2D wavelet-based spectra with applications

Orietta Nicolis, Pepa Ramírez-Cobo, Brani Vidakovic

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

Abstract

A wavelet-based spectral method for estimating the (directional) Hurst parameter in isotropic and anisotropic non-stationary fractional Gaussian fields is proposed. The method can be applied to self-similar images and, in general, to d-dimensional data which scale. In the application part, the problems of denoising 2D fractional Brownian fields and classification of digital mammograms to benign and malignant are considered. In the first application, a Bayesian inference calibrated by information from the wavelet-spectral domain is used to separate the signal from the noise. In the second application, digital mammograms are classified into benign and malignant based on the directional Hurst exponents which prove to be discriminatory summaries.

Original languageEnglish
Pages (from-to)738-751
Number of pages14
JournalComputational Statistics and Data Analysis
Volume55
Issue number1
DOIs
Publication statusPublished - 1 Jan 2011

Keywords

  • 2D wavelet spectra
  • Scaling
  • Self-similarity
  • Wavelets

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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