯华盛顿大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Cancer Center at Illinois（伊利诺伊癌症中心）
