Detection of edges from spectral data: new results

DOI10.1016/j.acha.2006.10.002zbMath1133.42006OpenAlexW2092104635MaRDI QIDQ877583

Musheng Wei, Ana Gabriela Martínez, Alvaro Rodolfo de Pierro

Publication date: 3 May 2007

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.acha.2006.10.002

zbMATH Keywords

Fourier transformGibbs phenomenon

Mathematics Subject Classification ID

Pattern recognition, speech recognition (68T10) Detection theory in information and communication theory (94A13) Numerical methods for trigonometric approximation and interpolation (65T40) Convergence and absolute convergence of Fourier and trigonometric series (42A20) Software, source code, etc. for problems pertaining to harmonic analysis on Euclidean spaces (42-04)

Related Items

Determination of jumps for functions via derivative Gabor series, Local and Global Geometry of Prony Systems and Fourier Reconstruction of Piecewise-Smooth Functions, Iterative methods based on spline approximations to detect discontinuities from Fourier data, Polynomial operators for spectral approximation of piecewise analytic functions, On a filter for exponentially localized kernels based on Jacobi polynomials, Algebraic Fourier reconstruction of piecewise smooth functions, Complete algebraic reconstruction of piecewise-smooth functions from Fourier data

Cites Work

• Unnamed Item
• Error estimates for two filters based on polynomial interpolation for recovering a function from its Fourier coefficients
• On the Gibbs phenomenon. I: Recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function
• Detection of edges in spectral data
• Exponentially accurate approximations to periodic Lipschitz functions based on Fourier series partial sums
• Locating discontinuities of a bounded function by the partial sums of its Fourier series
• Adaptive edge detectors for piecewise smooth data based on the minmod limiter
• Detection of Edges in Spectral Data II. Nonlinear Enhancement
• Reconstruction of a compactly supported function from the discrete sampling of its Fourier transform
• Convergence of Spectral Methods for Nonlinear Conservation Laws
• On the Gibbs Phenomenon and Its Resolution
• Accurate Reconstructions of Functions of Finite Regularity from Truncated Fourier Series Expansions
• Iterative methods based on polynomial interpolation filters to detect discontinuities and recover point values from Fourier data
• A hybrid approach to spectral reconstruction of piecewise smooth functions