Multivariate Dynamical Sampling in ℓ2(ℤd) and Shift-Invariant Spaces

References

• Aldroubi, A., Gröchenig, K. (2001). Nonuniform sampling and reconstruction in shift-invariant spaces. SIAM Rev. 43(4):585–620. doi:10.1137/S0036144501386986.
   Web of Science ®Google Scholar
• Aldroubi, A., Unser, M., Aldroubi, A. (1994). Sampling procedures in function spaces and asymptotic. Numer. Func. Anal. Opt. 15(1/2):1–21. doi:10.1080/01630569408816545.
   Web of Science ®Google Scholar
• Benedetto, J. J., Ferreira, P. J. S. G. (2001). Modern Sampling Theory, Mathematics and Applications. Boston: Birkhäuser.
   Google Scholar
• F, M. (2001). Nonuniform Sampling, Theory and Practice. New York: Kluwer Academic/Plenum Publishers.
   Google Scholar
• Shannon, C. (1949). Communication in the presence of noise. Proc. IRE 37(1):10–21. doi:10.1109/JRPROC.1949.232969.
   Google Scholar
• Shannon, C. (1998). Communication in the presence of noise. Proc. IEEE 86(2):447–457. doi:10.1109/JPROC.1998.659497.
   Web of Science ®Google Scholar
• Sun, Q. (2007). Nonuniform average sampling and reconstruction of signals with finite rate of innovation. SIAM J. Math. Anal. 38(5):1389–1422. doi:10.1137/05063444X.
   Web of Science ®Google Scholar
• Strohmer, T. (2000). Numerical analysis of the non-uniform sampling problem. J. Comput. Appl. Math. 122(1/2):297–316. doi:10.1016/S0377-0427(00)00361-7.
   Web of Science ®Google Scholar
• Song, Z., Liu, B., Pang, Y., Hou, C., Li, X. (2012). An improved Nyquist-Shannon irregular sampling theorem from local averages. IEEE Trans. Inform. Theory 58(9):6093–6100. doi:10.1109/TIT.2012.2199959.
   Web of Science ®Google Scholar
• Seidner, D., Feder, M., Cubanski, D., Blackstock, S. (1998). Introduction to vector sampling expansion. IEEE Signal Process. Lett. 5(5):115–117. doi:10.1109/97.668947.
   Web of Science ®Google Scholar
• Sun, Q. (2010). Local reconstruction for sampling in shift-invariant spaces. Adv. Comput. Math. 32(3):335–352. doi:10.1007/s10444-008-9109-0.
   Web of Science ®Google Scholar
• Sun, W. (2009). Local sampling theorems for spaces generated by splines with arbitrary points. Math. Comput. 78(265):225–239. doi:10.1090/S0025-5718-08-02151-0
   Web of Science ®Google Scholar
• Sun, W., Zhou, X. (2003). Average sampling in shift invariant subspaces with symmetric averaging functions. J. Math. Anal. Appl. 287(1):279–295. doi:10.1016/S0022-247X(03)00558-4.
   Web of Science ®Google Scholar
• Sun, W., Zhou, X. (2002). Average sampling in spline subspaces. Appl. Math. Lett. 15(2):233–237. doi:10.1016/S0893-9659(01)00123-9.
   Web of Science ®Google Scholar
• Sun, W., Zhou, X. (2003). Reconstruction of functions in spline subspaces from local averages. Proc. Am. Math. Soc. 131:2561–2571. doi:10.1090/S0002-9939-03-07082-5
   Web of Science ®Google Scholar
• Sun, W., Zhou, X. (1999). Sampling theorem for multiwavelet subspaces. Chin. Sci. Bull. 44(14):1283–1286. doi:10.1007/BF02885844.
   Google Scholar
• Venkataramani, R., Bresler, Y. (2003). Sampling theorems for uniform and periodic nonuniform MIMO sampling of multiband signals. IEEE Trans. Signal Process. 51(12):3152–3163. doi:10.1109/TSP.2003.819001.
   Web of Science ®Google Scholar
• Xian, J. (2012). Local sampling set conditions in weighted shift-invariant signal spaces. Appl. Anal. 91(3):447–457. doi:10.1080/00036811.2010.541448.
   Web of Science ®Google Scholar
• Xian, J., Sun, W. (2010). Local sampling and reconstruction in shift-invariant spaces and their applications in spline subspaces. Numer. Funct. Anal. Optim. 31(3):366–386. doi:10.1080/01630561003760128.
   Web of Science ®Google Scholar
• Aldroubi, A., Cabrelli, C., Molter, U., Tang, S. (2017). Dynamical sampling. Appl. Comput. Harmon. Anal. 42(3):378–401. doi:10.1016/j.acha.2015.08.014
   Web of Science ®Google Scholar
• Aldroubi, A., Davis, J., Krishtal, I. (2013). Dynamical sampling: Time space trade-off. Appl. Comput. Harmon. Anal. 34(3):495–503. doi:10.1016/j.acha.2012.09.002.
   Web of Science ®Google Scholar
• Aldroubi, A., Davis, J., Krishtal, I. (2015). Exact reconstruction of signals in evolutionary systems via spatiotemporal trade-off. J. Fourier Anal. Appl. 21(1):11–31. doi:10.1007/s00041-014-9359-9.
   Web of Science ®Google Scholar
• Aceska, R., Aldroubi, A., Davis, J., Petrosyan, A. (2013). Dynamical sampling in shift-invariant spaces. Commut. Noncommut. Harmon. Anal. Appl. 603:139–148.
   Google Scholar
• Zhang, Q., Liu, B., Li, R. (2017). Dynamical sampling in multiply generated shift-invariant spaces. Appl. Anal. 96(5):760–770. doi:10.1080/00036811.2016.1157586.
   Web of Science ®Google Scholar
• Jiang, Q. (1999). Multivariate matrix refinable functions with arbitrary matrix dilation. Trans. Am. Math. Soc. 351:2407–2438. doi:10.1090/S0002-9947-99-02449-6
   Web of Science ®Google Scholar
• Feichtinger, H. G. (1992). Wiener amalgams over Euclidean spaces and some of their applications. Proc Conf Function spaces, volume 136 of Lect Notes in Math, pages 123–137, Edwardsville IL, Dekker, New York, April 1990.
   Google Scholar
• Bhandari, A., Zayed, A. I. (2017). Shift-invariant and sampling spaces associated with the special affine Fourier transform. Appl. Comput. Harmon. Anal. (in press).
   Google Scholar
• Daubechies, I. (1992). Ten Lectures on Wavelets. Philadelphia: SIAM.
   Google Scholar