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ACD Fotocanvas Print Editorial Board Supported by NSFC . Honorary Editor General ZHOU GuangZhao (Zhou Guang Zhao) Editor General ZHU ZuoYan Institute of Hydrobiology, CAS Editor-in-Chief LI Wei Beihang University Executive Associate Editor-in-Chief WANG DongMing Centre National de la Recherche Scientifique Associate Editors-in-Chief GUO Lei Academy of Mathematics and Systems Science, CAS HUANG Ru Peking University QIN YuWen National Natural Science Foundation of China SUN ZengQi Tsinghua University YOU XiaoHu Southeast University ZHAO QinPing Beihang University ZHAO Wei University of Macau Members CHEN JianEr LI Joshua LeWei TSAI WeiTek Texas A&M University University of Electronic Science and Arizona State University Technology of China DU Richard LiMin WANG Ji Voxeasy Institute of Technology LIU DeRong National University of Defense Technology Institute of Automation, CAS GAO Wen WANG JiangZhou Peking University LIN HuiMin University of Kent Institute of Software, CAS GE ShuZhi Sam University of Electronic Science and WANG Long LIN ZongLi Peking University Technology of China University of Virginia GUO GuangCan WU YiRong LONG KePing University of Science and Technology of Institute of Electronics, CAS University of Science and Technology China Beijing XIE WeiXin HAN WenBao Shenzhen University LU Jian PLA Information Engineering University Nanjing University XU Jun Tsinghua University HE JiFeng MEI Hong East China Normal University Peking University XU Ke HU WeiWu MENG LuoMing Beihang University Institute of Computing Technology, CAS Beijing University of Posts and Telecommunications YIN QinYe HU ZhanYi Xi’an Jiaotong University Institute of Automation, CAS PENG LianMao YING MingSheng IDA Tetsuo Peking University Tsinghua University University of Tsukuba PENG QunSheng Zhejiang University ZHA HongBin JI YueFeng Peking University Beijing University of Posts and Telecommu- SHEN ChangXiang nications Computing Technology Institute of China ZHANG HuanGuo Navy Wuhan University JIN Hai Huazhong University of Science and SUN JiaGuang ZHOU Dian Technology Tsinghua University The University of Texas at Dallas JIN YaQiu TANG ZhiMin ZHOU ZhiHua Fudan University Institute of Computing Technology, CAS Nanjing University JING ZhongLiang TIAN Jie ZHUANG YueTing Shanghai Jiao Tong University Institute of Automation, CAS Zhejiang University Editorial Staff SONG Fei FENG Jing ZHAO DongXia Go To Website SCIENCE CHINA Information Sciences Contents Vol. 55 No. 11 November 2012 RESEARCH PAPER Study on co-occurrence character networks from Chinese essays in different periods ............................................................................. 2417 LIANG Wei, SHI YuMing, TSE Chi K & WANG YanLi Automatic composition of information-providing web services based on query rewriting ....................................................................... 2428 ZHAO WenFeng, LIU ChuanChang & CHEN JunLiang A construction method of matroidal networks ............................................................................................................................................ 2445 YUAN Chen, KAN HaiBin, WANG Xin & IMAI Hideki Communication network designing: Transmission capacity, cost and scalability ..................................................................................... 2454 ZHANG GuoQiang & ZHANG GuoQing Corner occupying theorem for the two-dimensional integral rectangle packing problem ......................................................................... 2466 HUANG WenQi, YE Tao & CHEN DuanBing Round-optimal zero-knowledge proofs of knowledge for NP .................................................................................................................... 2473 LI HongDa, FENG DengGuo, LI Bao & XUE HaiXia Binary particle swarm optimization with multiple evolutionary strategies ................................................................................................ 2485 ZHAO Jing, HAN ChongZhao & WEI Bin Communications and control co-design: a combined dynamic-static scheduling approach ...................................................................... 2495 LU ZiBao & GUO Ge Optimized statistical analysis of software trustworthiness attributes ......................................................................................................... 2508 ZHANG Xiao, LI Wei, ZHENG ZhiMing & GUO BingHui A new one-bit difference collision attack on HAVAL-128 ........................................................................................................................ 2521 ZHANG WenYing, LI YanYan & WU Lei Signcryption with fast online signing and short signcryptext for secure and private mobile communication .......................................... 2530 YOUN Taek-Young & HONG Dowon An ID-based authenticated dynamic group key agreement with optimal round ........................................................................................ 2542 TENG JiKai, WU ChuanKun & TANG ChunMing Evolutionary ciphers against differential power analysis and differential fault analysis ........................................................................... 2555 TANG Ming, QIU ZhenLong, YANG Min, CHENG PingPan, GAO Si, LIU ShuBo & MENG QinShu An oblivious fragile watermarking scheme for images utilizing edge transitions in BTC bitmaps ........................................................... 2570 ZHANG Yong, LU ZheMing & ZHAO DongNing The essential ability of sparse reconstruction of different compressive sensing strategies ........................................................................ 2582 ZHANG Hai, LIANG Yong, GOU HaiLiang & XU ZongBen Waveform design and high-resolution imaging of cognitive radar based on compressive sensing ........................................................... 2590 LUO Ying, ZHANG Qun, HONG Wen & WU YiRong An efficient sparse channel estimator combining time-domain LS and iterative shrinkage for OFDM systems with IQ-imbalances ..... 2604 SHU Feng, ZHAO JunHui, YOU XiaoHu, WANG Mao, CHEN Qian & STEVAN Berber Object registration for remote sensing images using robust kernel pattern vectors ................................................................................... 2611 DING MingTao, JIN Zi, TIAN Zheng, DUAN XiFa, ZHAO Wei & YANG LiJuan Quasi-linear modeling of gyroresonance between different MLT chorus and geostationary orbit electrons ............................................ 2624 ZHANG ZeLong, XIAO FuLiang, HE YiHua, HE ZhaoGuo, YANG Chang, ZHOU XiaoPing & TANG LiJun A variational method for contour tracking via covariance matching.......................................................................................................... 2635 WU YuWei, MA Bo & LI Pei Near lossless compression of hyperspectral images based on distributed source coding .......................................................................... 2646 NIAN YongJian, WAN JianWei, TANG Yi & CHEN Bo A 10 GHz multiphase LC VCO with a ring capacitive coupling structure ................................................................................................ 2656 CHEN YingMei, WANG Hui, YAN ShuangChao & ZHANG Li SCIENCE CHINA Information Sciences . RESEARCH PAPER . November 2012 Vol. 55 No. 11: 2582–2589 doi: 10.1007/s11432-011-4502-6 The essential ability of sparse reconstruction of different compressive sensing strategies ZHANG Hai1,2 ∗, LIANG Yong3, GOU HaiLiang1 & XU ZongBen1 1 Institute for Information and System Science, Xi’an Jiaotong University, Xi’an 710049,China; 2Department of Mathematics, Northwest University, Xi’an 710069,China; 3University of Science and Technology, Macau 999078,China Received March 30, 2010; accepted July 8, 2010; published online January 14, 2012 Abstract We show the essential ability of sparse signal reconstruction of different compressive sensing strate- gies,which include the L1 regularization, the L0 regularization(thresholding iteration algorithm and OMP algo- rithm), the Lq(0 <q 1) regularizations, the Log regularization and the SCAD regularization. Taking phase diagram as the basic tool for analysis, we find that (i) the solutions of the L0 regularization using hard thresh- olding algorithm and OMP algorithm are similar to those of the L1 regularization; (ii) the Lq regularization with the decreasing value of q, the Log regularization and the SCAD regularization can attain sparser solutions than the L1 regularization; (iii) the L1/2 regularization can be taken as a representative of the Lq(0 <q<1) regularizations. When 1/2 <q<1, the L1/2 regularization always yields the sparsest solutions and when 0 <q<1/2 the performance of the regularizations takes no significant difference. The results of this paper provide experimental evidence for our previous work. Keywords compressive sensing, regularization, sparsity, L1/2 regularization Citation Zhang H, Liang Y, Gou H L, et al. The essential ability of sparse reconstruction of different compressive sensing strategies. Sci China Inf Sci, 2012, 55: 2582–2589, doi: 10.1007/s11432-011-4502-6 1 Introduction Compressive sensing [1,2], also called sparse signal reconstruction, is a novel sampling paradigm to re- construct sparse signal. It has been widely used in the areas of signal processing, image processing and machine learning in recent years. Different from the traditional Shannon/Nyquist theory, the compressive sensing makes it possible to recover sparse signal from far fewer samples than the Shannon sampling. Therefore it provides a new way for acquiring, processing and applying the complex information. And the
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