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Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 4
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Articles

Tight frames, partial isometries, and signal reconstruction

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Pages 653-671 | Received 16 Nov 2013, Accepted 23 Mar 2014, Published online: 02 May 2014

References

  • Benedetto JJ, Powell A, Wu HC. MRI signal reconstruction by Fourier frames on interleaving spirals. In: Proceedings of IEEE International Symposium on Biomedical Imaging; Washington (DC); 2002. p. 717–720.
  • Benedetto JJ, Wu HC. A Beurling covering theorem and multidimensional irregular sampling. In: SampTA; Loen; 1999.
  • Benedetto JJ, Wu H. A multidimensional irregular sampling algorithm and applications. Phoenix (AZ): ICASSP; 1999.
  • Benedetto JJ, Wu HC. Nonuniform sampling and spiral MRI reconstruction. In: Proc. SPIE, Wavelet Applications in Signal and Image Processing; Vol. 4119; San Diego (CA); 2000. p. 130–141.
  • Paley REAC, Wiener N. Fourier transforms in the complex domain. Vol. XIX, American Mathematical Society Colloquium Publications. Providence (RI): American Mathematical Society; 1934.
  • Landau HJ. Necessary density conditions for sampling and interpolation of certain entire functions. Acta Math. J. 1967;117:37–52.
  • Redheffer RM, Young RM. Completeness and basis properties of complex exponentials. Trans. Amer. Math. Soc. 1983;277:93–111.
  • Olevskii A, Ulanovskii A. Universal sampling and interpolation of band-limited signals. Geom. Funct. Anal. 2008;18:1029–1052.
  • Olevskii A, Ulanovskii A. Universal sampling of band-limited signals. C. R. Math. Acad. Sci. Paris. 2006;342:927–931.
  • Kozma G, Lev N. Exponential Riesz bases, discrepancy of irrational rotations and BMO. J. Fourier Anal. Appl. 2011;17:879–898.
  • Matei B, Meyer Y. Simple quasicrystals are sets of stable sampling. Complex Var. Elliptic Equ. 2010;55:947–964.
  • Aldroubi A, Feichtinger HG. Exact iterative reconstruction algorithm for multivariate irregularly sampled functions in spline-like spaces: the Lp-theory. Proc. Amer. Math. Soc. 1998;126:2677–2686.
  • Feichtinger HG, Gröchenig K. Irregular sampling theorems and series expansions of band-limited functions. J. Math Anal. Appl. 1992;167:530–556.
  • Feichtinger HG, Gröchenig K. Iterative reconstruction of multivariate band-limited functions from irregular sampling values. SIAM J. Math. Anal. 1992;23:244–261.
  • Potts D, Steidl G. Fourier reconstruction of functions from their nonstandard sampled radon transform. J. Fourier Anal. Appl. 2002;8:513–533.
  • Unser M, Aldroubi A, Edon M. Polynomial spline signal approximations: filter design and asymptotic equivalence with shannon’s sampling theorem. IEEE Trans. Inform. Theory. 1992;38:95–103.
  • Aldroubi A, Gröchenig K. Nonuniform sampling and reconstruction in shift-invariant spaces. SIAM Rev. 2001;43:585–620.
  • Gröchenig K. Reconstruction algorithms in irregular sampling. Math. Comp. 1992;59:181–194.
  • Frank M, Paulsen VI, Tiballi TR. Symmetric approximation of frames and bases in Hilbert spaces. Trans. Amer. Math. Soc. 2002;354:777–793.
  • Christensen O. An introduction to frames and Riesz, bases. Boston: Birkhäuser; 2003.
  • Daubechies I. Ten lectures on wavelets. Philadelphia: SIAM; 1992.
  • Beurling A. Local harmonic analysis with some applications to differential operators. In: Some recent advances in the basic sciences, Vol. 1 (Proc. Annual Sci. Conf., Belfer Grad. School Sci., Yeshiva Univ., New York, 1962–1964). New York (NY): Belfer Graduate School of Science, Yeshiva University; 1966. p. 109-125.
  • Han D, Larson DR. Frames, bases and group representations. Mem. Amer. Math. Soc. 2000;147:x+94.
  • Golub GH, Van Loan CF. Matrix computations. 3rd ed. Baltimore (MD): Johns Hopkins University Press; 1996.

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