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Research Articles

Approximation of Nonhomogeneous Random Field from Local Averages

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Pages 743-763 | Received 07 Jul 2022, Accepted 05 Apr 2023, Published online: 08 May 2023

References

  • Sun, W., Zhou, X. (2002). Reconstruction of band-limited signals from local averages. IEEE. Trans. Inform. Theory. 48(11):2955–2963. DOI: 10.1109/tit.2002.804047.
  • Song, Z., Yang, S., Zhou, X. (2006). Approximation of signals from local averages. Appl. Math. Lett. 19(12):1414–1420. DOI: 10.1016/j.aml.2006.01.018.
  • Sun, W., Zhou, X. (2003). Reconstruction of functions in spline subspaces from local averages. Proc. Amer. Math. Soc. 131(8):2561–2571. DOI: 10.1090/S0002-9939-03-07082-5.
  • Xian, J., Luo, S., Lin, W. (2006). Weighted sampling and signal reconstruction in spline subspaces. Signal Process. 86(2):331–340. DOI: 10.1016/j.sigpro.2005.05.013.
  • 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.
  • 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.
  • Kumar, A., Sampath, S. (2020). Average sampling and reconstruction in shift-invariant spaces and variable bandwidth spaces. Appl. Anal. 99(4):672–699. DOI: 10.1080/00036811.2018.1508652.
  • Xian, J. (2014). Average sampling and reconstruction in a reproducing kernel subspace of homogeneous type space. Math. Nachr. 287(8–9):1042–1056. DOI: 10.1002/mana.201200203.
  • Jiang, Y., Wang, S., Yang, M. (2016). Average sampling and reconstruction for reproducing kernel stochastic signals. Math. Meth. Appl. Sci. 39(11):2930–2938. DOI: 10.1002/mma.3740.
  • Li, R., Liu, B., Liu, R., Zhang, Q. (2017). Nonuniform sampling in principal shift-invariant subspaces of mixed Lebesgue spaces. J. Math. Anal. Appl. 453(2):928–941. DOI: 10.1016/j.jmaa.2017.04.036.
  • Zhang, Q. (2020). Nonuniform average sampling in multiply generated shift-invariant subspaces of mixed Lebesgue spaces. Int. J. Wavelets Multiresol. Info. Process. 18(03):2050013. DOI: 10.1142/S0219691320500137.
  • Jiang, Y., Sun, W. (2020). Adaptive sampling of time-space signals in a reproducing kernel subspace of mixed Lebesgue space. Banach J. Math. Anal. 14(3):821–841. DOI: 10.1007/s43037-019-00040-2.
  • Jiang, Y., Li, W. (2021). Random sampling in multiply generated shift-invariant subspaces of mixed Lebesgue spaces. J. Comput. Appl. Math. 386:113237. DOI: 10.1016/j.cam.2020.113237.
  • Gröchenig, K. (1992). Reconstruction algorithms in irregular sampling. Math. Comp. 59(199):181–194. DOI: 10.2307/2152989.
  • Butzer, P. L., Lei, J. (1998). Errors in truncated sampling series with measured sampled values for non-necessarily bandlimited functions. Funct. Approx. Comment. Math. 26:25–39.
  • Butzer, P. L., Lei, J. (2000). Approximation of signals using measured sampled values and error analysis. Commun. Appl. Anal. 4(2):245–256.
  • He, G., Song, Z. (2011). Approximation of WKS sampling theorem on random signals. Numer. Funct. Anal. Optim. 32(4):397–408. DOI: 10.1080/01630563.2011.556287.
  • Song, Z., Zhou, X., He, G. (2006). Error estimate on non-bandlimited random signals by local averages. Int. Conf. Comput. Sci. Berlin: Springer-Verlag, p. 822–825.
  • Song, Z-j., Sun, W-c., Yang, S-y., Zhu, G-w (2007). Approximation of weak sense stationary stochastic processes from local averages. Sci. China Ser. A. 50(4):457–463. CNKI:SUN:JAXG.0.2007-04-001.
  • 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.
  • Jiang, Y. (2019). Average sampling and reconstruction of reproducing kernel signals in mixed Lebesgue spaces. J. Math. Anal. Appl. 480(1):123370. DOI: 10.1016/j.jmaa.2019.07.060.
  • Kumar, A., Sampath, S. (2020). Sampling and average sampling in quasi shift-invariant spaces. Numer. Funct. Anal. Optim. 41(10):1246–1271. DOI: 10.1080/01630563.2020.1748054.
  • Wang, S., Zhang, J. (2021). Average sampling and reconstruction for signals in shift-invariant subspaces of weighted mixed Lebesgue spaces. Math. Meth. Appl. Sci. 44(11):9507–9523. DOI: 10.1002/mma.7374.
  • Zakai, M. (1965). Band-limited functions and the sampling theorem. Inf. Control. 8(2):143–158. DOI: 10.1016/S0019-9958(65)90038-0.
  • Gardner, W. A. (1972). A sampling theorem for nonstationary random processes. IEEE Trans. Inform. Theory. 18(6):808–809. DOI: 10.1109/TIT.1972.1054917.
  • Parzen, E. (1956). A simple proof and some extensions of the sampling theorem. No. TR-7. California: Stanford University.
  • Miyakawa, H. (1959). Sampling theorem of stationary stochastic variables in multidimensional space. J. Inst. Electric. Commun. Eng. Jpn. 4(2):421–427.
  • Petersen, D. P., Middleton, D. (1962). Sampling and reconstruction of wave-number-limited vunctions in n-dimensional Euclidean spaces. Inf. Control. 5(4):279–323. DOI: 10.1016/S0019-9958(62)90633-2.
  • Splettstösser, W. (1982). Sampling approximation of continuous functions with multidimensional domain. IEEE Trans. Inform. Theory. 28:809–814. DOI: 10.1109/TIT.1982.1056561.
  • Kolmogorov, A. N. (1941). Local structure of turbulence in an incompressible viscous fluid for very high Reynolds numbers. Akad. Nauk SSSR Dokl. 30:301–305.
  • Yaglom, A. M. (1957). Some classes of random fields in n-dimensional space, Related to stationary random processes. Theory Probab. Appl. 2(3):273–320. DOI: 10.1137/1102021.
  • Yaglom, A. M. (1987). Correlation Theory of Stationary and Related Random Functions. Volume I: Basic Results. New York: Springer-Verlag.
  • Yaglom, A. M. (1987). Correlation Theory of Stationary and Related Random Functions. Volume II: Supplementary Notes and References. New York: Springer-Velag.
  • Vanmarcke, E. (2010). Random Fields: Analysis and Synthesis. Singapore: World Scientific.
  • Zhang, S., Song, Z., Li, Y. (2016). An advanced inversion algorithm for significant wave height estimation based on random field. Ocean Eng. 127:298–304. DOI: 10.1016/j.oceaneng.2016.10.022.
  • Hernández-Lemus, E. (2021). Random fields in physics, biology and data science. Front. Phys. 9:641859. DOI: 10.3389/fphy.2021.641859.
  • Sharma, B. D., Mehta, F. C. (1974). A generalized sampling theorem for non-stationary random processes. J. Cybernet. 4(3):87–95. DOI: 10.1080/01969727408621683.
  • Garcia, F. M., Lourtie, I. M. G., Buescu, J. (2001). L/sup 2/(R) nonstationary processes and the sampling theorem. IEEE Signal Process. Lett. 8(4):117–119. DOI: 10.1109/97.911476.
  • Zhang, S., Song, Z., Li, Y. (2017). Approximation of homogeneous random field from local averages. Commun. Stat. 46(8):3864–3877. DOI: 10.1080/03610926.2015.1073318.
  • Song, Z., Zhang, S. (2019). An almost sure result on approximation of homogeneous random field from local averages. Chin. J. Electron. 28(1):93–99. DOI: 10.1049/cje.2018.11.001.
  • Song, Z., Zhang, S. (2021). Average sampling theorems on multidimensional random signals. Numeric. Funct. Anal. Optim. 42(12):1461–1487. DOI: 10.1080/01630563.2021.1969949.
  • Splettstösser, W., Stens, R. L., Wilmes, G. (1980). On the approximation of the interpolating series of G. Valiron. Funct. Approx. Comment. Math. 11:39–56.
  • Belyaev, Y. K. (1959). Analytic random processes. Theory Probab. Appl. 4(4):402–409. DOI: 10.1137/1104040.
  • Zhang, S. (2017). Research on random fields theory from local average sampling and its applications in wave monitoring. Ph.D. dissertation. Tianjin University, Tianjin.

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