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2D wavelet-based spectra with applications

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  • Nicolis, Orietta
  • Ramírez-Cobo, Pepa
  • Vidakovic, Brani

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.

Suggested Citation

  • Nicolis, Orietta & Ramírez-Cobo, Pepa & Vidakovic, Brani, 2011. "2D wavelet-based spectra with applications," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 738-751, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:738-751
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    References listed on IDEAS

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    1. Guo, Hongwen & Lim, Chae Young & Meerschaert, Mark M., 2009. "Local Whittle estimator for anisotropic random fields," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 993-1028, May.
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    1. Ramírez-Cobo, Pepa & Vidakovic, Brani, 2013. "A 2D wavelet-based multiscale approach with applications to the analysis of digital mammograms," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 71-81.
    2. Bae, Suk Joo & Mun, Byeong Min & Chang, Woojin & Vidakovic, Brani, 2019. "Condition monitoring of a steam turbine generator using wavelet spectrum based control chart," Reliability Engineering and System Safety, Elsevier, vol. 184(C), pages 13-20.
    3. Yeliz Karaca & Carlo Cattani & Majaz Moonis & Şengül Bayrak, 2018. "Stroke Subtype Clustering by Multifractal Bayesian Denoising with Fuzzy Means and -Means Algorithms," Complexity, Hindawi, vol. 2018, pages 1-15, April.

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