Abstract
In this paper, we introduce integral sampling and study the reconstruction of signals based on non-uniform average samples in spline subspace. By using a new method, we obtain a new reconstruction formula.
This work is supported in part by the Mathematical Tanyuan Foundation and China Postdoctoral Science Foundation.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Aldroubi, A., Gröchenig, K.: Beuling-Landau-type theorems for non-uniform sampling in shift invariant spline spaces. J. Fourier. Anal. Appl. 6, 93–103 (2000)
Aldroubi, A., Gröchenig, K.: Non-uniform sampling and reconstruction in shift-invariant spaces. SIAM Rev. 43, 585–620 (2001)
Aldroubi, A., Unser, M., Eden, M.: Cardinal spline filters: Stability and convergence to the ideal sinc interpolator. Singal. Processing. 28, 127–138 (1992)
Chui, C.K.: An introduction to Wavelet. Academic Press, New York (1992)
Jerri, A.J.: The Gibbs phenomenon in Fourier analysis, splines and wavelet approximations. In: Mathematics and its Applications, vol. 446. Kluwer Academic Publishers, Dordrecht (1998)
Gröchenig, K., Janssen, A., Kaiblinger, N., Norbert, P.: Note on B-splines, wavelet scaling functions, and Gabor frames. IEEE Trans. Inform. Theory 49(12), 3318–3320 (2003)
Liu, Y.: Irregular sampling for spline wavelet subspaces. IEEE Trans. Inform. Theory 42, 623–627 (1996)
Sun, W.C., Zhou, X.W.: Average sampling in spline subspaces. Appl. Math. Letter 15, 233–237 (2002)
Sun, W.C., Zhou, X.W.: Reconstruction of bandlimited signals from local averages. IEEE Trans. Inform. Theory 48, 2955–2963 (2002)
Unser, M., Blu, T.: Fractional splines and wavelets. SIAM Rev. 42(1), 43–67 (2000)
Van De Ville, D., Blu, T., Unser, M., et al.: Hex-splines: a novel spline family for hexagonal lattices. IEEE Trans. Image Process. 13(6), 758–772 (2004)
Walter, G.G.: Negative spline wavelets. J. Math. Anal. Appl. 177(1), 239–253 (1993)
Wang, J.: Spline wavelets in numerical resolution of partial differential equations. In: International Conference on Wavelet Analysis and its application, AMS/IP Studies in Advanced Mathematics, vol. 25, pp. 257–276 (2002)
Xian, J., Lin, W.: Sampling and reconstruction in time-warped spaces and their applications. Appl. Math. Comput. 157(1), 153–173 (2004)
Xian, J., Luo, S.P., Lin, W.: Improved A-P iterative algorithm in spline subspaces. In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2004. LNCS, vol. 3037, pp. 60–67. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Xian, J., Li, D. (2005). Reconstruction Algorithm of Signals from Special Samples in Spline Spaces. In: Sunderam, V.S., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science – ICCS 2005. ICCS 2005. Lecture Notes in Computer Science, vol 3516. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11428862_106
Download citation
DOI: https://doi.org/10.1007/11428862_106
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26044-8
Online ISBN: 978-3-540-32118-7
eBook Packages: Computer ScienceComputer Science (R0)