Let us consider a case where all of the elements in some continuous slices are missing in tensor data.
In this case, the nuclear-norm and total variation regularization methods usually fail to recover the missing elements.
The key problem is capturing some delay/shift-invariant structure.
In this study, we consider a low-rank model in an embedded space of a tensor.
For this purpose, we extend a delay embedding for a time series to a "multi-way delay-embedding transform" for a tensor, which takes a given incomplete tensor as the input and outputs a higher-order incomplete Hankel tensor.
The higher-order tensor is then recovered by Tucker-based low-rank tensor factorization.
Finally, an estimated tensor can be obtained by using the inverse multi-way delay embedding transform of the recovered higher-order tensor.
Our experiments showed that the proposed method successfully recovered missing slices for some color images and functional magnetic resonance images.
SAGCNet: Spatial-Aware Graph Completion Network for Missing Slice Imputation in Population CMR Imaging
School of Engineering, College of Engineering and Physical Sciences（工程学院，工程与物理科学学院）；University of Birmingham（伯明翰大学）；Oxford Center for Clinical Magnetic Resonance Research (OCMR)（牛津临床磁共振研究中心）；University of Oxford（牛津大学）；John Radcliffe Hospital（约翰·拉德克利夫医院）；Johns Hopkins University School of Medicine（约翰霍普金斯大学医学院）；Queen Mary University London（伦敦女王大学）；Barts Health NHS Trust（巴特勒医院 NHS 信托）
End-to-End 4D Heart Mesh Recovery Across Full-Stack and Sparse Cardiac MRI
School of Computer and Communication Science, EPFL（计算机与通信科学学院，瑞士联邦理工学院）；ELLIS Institute Finland, Aalto University, Finland（芬兰ELLIS研究所，阿尔托大学，芬兰）；University of North Carolina at Charlotte（北卡罗来纳大学夏洛特分校）；Center for Interventional MRI, CHUV（介入MRI中心，CHUV）
RoHyDR: Robust Hybrid Diffusion Recovery for Incomplete Multimodal Emotion Recognition
School of Computer Science and Engineering（计算机科学与工程学院）；South China University of Technology（华南理工大学）；School of Future Technology（未来技术学院）；University of Oxford（牛津大学）；Pengcheng Laboratory（鹏城实验室）；Department of Computer Science（计算机科学系）
DTR: A Unified Deep Tensor Representation Framework for Multimedia Data Recovery
University of Electronic Science and Technology of China（电子科技大学）；Southwest Jiaotong University（西南交通大学）；Jiangxi University of Finance and Economics（江西财经大学）；City University of Hong Kong（香港城市大学）
Smooth Robust Tensor Completion for Background/Foreground Separation with Missing Pixels: Novel Algorithm with Convergence Guarantee
Virginia Tech（弗吉尼亚理工大学）
本研究的目的是通过将视频采集、视频恢复、背景/前景分离结合到一个框架中来解决具有缺失像素的背景/前景分离问题。为了实现这一点，平滑鲁棒张量完成（SRTC）模型被提出来恢复数据，并将其分解为静态背景和平滑前景，分别。具体地说，静态背景建模的低秩塔克分解和平滑的前景（运动物体）建模的时空连续性，这是由总变分正则化。基于张量近似交替最小化（tensor proximate alternative minimization，tenPAM）的有效算法实现求解所提出的模型，在非常温和的条件下具有全局收敛性保证。大量的实验表明，该方法显着优于国家的最先进的方法，背景/前景分离与丢失像素。
