Local reconstruction for sampling in shift-invariant spaces

Qiyu Sun1
1Department of Mathematics, University of Central Florida, 32816 Orlando, FL, USA

Tóm tắt

Từ khóa


Tài liệu tham khảo

Acosta-Reyes, E., Aldroubi, A., Krishta, I.: On stability of sampling-reconstruction models. Adv. Comput. Math. (2008). doi: 10.1007/s10444-008-9083-6

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

Aldroubi, A., Gröchenig, K.: Nonuniform sampling and reconstruction in shift-invariant space. SIAM Rev. 43, 585–620 (2001)

Aldroubi, A., Sun, Q., Tang, W.-S.: p-frames and shift invariant subspaces of L p . J. Fourier Anal. Appl. 7, 1–21 (2001)

Aldroubi, A., Sun, Q., Tang, W.-S.: Non-uniform average sampling and reconstruction in multiply generated shift-invariant spaces. Constr. Approx. 20, 173–189 (2004)

Aldroubi, A., Sun, Q., Tang, W.-S.: Convolution, average sampling and a Calderon resolution of the identity for shift-invariant spaces. J. Fourier Anal. Appl. 11, 215–244 (2005)

Aldroubi, A., Sun, Q.: Locally finite dimensional shift-invariant spaces in R d . Proc. Amer. Math. Soc. 130, 2641–2654 (2002)

Bi, N., Nashed, Z.M., Sun, Q.: Reconstructing signals with finite rate of innovation from noisy samples. Acta Appl. Math. (2008, submitted)

Bownik, M.: The structure of shift-invariant subspaces of L 2(R n ). J. Funct. Anal. 177, 282–309 (2000)

de Boor, C., Devore, R., Ron, A.: The structure of finitely generated shift-invariant spaces in $L_2({\mathbb R}^d)$ . J. Funct. Anal. 119, 37–78 (1994)

Butzer, P.L., Hinsen, G.: Reconstruction of bounded signals from pseudo-periodic irregularly spaced samples. Signal Process. 17, 1–17 (1989)

Cavaretta, A.S., Dahmen, W., Micchelli, C.A.: Stationary subdivision. Mem. Amer. Math. Soc. 453, 1–186 (1991)

Chen, W., Han, B., Jia, R.-Q.: Maximal gap of a sampling set for the iterative reconstruction algorithm in shift invariant spaces. IEEE Signal Process. Lett. 11, 655–658 (2004)

Chen, W., Han, B., Jia, R.-Q.: On simple oversampled A/D conversion in shift invariant spaces. IEEE Trans. Inform. Theory 51, 648–657 (2005)

Chen, W., Han, B., Jia, R.-Q.: Estimate of aliasing error for non-smooth signal prefiltered by quasi-projection into shift invariant spaces. IEEE Trans. Signal Process. 53, 1927–1933 (2005)

Chen, W., Itoh, S., Shiki, J.: On sampling in shift invariant spaces. IEEE Trans. Inform. Theory 48, 2802–2810 (2002)

Daubechies, I.: Ten lectures on wavelets. In: CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 61. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1992)

Devore, R.A., Lorentz, G.G.: Constructive Approximation. Springer, New York (1993)

Djokovic, I., Vaidyanathan, P.P.: Generalized sampling theorems in multiresolution subspaces. IEEE Trans. Signal Process. 45, 583–599 (1997)

Eldar, Y., Unser, M.: Nonideal sampling and interpolation from noisy observations in shift-invariant spaces. IEEE Trans. Signal Process. 54, 2636–2651 (2006)

Feichtinger, H.G., Gröchenig, K., Strohmer, T.: Efficient numerical methods in non-uniform sampling theory. Numer. Math. 69, 423–440 (1995)

Goodman, T.N.T., Jia, R.-Q., Zhou, D.-X.: Local linear independence of refinable vectors of functions. Proc. Roy. Soc. Edinburgh. 130A, 813–826 (2000)

Goodman, T.N.T., Micchelli, C.A.: On refinement equations determined by Pólya frequency sequences. SIAM J. Math. Anal. 23, 766–784 (1992)

Goodman, T.N.T, Sun, Q.: Total positivity and refinable functions with general dilation. Appl. Comput. Harmon. Anal. 16, 69–89 (2004)

Gröchenig, K., Schwab, H.: Fast local reconstruction methods for nonuniform sampling in shift-invariant spaces. SIAM J. Matrix Anal. Appl. 24, 899–913 (2003)

Hogan, J.A., Lakey, J.D.: Sampling and oversampling in shift-invariant and multiresolution spaces I: validation of sampling schemes. Int. J. Wavelets Multiresolut. Inf. Process. 3, 257–281 (2005)

Hogan, J.A., Lakey, J.D.: Periodic nonuniform sampling in shift-invariant spaces. In: Heil, C. (ed.) Harmonic Analysis and Applications in Honor of John J. Benedetto, pp. 253–287. Birkhäuser, Boston (2006)

Huang, D., Sun, Q.: Affine similarity of refinable functions. Approx. Theory Appl. 15(3), 81–91 (1999)

Janssen, A.J.E.M.: The Zak transform and sampling for wavelet subspaces. IEEE Trans. Signal Process. 41, 3360–3364 (1993)

Jia, R.-Q., Micchelli, C.A.: On linear independence of integer translates of a finite number of functions. Proc. Edinburgh Math. Soc. 36, 69–75 (1992)

Lawton, W., Lee, S.L., Shen, Z.: An algorithm for matrix extension and wavelet construction. Math. Comp. 65, 723–737 (1996)

Lemarié, P.G.: Fonctions á support compact dans les analyses multi-résolutions. Rev. Mat. Iberoamericana 7, 157–182 (1991)

Mallat, S.: A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989)

Maravic, I., Vetterli, M.: Sampling and reconstruction of signals with finite rate of innovation in the presence of noise. IEEE Trans. Signal Process. 53, 2788–2805 (2005)

Meyer, Y.: Ondelettes sur l’intervalle. Rev. Mat. Iberoamericana 7, 115–133 (1991)

Pena, J.M.: Refinable functions with general dilation and a stable test for generalized Routh-Hurwitz conditions. Comm. Pure Appl. Anal. 6, 809–818 (2007)

Papoulis, A.: Signal Processing. Mcgraw-Hill, New York (1977)

Ron, A.: A necessary and sufficient condition for the linear independence of the integer translates of a compactly supported distribution. Constr. Approx. 5, 297–308 (1989)

Smale, S., Zhou, D.-X.: Shannon sampling and function reconstruction from point values. Bull. Amer. Math. Soc. 41, 279–305 (2004)

Stein, E.M.: Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton (1970)

Strohmer, T., Tanner, J.: Fast reconstruction methods for band-limited functions from periodic nonuniform sampling. SIAM J. Numer. Anal. 44, 1073–1094 (2006)

Sun, Q.: Two-scale difference equation: local and global linear independence. Manuscript. http://math.ucf.edu/∼qsun/Preprints/Local.ps (1991)

Sun, Q.: Non-uniform average sampling and reconstruction of signals with finite rate of innovation. SIAM J. Math. Anal. 38, 1389–1422 (2006)

Sun, Q.: Frames in spaces with finite rate of innovation. Adv. Comput. Math. 28, 301–329 (2008)

Sun, W., Zhou, X.: Characterization of local sampling sequences for spline subspaces. Adv. Comput. Math. (2008). doi: 10.1007/s10444-008-9062-y

Triebel, H.: Theory of Function Spaces. Birkhauser, Boston (1983)

Vetterli, M., Marziliano, P., Blu, T.: Sampling signals with finite rate of innovation. IEEE Trans. Signal Process. 50, 1417–1428 (2002)

Unser, M., Aldroubi, A.: A general sampling theory for nonideal acquisition devices. IEEE Trans. Signal Process. 42, 2915–2925 (1994)

Unser, M.: Sampling – 50 years after Shannon. Proc. IEEE 88, 569–587 (2000)

Vaidyanathan, P.P.: Generalizations of the sampling thoerem: seven decades after Nyquist. IEEE Trans. Circuits Systems I Fund. Theory Appl. 48, 1094–1109 (2001)

Walter, G.G.: A sampling theorem for wavelet subspaces. IEEE Trans. Inform. Theory 38, 881–884 (1992)