Denoising and Robust Non-Linear Wavelet Analysis,

Abstract

In a series of papers, Donoho and Johnstone develop a powerful theory based on wavelets for extracting non-smooth signals from noisy data. Several nonlinear smoothing algorithms are presented which provide high performance for removing Gaussian noise from a wide range of spatially inhomogeneous signals. However, like other methods based on the linear wavelet transform, these algorithms are very sensitive to certain types of non-Gaussian noise, such as outliers. In this paper, we develop outilier resistance wavelet transforms. In these transforms, outliers and outlier patches are localized to just a few scales. By using the outlier resistant wavelet transforms, we improve upon the Donoho and Johnstone nonlinear signal extraction methods. The outlier resistant wavelet algorithms are included with the S+Wavelets object-oriented toolkit for wavelet analysis.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1994
Accession Number
ADA291668

Entities

People

  • Andrew G. Bruce
  • David L. Donoho
  • Hong-ye Gao
  • R. D. Martin

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Computational Complexity
  • Contrast
  • Data Analysis
  • Data Science
  • Filters
  • Filtration
  • Frequency
  • Gaussian Noise
  • Information Science
  • Residuals
  • Sequences
  • Statistical Algorithms
  • Statistical Analysis
  • Statistics
  • Time Series Analysis
  • Wavelet Transforms

Fields of Study

  • Engineering

Readers

  • Approximation Theory.
  • Computational Fluid Dynamics (CFD)
  • Image Processing and Computer Vision.