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一类带限函数的外推算法及应用

Extrapolation Algorithm of a Class of Band-limited Function and Its Application
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摘要 将带限函数的外推Gerchberg-Papoulis算法在维数和已知区域方面进行了推广,证明了推广的算法在L2范数下的收敛性,并应用于限制角图像重建。在一维情形下进行数值模拟,验证了推广后算法的有效性。 The Gerchberg-Papoulis algorithm of band-limited function in dimensional number and known region are generalized, and proved the convergence of the generalized algorithm in-Norm. This algorithm is also applied to the angle-limited image reconstruction. The numerical simulation in one-dimension situation is given and shows the efficiency of this algorithm.
作者 朱季云 渠刚荣
机构地区 北京交通大学理学院
出处 《科学技术与工程》 2006年第23期4756-4758,共3页 Science Technology and Engineering
基金 国家自然科学基金(60372015)资助
关键词 带限函数外推 Gerchberg-Papoulis算法 限制角图像重建 RADON变换 band-limited function extrapolation Gerchberg-Papoulis algorithm angle-limited image reconstruction Radon transform
分类号 O174.2 [理学—基础数学] O177.6 [理学—基础数学]
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参考文献6

  • 1[1]Athanasios P.A new algorithm in spectral analysis and band limited extrapolation.IEEE Transactions on Circuits and Systems,1975; CAS-22 (9):735-742
  • 2张兆田,渠刚荣,姜明.带限函数外推算法收敛性研究[J].工程数学学报,2004,21(2):143-148. 被引量：10
  • 3[3]李衍达,常迥.信号重建理论及其应用.北京:清华大学出版社,1991,11-14
  • 4[4]David S.Prolate spheroidal wave functions Fourier analysis and uncertainty-Ⅳ:extensions to many dimensions; generalized prolate spheroidal functions.The Bell Systerm Technical Journal,1964:3009-3057
  • 5[7]Chatelin F.Spectral approximation of linear operators.Academic Press,1983:117-119
  • 6[8]Falberto C.A study of Fourier space methods for "limited angle" image reconstruction.Numer funct anal and Optimiz,1980; 2 (1):31-42

二级参考文献8

  • 1Chamzas C, Xu W Y. An improved version of papoulis-gerchberg algorithm on band-limited extrapolation[J]. IEEE Trans Acoustics, Speech Signal Processing, 1984 ;32:437- 440
  • 2Papoulis A. Signal analysis[M]. New York: Mc Graw-Hill,1977
  • 3Papoulis A. A new algorithm in spectral analysis and band-limited signal extrapolation[J]. IEEE on Trans Circuits Syst, 1975 ;22:735 - 742
  • 4Gerchberg R W. Super-resolution through error energy reduction[J]. Opt Acta,1974;21:709- 720
  • 5Xu W Y, Chamzas C. On the extrapolation of band-limited functions with energy constraints[J]. IEEE Trans Acoustic Speech Signal Processing, 1983; 31:1222 - 1234
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共引文献9

科学技术与工程
2006年 第23期

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