from ancient astronomy to modern signal and image processing

[259] I. German, “Short kernel fifth-order interpolation,” IEEE Trans.Signal Processing, vol. 45, pp. 1355–1359, May 1997.[260] E. H. W. Meijering, K. J. Zuiderveld, and M. A. Viergever, “Imagereconstruction by convolution with symmetrical piecewise nthorder polynomial kernels,” IEEE Trans. Image Processing, vol. 8,pp. 192–201, Feb. 1999.[261] M. Unser, “Approximation power of biorthogonal wavelet expansions,”IEEE Trans. Signal Processing, vol. 44, pp. 519–527, Mar.1996.[262] M. Unser and I. Daubechies, “On the approximation power of convolution-basedleast squares versus interpolation,” IEEE Trans. SignalProcessing, vol. 45, pp. 1697–1711, July 1997.[263] G. Strang and G. Fix, “A Fourier analysis of the finite elementvariational method,” in Constructive Aspects of FunctionalAnalysis. Rome, Italy: Edizioni Cremonese, 1973, Centro InternazionaleMatematico Estivo, pp. 793–840.[264] C. de Boor and R.-Q. Jia, “Controlled approximation and a characterizationof the local approximation order,” Proc. Amer. Math. Soc.,vol. 95, no. 4, pp. 547–553, 1985.[265] W. A. Light, “Recent developments in the Strang-Fix theory for approximationorders,” in Curves and Surfaces, P. J. Laurent, A. leMéhauté, and L. L. Schumaker, Eds. New York: Academic, 1991,pp. 285–292.[266] W. A. Light and E. W. Cheney, “Quasiinterpolation with translates ofa function having noncompact support,” Constructive Approx., vol.8, no. 1, pp. 35–48, 1992.[267] R.-Q. Jia and J. Lei, “Approximation by multiinteger translates offunctions having global support,” J. Approx. Theory, vol. 72, no. 1,pp. 2–23, 1993.[268] T. Blu and M. Unser, “Approximation error for quasiinterpolatorsand (multi-)wavelet expansions,” Appl. Comput. Harmonic Anal.,vol. 6, no. 2, pp. 219–251, 1999.[269] C. de Boor, “Approximation from shift-invariant subspaces ofL ( ),” Trans. Amer. Math. Soc., vol. 341, no. 2, pp. 787–806,1994.[270] , “Quasiinterpolants and approximation power of multivariatesplines,” in Computation of Curves and Surfaces, W. Dahmen, M.Gasca, and C. A. Micchelli, Eds. Norwell, MA: Kluwer, 1990, pp.313–345.[271] J. Lei, “L -approximation by certain projection operators,” J. Math.Anal. Applicat., vol. 185, no. 1, pp. 1–14, 1994.[272] C. de Boor, “The polynomials in the linear span of integer translatesof a compactly supported function,” Constructive Approx., vol. 3,no. 2, pp. 199–208, 1987.[273] C. K. Chui and H. Diamond, “A characterization of multivariatequasiinterpolation formulas and its applications,” Numerische Mathematik,vol. 57, no. 2, pp. 105–121, 1990.[274] T. Blu and M. Unser, “Quantitative Fourier analysis of approximationtechniques: Part I—Interpolators and projectors,” IEEE Trans.Signal Processing, vol. 47, pp. 2783–2795, Oct. 1999.[275] , “Quantitative Fourier analysis of approximation techniques:Part II—Wavelets,” IEEE Trans. Signal Processing, vol. 47, pp.2796–2806, Oct. 1999.[276] P. Thévenaz, T. Blu, and M. Unser, “Interpolation revisited,” IEEETrans. Med. Imag., vol. 19, pp. 739–758, July 2000.[277] , “Image interpolation and resampling,” in Handbook of MedicalImaging, Processing and Analysis, I. N. Bankman, Ed. SanDiego, CA: Academic, 2000, ch. Ch. 25, pp. 393–420.[278] T. Blu, P. Thévenaz, and M. Unser, “MOMS: Maximal-order interpolationof minimal support,” IEEE Trans. Image Processing, vol.10, pp. 1069–1080, July 2001.[279] A. Ron, “Factorization theorems for univariate splines on regulargrids,” Isr. J. Math., vol. 70, no. 1, pp. 48–68, 1990.[280] S. Dubuc, “Interpolation through an iterative scheme,” J. Math. Anal.Applicat., vol. 114, no. 1, pp. 185–204, 1986.[281] G. Deslauriers and S. Dubuc, “Symmetric iterative interpolation processes,”Constructive Approx., vol. 5, no. 1, pp. 49–68, 1989.[282] J.-L. Merrien, “A family of Hermite interpolants by bisection algorithms,”Numer. Algor., vol. 2, no. 2, pp. 187–200, 1992.[283] S. Dubuc and J.-L. Merrien, “Dyadic Hermite interpolation on a rectangularmesh,” Adv. Comput. Math., vol. 10, no. 3/4, pp. 343–365,1999.[284] I. Daubechies, Ten Lectures on Wavelets. Philadelphia, PA: SIAM,1992.[285] S. Mallat, A Wavelet Tour of Signal Processing. San Diego, CA:Academic, 1998.[286] D.-Q. Dai, T.-M. Shih, and F.-T. Chau, “Polynomial preserving algorithmfor digital image interpolation,” Signal Process., vol. 67, no.1, pp. 109–121, 1998.[287] R. N. Bracewell, The Fourier Transform and Its Applications, 2nded. New York: McGraw-Hill, 1978.[288] D. Kramer, A. Li, I. Simovsky, C. Hawryszko, J. Hale, and L.Kaufman, “Applications of voxel shifting in magnetic resonanceimaging,” Invest. Radiol., vol. 25, no. 12, pp. 1305–1310, 1990.[289] N. M. Hylton, I. Simovsky, A. J. Li, and J. D. Hale, “Impact ofsection doubling on MR angiography,” Radiol., vol. 185, no. 3, pp.899–902, 1992.[290] Y. P. Du, D. L. Parker, W. L. Davis, and G. Cao, “Reduction of partial-volumeartifacts with zero-filled interpolation in three-dimensionalMR angiography,” J. Magn. Reson. Imag., vol. 4, no. 5, pp.733–741, 1994.[291] W. F. Eddy, M. Fitzgerald, and D. C. Noll, “Improved image registrationby using Fourier interpolation,” Magn. Reson. Med., vol. 36,no. 6, pp. 923–931, 1996.[292] Q.-S. Chen, R. Crownover, and M. S. Weinhous, “Subunity coordinatetranslation with Fourier transform to achieve efficient andquality three-dimensional medical image interpolation,” Med. Phys.,vol. 26, no. 9, pp. 1776–1782, 1999.[293] K. P. Prasad and P. Satyanarayana, “Fast interpolation algorithmusing FFT,” Electron. Lett., vol. 22, no. 4, pp. 185–187, 1986.[294] S. Holm, “FFT pruning applied to time domain interpolation andpeak localization,” IEEE Trans. Acoust., Speech, Signal Processing,vol. ASSP-35, pp. 1776–1778, Dec. 1987.[295] M. R. Smith and S. T. Nichols, “Efficient algorithms for generatinginterpolated (zoomed) MR images,” Magn. Reson. Med., vol. 7, no.2, pp. 156–171, 1988.[296] D. Fraser, “Interpolation by the FFT revisited—An experimental investigation,”IEEE Trans. Acoustics, Speech, Signal Processing, vol.37, pp. 665–675, May 1989.[297] T. Smit, M. R. Smith, and S. T. Nichols, “Efficient sinc function interpolationtechnique for center padded data,” IEEE Trans. Acoust.,Speech, Signal Processing, vol. 38, pp. 1512–1517, Sept. 1990.[298] T. J. Cavicchi, “DFT time-domain interpolation,” Proc. Inst. Electr.Eng. F, vol. 139, no. 3, pp. 207–211, 1992.[299] T. Schanze, “Sinc interpolation of discrete periodic signals,” IEEETrans. Signal Processing, vol. 43, pp. 1502–1503, June 1995.[300] L. P. Yaroslavsky, “Signal sinc-interpolation: A fast computer algorithm,”Bioimaging, vol. 4, pp. 225–231, 1996.[301] , “Efficient algorithm for discrete sinc interpolation,” Appl.Opt., vol. 36, no. 2, pp. 460–463, 1997.[302] F. Candocia and J. C. Principe, “Sinc interpolation of discreteperiodic signals,” IEEE Trans. Signal Processing, vol. 46, pp.2044–2047, July 1998.[303] S. R. Dooley and A. K. Nandi, “Notes on the interpolation of discreteperiodic signals using sinc function related approaches,” IEEETrans. Signal Processing, vol. 48, pp. 1201–1203, Apr. 2000.[304] J. I. Agbinya, “Fast interpolation algorithm using fast Hartley transform,”Proc. IEEE, vol. 75, pp. 523–524, Apr. 1987.[305] C.-Y. Hsu and T.-P. Lin, “Novel approach to discrete interpolaionusing the subsequence FHT,” Electron. Lett., vol. 24, no. 4, pp.223–224, 1988.[306] D. Liu, D. Wang, and Z. Wang, “Interpolation using Hartley transform,”Electron. Lett., vol. 28, no. 2, pp. 209–210, 1992.[307] Z. Wang, “Interpolation using type I discrete cosine transform,”Electron. Lett., vol. 26, no. 15, pp. 1170–1172, 1990.[308] J. I. Agbinya, “Interpolation using the discrete cosine transform,”Electron. Lett., vol. 28, no. 20, pp. 1927–1928, 1992.[309] , “Two dimensional interpolation of real sequences using theDCT,” Electron. Lett., vol. 29, no. 2, pp. 204–205, 1993.[310] G. Matheron, “Principles of geostatistics,” Econom. Geology, vol.58, pp. 1246–1266, 1963.[311] D. G. Krige, “A statistical approach to some basic mine valuationproblems on the Witwatersrand,” J. Chem., Metalll, Mining Soc. S.Africa, vol. 52, no. 6, pp. 119–139, 1951.[312] N. A. C. Cressie, Statistics for Spatial Data. New York: Wiley,1993.[313] N. Cressie, “The origins of kriging,” Math. Geology, vol. 22, no. 3,pp. 239–252, 1990.[314] J.-P. Chilès and P. Delfiner, Geostatistics: Modeling Spatial Uncertainty.New York: Wiley, 1999.[315] M. L. Stein, Interpolation of Spatial Data: Some Theory forKriging. Berlin, Germany: Springer-Verlag, 1999.MEIJERING: A CHRONOLOGY OF INTERPOLATION 341