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Hurst exponent estimation of fractional surfaces for mammogram images analysis

Author

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  • Dlask, Martin
  • Kukal, Jaromir

Abstract

The work presents a methodology to precise simulation and parameter estimation of multidimensional fractional Brownian motion (fBm). The simulation approach uses circulant embedding algorithm and solution of Poisson equation, while generalizing it to multiple dimensions. For estimation, a method using Wishart distribution and maximum likelihood is presented and verified on simulated data. Unlike approximate methods for generating multidimensional fBm and its Hurst exponent estimation, this approach shows unbiased results for all processes with short memory and majority of cases with long memory. The methodology is applied to mammography screening images to find significant differences between benign and cancerous breast lumps.

Suggested Citation

  • Dlask, Martin & Kukal, Jaromir, 2022. "Hurst exponent estimation of fractional surfaces for mammogram images analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    • Handle: RePEc:eee:phsmap:v:585:y:2022:i:c:s037843712100697x
    DOI: 10.1016/j.physa.2021.126424
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    References listed on IDEAS

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    1. McGaughey, Donald R. & Aitken, G.J.M., 2002. "Generating two-dimensional fractional Brownian motion using the fractional Gaussian process (FGp) algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(3), pages 369-380.
    2. Dlask, Martin & Kukal, Jaromir, 2017. "Application of rotational spectrum for correlation dimension estimation," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 256-262.
    3. Dlask, Martin & Kukal, Jaromir, 2018. "Translation and rotation invariant method of Renyi dimension estimation," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 536-541.
    4. Unterberger, Jérémie, 2010. "A rough path over multidimensional fractional Brownian motion with arbitrary Hurst index by Fourier normal ordering," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1444-1472, August.
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