基于非凸优化模型的块稀疏信号恢复条件
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摘要
压缩感知(compressed sensing,CS)是一种全新的信息采集与处理理论,它表明稀疏信号能够在远低于Shannon-Nyquist采样率的条件下被精确重构.现从压缩感知理论出发,对块稀疏信号重构算法进行研究,通过混合l2/lq(0 Compressed sensing(CS) is a newly developed theoretical framework for information acquisition and processing,which shows that sparse signals can be recovered exactly from far less samples than those required by the classical Shannon-Nyquist theorem.The block-sparse signal recovery algorithm under the compressed sensing framework was mainly studied,and a class of improved exact recovery conditions based on the block restricted isometry property(RIP) were established in the noiseless cases via the mixed l2/lq(0
引文
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[19]ZHOU Shenglong,KONG Lingchen,LUO Ziyan,et al.New RIC bounds via lq-minimization with 0
[2]CANDES E J,ROMBERG J,TAO T.Stable signal recovery from incomplete and inaccurate measurements[J].Communications Pure and Applied Mathematics,2006,59(8):1207-1223.
[3]CANDES E J.The restrictedisometry property and its implications for compressed sensing[J].Comptes Rendus Mathematique,2008,346(9/10):589-592.
[4]CAI T,WANG L,XU G W.New bounds for restricted isometry constants[J].IEEE Transactions on Information Theory,2010,56(9):4388-4394.
[5]CAI T,ZHANG A R.Compressed sensing and affine rank minimization under restricted isometry[J].IEEE Transactions on Signal Processing,2013,61(13):3279-3290.
[6]FOUCART S.A note on guaranteed sparse recovery via l1-minimization[J].Applied and Computational Harmonic Analysis,2010,29(1):97-103.
[7]DAVIES M,GRIBONVAL R.Restricted isometry constants where lpsparse recovery can fail for 0
[9]DUARTE M,DAVENPORT M,TAKBAR D,et al.Single-pixel imaging via compressive sampling[J].IEEE Signal Processing Magazine,2008,25(2):83-91.
[10]BARANIUK R,STEEGHS P.Compressive radar imaging[C]//Proceeding of the IEEE Radar Conference.Washington DC,USA,2007.
[11]BAJWA W,HAUPT J,SAYEED A,et al.Joint source-channel communication for distributed estimation in sensor networks[J].IEEE Transactions on Information Theory,2007,53(10):3629-3653.
[12]ELDER Y,MISHALI M.Robust recovery of signals from a structured union of subspaces[J].IEEETransactions on Information Theory,2009,55(11):5302-5316.
[13]MISHALI M,ELDAR Y.Blind multiband signalreconstruction:compressed sensing for analog signals[J].IEEE Transactions on Signal Processing,2009,57(3):993-1009.
[14]DAI W,SHEIKH M A,MILENKOVIC O,et al.Compressed sensing DNA microarrays[J].EURASIPJournal on Bioinformatics and Systerms Biology,2009,2009(1):162824.
[15]ENDER J.On compressive sensing applied to radar[J].Signal Processing,2010,90(5):1402-1414.
[16]YANG Z,XIE L.Continuous compressed sensing with a single or multiple measurement vectors[C]//2014 IEEE Workshop on Statistical Signal Processing(SSP),2014:308-311.DOI:10.1109/SSP.2014.6884632.
[17]LIN J H,LI S.Block sparse recovery via mixed l2/l1minimization[J].Acta Mathematica Sinica,2013,29(7):1401-1412.
[18]CHEN W,LI Y.The high order block RIP condition for signal recovery[J].Journal of Computational Mathematics,2016,37(1):61-75.
[19]ZHOU Shenglong,KONG Lingchen,LUO Ziyan,et al.New RIC bounds via lq-minimization with 0