Classification: 42A10, 42A50, 65T40

Keywords: edge detection, nonlinear enhancement, concentration method, piecewise smoothness, localized reconstruction

@article{M2AN_2002__36_2_155_0, author = {Gelb, Anne and Tadmor, Eitan}, title = {Spectral reconstruction of piecewise smooth functions from their discrete data}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, publisher = {EDP-Sciences}, volume = {36}, number = {2}, year = {2002}, pages = {155-175}, doi = {10.1051/m2an:2002008}, zbl = {1056.42001}, mrnumber = {1906813}, language = {en}, url = {http://www.numdam.org/item/M2AN_2002__36_2_155_0} }

Gelb, Anne; Tadmor, Eitan. Spectral reconstruction of piecewise smooth functions from their discrete data. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 36 (2002) no. 2, pp. 155-175. doi : 10.1051/m2an:2002008. http://www.numdam.org/item/M2AN_2002__36_2_155_0/

[0] Exponential approximations using Fourier series partial sums, ICASE Report No. 97-56, NASA Langley Research Center (1997).

and ,[0] Treatise of Trigonometric Series. The Macmillan Company, New York (1964). | MR 171116 | Zbl 0129.28002

,[0] Introduction to the Theory of Fourier's Series and Integrals. Dover (1950).

,[0] Accurate reconstructions of functions of finite regularity from truncated series expansions. Math. Comp. 64 (1995) 671-690. | Zbl 0830.65144

,[0] On a high order numerical method for functions with singularities. Math. Comp. 67 (1998) 1063-1087. | Zbl 0895.65067

,[0] Detection of edges in spectral data. Appl. Comput. Harmon. Anal. 7 (1999) 101-135. | Zbl 0952.42001

and ,[0] Detection of edges in spectral data. II. Nonlinear Enhancement. SIAM J. Numer. Anal. 38 (2001) 1389-1408. | Zbl 0990.42025

and ,[0] Determination of the jump of a function of bounded $p$-variation by its Fourier series. Math. Notes 12 (1972) 444-449. | Zbl 0259.42007

,[0] On the Gibbs phenomenon and its resolution. SIAM Rev. (1997). | MR 1491051 | Zbl 0885.42003

and ,[0] Recovering pointwise values of discontinuous data within spectral accuracy, in Progress and Supercomputing in Computational Fluid Dynamics, Proceedings of a 1984 U.S.-Israel Workshop, Progress in Scientific Computing, Vol. 6, E.M. Murman and S.S. Abarbanel Eds., Birkhauser, Boston (1985) 357-375. | Zbl 0597.65099

and ,[0] Determination of the jump of a bounded function by its Fourier series. J. Approx. Theory 92 (1998) 167-190. | Zbl 0902.42001

,[0] Adaptive mollifiers for high resolution recovery of piecewise smooth data from its spectral information, Foundations of Comput. Math. Online publication DOI: 10.1007/s002080010019 (2001), in press. | MR 1894374 | Zbl 1056.42002

and ,[0] Trigonometric Series. Cambridge University Press (1959). | MR 107776 | Zbl 0085.05601

,