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CLC number: O174.41; TN911.7

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Received: 2005-01-07

Revision Accepted: 2005-05-27

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Journal of Zhejiang University SCIENCE A 2005 Vol.6 No.7 P.760~763

http://doi.org/10.1631/jzus.2005.A0760


Reconstruction algorithm in lattice-invariant signal spaces


Author(s):  XIAN Jun

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   mathxj@zju.edu.cn

Key Words:  Lattice-invariant space, Reconstruction algorithm, Irregular sampling


XIAN Jun. Reconstruction algorithm in lattice-invariant signal spaces[J]. Journal of Zhejiang University Science A, 2005, 6(7): 760~763.

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publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2005.A0760"
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A1 - XIAN Jun
J0 - Journal of Zhejiang University Science A
VL - 6
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2005.A0760


Abstract: 
In this paper, we mainly pay attention to the weighted sampling and reconstruction algorithm in lattice-invariant signal spaces. We give the reconstruction formula in lattice-invariant signal spaces, which is a generalization of former results in shift-invariant signal spaces. That is, we generalize and improve Aldroubi, Gröchenig and Chen’s results, respectively. So we obtain a general reconstruction algorithm in lattice-invariant signal spaces, which the signal spaces is sufficiently large to accommodate a large number of possible models. They are maybe useful for signal processing and communication theory.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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[2] Aldroubi, A., Feichtinger, H., 1998. Exact iterative reconstruction algorithm for multivate irregular sampled functions in spline-like spaces: The Lp theory. Proc. Amer. Math. Soc., 126(9):2677-2686.

[3] Aldroubi, A., Feichtinger, H., 2002. Non-uniform Sampling: Exact Reconstruction from Non-uniformly Distributed Weighted-averages. In: Zhou, D.X. (Ed.), Wavelet Analysis: Twenty Years’ Developments. World Science Publishing, River Edge, NJ.

[4] Aldroubi,, A., Gröchenig, K., 2000. Beurling-Landau-type theorems for non-uniform sampling in shift invariant spline spaces. J. Fourier. Anal. Appl., 6(1):93-103.

[5] Aldroubi, A., Gröchenig, K., 2001. Non-uniform sampling and reconstruction in shift-invariant spaces. SIAM Rev. 43(4):585-620.

[6] Bergh, J., Löfström, J., 1976. Interpolation Spaces. An Introduction. Springer-Verlag, Berlin.

[7] Chen, W., Itoh, S., Shiki, J., 2002. On sampling in shift invariant spaces. IEEE Trans. Information Theory, 48(10):2802-2810.

[8] Gröchenig, K., 2004. Localization of frames, Banach frames, and the invertibility of the frame operator. J. Fourier. Anal. Appl., 10(2):105-132.

[9] Jaffard, S., 1990. Propriétés des matrices “bien localisées” près de leur diagonale et quelques applications. Ann. Inst. H. Poincaré Anal. Non Linéaire, 7(5):461-476.

[10] Lewitt, R.M., 1992. Alternatives to voxels for image representation in iterative reconstruction algorithm. Phys. Med. Biol., 37:705-716.

[11] Luo, S.P., Lin, W., 2004. Non-uniform sampling in shift-invariant spaces. Appl. Math. J. Chinese Univ. Ser. A, 19(1):62-74 (in Chinese).

[12] Sun, W.C., Zhou, X.W., 2002. Average sampling in spline subspaces. Appl. Math. Letter, 15:233-237.

[13] Xian, J., Qiang, X.F., 2003. Non-uniform sampling and reconstruction in weighted multiply generated shift-invariant spaces. Far. East. J. Math. Sci., 8(3):281-293.

[14] Xian, J., Lin, W., 2004. Sampling and reconstruction in time-warped spaces and their applications. Appl. Math. Comput., 157:153-173.

[15] Xian, J., Luo, S.P., Lin, W., 2004. Improved A-P iterative algorithm in spline subspaces. Lecture Notes in Computer Science, 3037:60-67.

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