COMPUTATION of the GIBBS PHENOMENON
A collection of selected references on
Detection of edges and reconstruction of discontinuous data from its (pseudo-)spectral information
-
D. Gottlieb & E. Tadmor (1985)

Recovering pointwise values of discontinuous data within spectral accuracy
``Progress and Supercomputing in Computational Fluid Dynamics", Proc. of a 1984 U.S.-Israel Workshop (E. M. Murman and S. S. Abarbanel, eds.), Birkhauser, Boston v. 6 (1985) 357-375.
-
S. Abarbanel, D. Gottlieb & E. Tadmor (1986)

Spectral methods for discontinuous problems
``Numerical Methods for Fluid Dynamics II", Proc. 1985 Conference on Numerical Methods for Fluid Dynamics (K. W. Morton and M. J. Baines, eds.), Clarendon Press, Oxford(1986) 129-153.
-
S. Mallat & W. L. Hwang (1992)

Singularity detection and processing with wavelets
IEEE Transactions on Information Theory 38(2) (1992) 617-643.
-
A. Gelb & E. Tadmor (1999)

Detection of edges in spectral data
Applied and Computational Harmonic Analysis 7 (1999) 101-135.
-
A. Gelb & E. Tadmor (2000)

Detection of edges in spectral data II. Nonlinear enhancement
SIAM Journal on Numerical Analysis 38 (2000), 1389-1408.
-
A. Gelb (2000)

A hybrid approach to spectral reconstruction of piecewise smooth functions
Journal of Scientific Computing 15(3) (2000), 293-322.
-
G. Kvernadze (2001)

Approximation of the singularities of a bounded function by the partial sums of its differentiated Fourier series
Applied Comput. Harmonic Analysis 11(3) (2001), 439-454.
Back to Top
-
E. Tadmor & J. Tanner (2002)

Adaptive mollifiers -- high resolution recovery of piecewise smooth data from its spectral information
Foundations of Computational Mathematics 2(2) (2002) 155-189.
-
R. Archibald & A. Gelb (2002)

A method to reduce the Gibbs ringing artifact in MRI scans while keeping tissue boundary integrity
IEEE Transactions of Medical Imaging (2002) 100-114.
-
R. Archibald & A. Gelb (2002)

Reducing the effects of noise in image reconstruction
Journal of Scientific Computing 17(1-4) (2002) 100-114.
-
A. Gelb & E. Tadmor (2002)

Spectral reconstruction of one- and two-dimensional piecewise smooth functions from their discrete data
Mathematical Modeling and Numerical Analysis 36 (2002) 167-180.
-
E. Tadmor & J. Tanner (2003)

An adaptive order Godunov type central scheme
``Hyperbolic Problems: Theory, Numerics, Applications'', Proc. 9th International Conference held in CalTech Pasadena,
(T. Hou and E. Tadmor, eds.), Springer (2003) 871-880.
-
S. Sarra (2003)

The spectral signal processing suite
ACM Transactions on Mathematical Software 29(2) (2003), 195-217.
-
G. Kvernadze (2004)

Approximating the jump discontinuities of a function by its Fourier-Jacobi coefficients
Mathematics of Computation 73(246) (2004), 731-751.
-
E. Tadmor & J. Tanner (2005)

Adaptive filters for piecewise smooth spectral data
IMA Journal of Numerical Analysis 25(4) (2005) 635-647.
-
J. Boyd (2005)

Trouble with Gegenbauer reconstruction for defeating Gibbs' phenomenon:
Runge phenomenon in the diagonal limit of Gegenbauer polynomial approximations
Journal o Computational Physics 204 (2005) 253-264.
-
A. Gelb & E. Tadmor (2006)

Adaptive edge detectors for piecewise smooth data based on the minmod limiter
Journal of Scientific Computing 28(2-3) (2006) 279-306.
-
A. Gelb & J. Tanner (2006)

Robust reprojection methods for the resolution of the Gibbs phenomenon
Applied Computtaional Harmonic Analysis 20 (2006) 3-25.
-
J. Tanner (2006)

Optimal filter and mollifier for piecewise smooth spectral data
Mathematics of Computations 75(254) (2006) 767-790.
-
Q. Shi & X. Shi (2006)

Determination of jumps in terms of spectral data
Acat Math. Hungar. 110(3) (2006) 193-206.
Back to Top
-
E. Tadmor (2007)

Filters, mollifiers and the computation of the Gibbs phenomenon
Acta Numerica 16 (2007) 305-378.
-
L. Hu & X. L. Shi (2007)

Concentration factors for functions with harmonic bounded mean variation
Acta Math. Hungar. (2007).
-
S. Engelberg (2008)

Edge detection using Fourier coefficients
American Mathematical Monthly (2008) 499-513.
-
S. Engelberg & E. Tadmor (2008)

Recovery of edges from spectral data with noise---a new perspective
SIAM Journal on Numerical Analysis 46(5) (2008) 2620-2635.
-
E. Tadmor & J. Zou (2008)

Novel edge detection methods for incomplete and noisy spectral data
Journal of Fourier Analysis and Applications 14(5) (2008) 744-763.
-
A. Gelb & D. Cates (2009)

Segmentation of images from Fourier spectral data
Communications in Computational Physics 5(2-4) (2009) 326-349.
-
B. I. Yun, K. S. Rim (2013)

Local edge detectors using a sigmoidal transformation for piecewise smooth data
Applied Mathematics Letters 26(2) (2013) 270-276.
|