Local Measurement and Reconstruction for Noisy Graph Signals

The emerging field of signal processing on graph plays a more and more important role in processing signals and information related to networks. Existing works have shown that under certain conditions a smooth graph signal can be uniquely reconstructed from its decimation, i.e., data associated with a subset of vertices. However, in some potential applications (e.g., sensor networks with clustering structure), the obtained data may be a combination of signals associated with several vertices, rather than the decimation. In this paper, we propose a new concept of local measurement, which is a generalization of decimation. Using the local measurements, a local-set-based method named iterative local measurement reconstruction (ILMR) is proposed to reconstruct bandlimited graph signals. It is proved that ILMR can reconstruct the original signal perfectly under certain conditions. The performance of ILMR against noise is theoretically analyzed. The optimal choice of local weights and a greedy algorithm of local set partition are given in the sense of minimizing the expected reconstruction error. Compared with decimation, the proposed local measurement sampling and reconstruction scheme is more robust in noise existing scenarios.Comment: 24 pages, 6 figures, 2 tables, journal manuscrip

Eigenvalue estimates for the fractional Laplacian on lattice subgraphs

We introduce the the fractional Laplacian on a subgraph of a graph with Dirichlet boundary condition. For a lattice graph, we prove the upper and lower estimates for the sum of the first $k$ Dirichlet eigenvalues of the fractional Laplacian, extending the classical results by Li-Yau and Kr\"{o}ger

Occluded Person Re-identification

Person re-identification (re-id) suffers from a serious occlusion problem when applied to crowded public places. In this paper, we propose to retrieve a full-body person image by using a person image with occlusions. This differs significantly from the conventional person re-id problem where it is assumed that person images are detected without any occlusion. We thus call this new problem the occluded person re-identitification. To address this new problem, we propose a novel Attention Framework of Person Body (AFPB) based on deep learning, consisting of 1) an Occlusion Simulator (OS) which automatically generates artificial occlusions for full-body person images, and 2) multi-task losses that force the neural network not only to discriminate a person's identity but also to determine whether a sample is from the occluded data distribution or the full-body data distribution. Experiments on a new occluded person re-id dataset and three existing benchmarks modified to include full-body person images and occluded person images show the superiority of the proposed method.Comment: 6 pages, 7 figures, IEEE International Conference of Multimedia and Expo 201

The existence of topological solutions to the Chern-Simons model on lattice graphs

We prove the existence of topological solutions to the self-dual Chern-Simons model and the Abelian Higgs system on the lattice graphs Z^n for n>1. This extends the results in Huang, Lin and Yau [HLY20] from finite graphs to lattice graphs