Ridgelets and their Derivatives: Representation of Images with Edges

Abstract

This paper reviews the development of several recent tools from computational harmonic analysis. These new systems are presented under a coherent perspective, namely, the representation of bivariate functions that are singular along smooth curves (edges). First, the representation of functions that are smooth away from straight edges is presented, and ridgelets will be shown to provide near optimal nonlinear approximations to these objects. Motivated by the limitations of the ridgelet methodology, new representation systems, namely, monoscale ridgelets and curvelets - both of which use the ridgelet transform as a building block - will be introduced. Curvelets are shown to provide concrete and constructive optimal nonlinear approximations to smooth functions with twice differentiable singularities. In addition, these approximations are obtained simply by thresholding the curvelet series.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2000
Accession Number
ADP011977

Entities

People

  • Emmanuel Candès

Organizations

  • Stanford University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Coefficients
  • Construction
  • Convergence
  • Data Compression
  • Dictionaries
  • Filters
  • Fourier Series
  • Frequency
  • Frequency Domain
  • Harmonic Analysis
  • Hilbert Space
  • Sequences
  • Statistical Estimation
  • Technical Information Centers
  • Two Dimensional
  • Wavelet Transforms

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis
  • Graph Algorithms and Convex Optimization.