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一种最优的紧框构造算法 被引量:2

Custom Building Finite Tight Frames
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摘要 设{φm}M m=1是C^N中一组不全为零的向量,本文提出了一种通过增添N-d_1个向量使其构成C^N的一个紧框的最优算法,其中d_1由{φm}M m=1确定。 Let {φM}^Mm=1be not all zeros vectors of CN. This paper introduced an M algorithm to construct a tight finite frame by adding N - d1 vectors to {φM}^Mm=1, where d1 is determined by {φM}^Mm=1.
作者 辛友明
出处 《华东师范大学学报(自然科学版)》 CAS CSCD 北大核心 2007年第3期58-61,共4页 Journal of East China Normal University(Natural Science)
关键词 有限框 紧框 特征值 finite frame tight frame eigenvalue
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参考文献7

  • 1DUFFIN R J,SCHAEFFER A C.A class of nonharmononic Fouroer series[J].Trans Amer Math Soc,1952,72:341-366.
  • 2GROCHENIG K H.Foundations Of Time-Frequency Analysis[M].Boston:Brikhauser,2000.
  • 3DAUBECHIES I.Ten Lectures On Wavelets[M].Philadelphia:SIASM,1992.
  • 4ROBERT R,SHANYNE W.Isometric tight frames[J].The Journal of Linear Algebra,2002(9):122-128.
  • 5CASAZZA P G.Custom building finite frames[C]// Contemp Math 345:Wavelets,Frames and Operator Theory.Providence,RI:Amer Math Soc,2004:61-86.
  • 6CASAZZA P G,LEON M.Existence and construction of finite frames[J].J Concr Appl Math,2006,4(3):277-289.
  • 7VELISAVLJEVIC V,DRAGOTTI P L,VETTERLI M.Directional wavelet transforms and frames[C]// Proceedings of IEEE International Conference on Image Processing (ICIP2002),Rochester:IEEE Press,2002,9(3):589-592.

同被引文献12

  • 1DUFFIN R J, SCHAEFFER A C. A class of nonharmononic Fouroer series[J]. Trans Amer Math Soe, 1952, 72: 341-366.
  • 2CASAZZA P G. The art of frame theory[J]. Tanwanese Journal of Math, 2000, 4(2): 129-202.
  • 3GROCHENIG K H. Foundations of Time-Frequency Analysis[M]. Boston: Brikhauser, 2000.
  • 4DAUBECHIES I. Ten Lectures on Wavelets[M]. philadelphia: SIAM, 1992.
  • 5BENEDETTO J J, LI S. The theory of multiresolution analysis frames and application to filter banker[J]. Appl Comput Harmon Anal, 1998, 5: 398-427.
  • 6VELISAVLJEVIC V, DRAGOTTI P L, VETTERLI M. Directional wavelettransforms and frames[C]// Proceedings of IEEE International Conference on Image Processing (ICIP2002), Rochester, USA. 2002, 9(3): 589-592.
  • 7CHRISTENSEN O. An Introduction to Frames and Riesz Bases[M]. Boston: Birkhauser, 2002.
  • 8ROBERT R, SHANYNE W. Isometric tight frames[J]. The Journal of Linear Algebra, 2002, 9: 122-128.
  • 9CASAZZA P G. Custom building finite frames[C]//Contemp. Math 345: Wavelets, frames and operator theory. Providence, RI: Amer Math Soc, 2004:61-86
  • 10CASAZZA P G, LEON M. Existence and construction of finite frames[J]. J Concr Appl Math, 2006, 4(3): 277-289.

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