Recovering a large matrix from a small subset of its entries is a challenging problem arising in many real applications, such as image inpainting and recommender systems. Many existing approaches formulate this problem as a general low-rank matrix approximation problem. Since the rank operator is nonconvex and discontinuous, most of the recent theoretical studies use the nuclear norm as a convex relaxation. One major limitation of the existing approaches based on nuclear norm minimization is that all the singular values are simultaneously minimized, and thus the rank may not be well approximated in practice. In this paper, we propose to achieve a better approximation to the rank of matrix by truncated nuclear norm, which is given by the nuclear norm subtracted by the sum of the largest few singular values. In addition, we develop a novel matrix completion algorithm by minimizing the Truncated Nuclear Norm. We further develop three efficient iterative procedures, TNNR-ADMM, TNNR-APGL, and TNNR-ADMMAP, to solve the optimization problem. TNNR-ADMM utilizes the alternating direction method of multipliers (ADMM), while TNNR-AGPL applies the accelerated proximal gradient line search method (APGL) for the final optimization. For TNNR-ADMMAP, we make use of an adaptive penalty according to a novel update rule for ADMM to achieve a faster convergence rate. Our empirical study shows encouraging results of the proposed algorithms in comparison to the state-of-the-art matrix completion algorithms on both synthetic and real visual datasets.

Robotic-assisted tracheal intubation requires the robot to distinguish anatomical features like an experienced physician using deep-learning techniques. However, real datasets of oropharyngeal organs are limited due to patient privacy issues, making it challenging to train deep-learning models for accurate image segmentation. We hereby consider generating a new data modality through a virtual environment to assist the training process. Specifically, this work introduces a virtual dataset generated by the Simulation Open Framework Architecture (SOFA) framework to overcome the limited availability of actual endoscopic images. We also propose a domain adaptive Sim-to-Real method for oropharyngeal organ image segmentation, which employs an image blending strategy called IoU-Ranking Blend (IRB) and style-transfer techniques to address discrepancies between datasets. Experimental results demonstrate the superior performance of the proposed approach with domain adaptive models, improving segmentation accuracy and training stability. In the practical application, the trained segmentation model holds great promise for robotassisted intubation surgery and intelligent surgical navigation.

The issue of virtual network (VN) embedding constitutes an important aspect of network virtualization, which is considered to be one of the most crucial techniques to overcome the Internet ossification problem. The main purpose of VN embedding is to efficiently utilize the limited physical network resources to offer the supporting of virtual nodes and virtual links from the VNs. Due to the fact that the VN embedding problem is proved to be NP-hard, previous works have put forward some of heuristic algorithms to solve this VN embedding problem. However, most of the existing research works only consider the local resources of nodes, ignoring the topological attributes of its neighborhood nodes, and lead to lower resource utilization of the substrate network. To address this issue, we proposed an approach of VN embedding algorithm called VNE-DCC, which based on the node degree and the clustering coefficient information, we adopted the technique of node importance metric to rank the substrate nodes aim to select the node with the most embedding potential for every virtual node in each VN requests, and exploited the breadth-first-search algorithm to embed the virtual nodes aiming at reducing the resource utilization of substrate links so as to increase the acceptance ratio of VN requests and increase the revenues of operational providers. Extensive simulations have shown that the efficiency of our algorithm is better than the other state-of-the-art algorithms in terms of Revenue/Cost ratio and acceptance ratio.INDEX TERMS Virtual network embedding, degree and clustering coefficient, network virtualization, virtual node mapping, virtual link mapping.

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