Proof of Convergence and Performance Analysis for Sparse Recovery via Zero-point Attracting Projection

A recursive algorithm named Zero-point Attracting Projection (ZAP) is proposed recently for sparse signal reconstruction. Compared with the reference algorithms, ZAP demonstrates rather good performance in recovery precision and robustness. However, any theoretical analysis about the mentioned algorithm, even a proof on its convergence, is not available. In this work, a strict proof on the convergence of ZAP is provided and the condition of convergence is put forward. Based on the theoretical analysis, it is further proved that ZAP is non-biased and can approach the sparse solution to any extent, with the proper choice of step-size. Furthermore, the case of inaccurate measurements in noisy scenario is also discussed. It is proved that disturbance power linearly reduces the recovery precision, which is predictable but not preventable. The reconstruction deviation of $p$-compressible signal is also provided. Finally, numerical simulations are performed to verify the theoretical analysis.Comment: 29 pages, 6 figure

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

Modeling and performance analysis of a UAV-based sensor network for improved ATR

Automatic Target Recognition (ATR) is computer processing of images or signals acquired by sensors with the purpose to identify objects of interest (targets). This technology is a critical element for surveillance missions. Over the past several years there has been an increasing trend towards fielding swarms of unattended aerial vehicles (UAVs) operating as sensor networks in the air. This trend offers opportunities of integration ATR systems with a UAV-based sensor network to improve the recognition performance. This dissertation addresses some of design issues of ATR systems, explores recognition capabilities of sensor networks in the presence of various distortions and analyzes the limiting recognition performance of sensor networks.;We assume that each UAV is equipped with an optical camera. A model based recognition method for single and multiple frames is introduced. A complete ATR system, including detection, segmentation, recognition and clutter rejection, is designed and tested using synthetic and realistic images. The effects of environmental conditions on target recognition are also investigated.;To analyze and predict ATR performance of a recognition sensor network, a general methodology from information theory view point is used. Given the encoding method, the recognition system is analyzed using a recognition channel. The concepts of recognition capacity, error exponents and probability of outage are defined and derived for a PCA-based ATR system. Both the case of a single encoded image and the case of encoded correlated multiple frames are analyzed. Numerical evaluations are performed. Finally we discuss the joint recognition and communication problems. Three scenarios of a two node recognition sensor network are analyzed. The communication and recognition performances for each scenario are evaluated numerically

Follow Whom? Chinese Users Have Different Choice

Sina Weibo, which was launched in 2009, is the most popular Chinese micro-blogging service. It has been reported that Sina Weibo has more than 400 million registered users by the end of the third quarter in 2012. Sina Weibo and Twitter have a lot in common, however, in terms of the following preference, Sina Weibo users, most of whom are Chinese, behave differently compared with those of Twitter. This work is based on a data set of Sina Weibo which contains 80.8 million users' profiles and 7.2 billion relations and a large data set of Twitter. Firstly some basic features of Sina Weibo and Twitter are analyzed such as degree and activeness distribution, correlation between degree and activeness, and the degree of separation. Then the following preference is investigated by studying the assortative mixing, friend similarities, following distribution, edge balance ratio, and ranking correlation, where edge balance ratio is newly proposed to measure balance property of graphs. It is found that Sina Weibo has a lower reciprocity rate, more positive balanced relations and is more disassortative. Coinciding with Asian traditional culture, the following preference of Sina Weibo users is more concentrated and hierarchical: they are more likely to follow people at higher or the same social levels and less likely to follow people lower than themselves. In contrast, the same kind of following preference is weaker in Twitter. Twitter users are open as they follow people from levels, which accords with its global characteristic and the prevalence of western civilization. The message forwarding behavior is studied by displaying the propagation levels, delays, and critical users. The following preference derives from not only the usage habits but also underlying reasons such as personalities and social moralities that is worthy of future research.Comment: 9 pages, 13 figure