基于原子库树状结构划分的诱导式信号稀疏分解

Abstract

Abstract: To overcome the deficiency of traditional sparse decomposition algorithm,in which the performance improvement is merely made either by improving the mode of constructing atom dictionary or by decomposing method,and it also has a high calculative complexity,a new guiding pyramidal algorithm of sparse decomposition is presented.The algorithm firstly divides the atom dictionary into several subsets by its characteristics and forms a tree structure atom dictionary after several layer-by-layer partition of the atom set.Then the decomposing of signals can be purposefully performed along the course charted by the tree structure at each iteration and the decomposing speed is greatly increased,and the calculative complexity is sharply decreased.Experiment results show that the calculating amount of the new algorithm is only about 1/40 of MP algorithm,and the computing time 1/100 of MP algorithm,under the condition of the same sparsity and similar approximation error.The simulation results indicate that the presented method is efficient.

CLC Number:

TN911.7

LIU Dan-hua, SHI Guang-ming, GAO Da-hua, ZHOU Jia-she. Guiding method of signal sparse decomposition based on tree-structured partition of atom dictionary [J]. Journal of Systems Engineering and Electronics, 2009, 31(8): 1976-1981.

References

[1] Mallat S,Zhang Z.Matching pursuit with time-frequency dictionaries[J].IEEE Trans.on Signal Processing,1993,41(12):3397-3415.
[2] 尹忠科,解梅,王建英.基于稀疏分解的图像去噪[J].电子科技大学学报,2006,35(6):876-878.
[3] 张文耀.基于匹配跟踪的低位率语音编码研究[D].北京:中国科学院研究生院软件研究所,2002.
[4] Arthur P L,Philipos C L.Voiced/unvoiced speech discrimination in noise using gabor atomic decomposition[C]//Proc.International Conference on Acoustics,Speech and Signal Processing,Hong Kong:Institute of Electrical and Electronics Engineers Inc,2003,1:820-823.
[5] 邹红星,周小波,李衍达.时频分析:回溯与前瞻[J].电子学报,2000,28(9):78-84.
[6] 傅霆,尧德中.稀疏分解的加权迭代方法及其初步应用[J].电子学报,2004,32(4):567-570.
[7] 王建英,尹忠科,张春梅.信号与图像的稀疏分解及初步应用[M].成都:西南交通大学出版社.2006.
[8] Donoho D L.Compressed sensing[J].IEEE Trans.on Informarion Theory,2006,52(4):1289-1306.
[9] Emmanuel Candès.Compressive sampling[C]//International Congress of Mathematics,Madrid,Spain,2006:1433-1452.
[10] Temlyakov V N.Greedy algorithms and m-term approximation[J].Journal of Approx.Theory,1999:117-145.
[11] Tropp J A.Greed is good:algorithmic results for sparse ap-proximation[J].IEEE Trans.on Information Theory,2003,50(11):2231-2242.
[12] Pati Y C,Rezaiifar R,Krishnaprasad P S.Orthogonal matching pursuits:recursive function approximation with applications to wavelet decomposition[C]//Conference Record of the 27th Asilomar Conference on Signals,Systems & Computers,IEEE,Los Alamitos,CA,USA,1993,1:40-44.
[13] Gribonval R,Vandergheynst P.On the exponential convergence of matching pursuits in quasi-incoherent dictionaries[J].IEEE Trans.on Information Theory,2006,52(1):255-261.
[14] Temlyakov V N.Nonlinear methods of approximation[J].Found.Comput.Math.,2003,3(1):33-107.
[15] Tropp J A,Gilbert A C.Signal recovery from random measurements via orthogonal matching pursuit[J].IEEE Trans.on In formation Theory,2007,53(12):4655-4666.
[16] Chen S B,Donoho D L,Saunders M A.Atomic decomposition by basis pursuit[J].SIAM Review,2001,43(1):129-159.
[17] Daubechies I.Time-frequency localization operators:a geometric phase space approach[J].IEEE Trans.on Information Theory,1988,34(4):605-612.
[18] Coif man R R,Wickerhauser M V.Entropy-based algorithms for best-basis selection[J].IEEE Trans.on Information Theory,1992,38(2):713-718.
[19] Mallat S.信号处理的小波导引[M].2版.杨力华,戴道清,黄文良,等译.北京:机械工业出版社,2002.
[20] Donoho D L,Tsaig Y,Drori I,et al.Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit[R].Dept.of Statistics,Stanford Univ.,2006.http://stat.Stanford.edu/-idrori/StOMP.pdf.
[21] Marco F Duarte,Michael B Wakin,Richard G Baraniuk.Fast reconstruction of piecewise smooth signals from incoherent projections.workshop on signal processing with adaptative sparse structured representations(SPARS),Rennes,France,2005,http://spars05.irisa.fr/ACTES/TS5-3.pdf.
[22] Chinh L,Minh N D.Tree-based orthogonal matching pursuit algorithm for signal reconstruction[C]//International Conference on Image Processing,Atlanta,GA,USA,2006:1277-1280.
[23] Gabriel P.Best basis compressed sensing[C]//Lecture Notes in Computer Science,Scale Space and Variational Methods in Computer Vision,Germany,Springer,2007:80-91.
[24] 刘丹华,石光明,周佳社.一种冗余字典下的信号稀疏分解新方法[J].西安电子科技大学学报(自然科学版),2008,35(2):228-232.
[25] 邵君,尹忠科,王建英,等.信号稀疏分解中过完备原子库的集合划分[J].铁道学报,2006,28(1):68-71.
[26] Davis G,Mallat S,Avellaneda M.Adaptive greedy approximation[J].Constr.Approx.,1997,13(1):57-98.
[27] 张春梅,尹忠科,肖明霞.基于冗余字典的信号超完备表示与稀疏分解[J].科学通报,2006,51(6):628-633.
[28] Shrijver A.Theory of Linear and Integer Programming[M].US:Wiley Press,1998.

Guiding method of signal sparse decomposition based on tree-structured partition of atom dictionary

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