Adaptive Filters for Piecewise Smooth Spectral Data

Abstract

We introduce a new class of exponentially accurate filters for processing piecewise smooth spectral data. Our study is based on careful error decompositions, focusing on a rather precise balance between physical space localization and the usual moments condition. Exponential convergence is recovered by optimizing the order of the filter as an adaptive function of both the projection order, and the distance to the nearest discontinuity. Combined with the automated edge detection methods, adaptive filters provide a robust, computationally efficient, black box procedure for the exponentially accurate reconstruction of a piecewise smooth function from its spectral information.

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Document Details

Document Type
Technical Report
Publication Date
Nov 30, 2004
Accession Number
ADA448329

Entities

People

  • Eitan Tadmor
  • Jared Tanner

Organizations

  • University of Maryland

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Accuracy
  • Adaptive Filters
  • Analytic Functions
  • Change Detection
  • Coefficients
  • Convergence
  • Detection
  • Discontinuities
  • Errors
  • Filters
  • Filtration
  • Fourier Series
  • High Resolution
  • Mathematics
  • Periodic Functions
  • Universities

Readers

  • Approximation Theory.
  • Computer Vision.
  • Phased Array Antenna Design.

Technology Areas

  • Space