Sampling in shift-invariant spaces of functions with polynomial growth

References

• Unser , M . 2000 . Sampling–50 years after Shannon . Proc. IEEE , 88 ( 4 ) : 569 – 587 .
   Web of Science ®Google Scholar
• De Boor , C , Höllig , K and Riemenschneider , S . 1985 . Bivariate cardinal interpolation by splines on a three-direction mesh . Illinois J. Math , 29 ( 4 ) : 533 – 566 .
   Web of Science ®Google Scholar
• Chui , CK , Jetter , K and Ward , JD . 1987 . Cardinal interpolation by multivariate splines . Math. Comput. , 48 ( 178 ) : 711 – 724 .
   Web of Science ®Google Scholar
• Schoenberg , IJ . Cardinal Spline Interpolation, SIAM Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics, Philadelphia, 1973
   Google Scholar
• Kang , S and Kwon , KH . 2011 . Generalized average sampling in shift-invariant spaces . J. Math. Anal. Appl. , 377 : 70 – 78 .
   Web of Science ®Google Scholar
• Sun , W and Zhou , X . 2002 . Average sampling in spline subspaces . Appl. Math. Lett. , 15 : 233 – 237 .
   Web of Science ®Google Scholar
• Sun , W and Zhou , X . 2003 . Average sampling in shift-invariant subspaces with symmetric averaging functions . J. Math. Anal. Appl. , 287 : 279 – 295 .
   Web of Science ®Google Scholar
• Unser , M and Aldroubi , A . 1994 . A general sampling theory for nonideal acquisition devices . IEEE Trans. Signal Process. , 42 ( 11 ) : 2915 – 2925 .
   Web of Science ®Google Scholar
• Xian , J and 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 .
   Web of Science ®Google Scholar
• García , AG , Muñoz-Bouzo , MJ and Pérez-Villalón , G . 2011 . Regular multivariate sampling and approximation in L p shift-invariant spaces . J. Math. Anal. Appl. , 380 : 607 – 627 .
   Web of Science ®Google Scholar
• Chui , CK . 1997 . Wavelets: A Mathematical Tool for Signal Analysis , Philadelphia : SIAM .
   Google Scholar
• Pérez-Villalón , G and Portal , A . Computation of wavelet coefficients from average samples . Preprint, 2012
   Google Scholar
• Ron , A . 1989 . A necessary and sufficient condition for the linear independence of the integer translates of a compactly supported distribution . Construct. Approx. , 5 : 297 – 308 .
   Web of Science ®Google Scholar
• Chui , CK . 1992 . An Introduction to Wavelets , San Diego, CA, USA : Academic Press .
   Google Scholar
• Walter , GG and Shen , X . 2001 . Wavelets and Other Orthogonal Systems , Boca Raton, FL : Chapman & Hall/CRC .
   Google Scholar
• Walter , GG . 1992 . A sampling theorem for wavelet subspaces . IEEE Trans. Inform. Theory , 38 : 881 – 884 .
   Web of Science ®Google Scholar
• Pérez-Villalón , G and Portal , A . 2012 . Reconstruction of splines from local average samples . Appl. Math. Lett. , 25 : 1315 – 1319 .
   Web of Science ®Google Scholar