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Two-dimensional multifractal cross-correlation analysis

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  • Xi, Caiping
  • Zhang, Shuning
  • Xiong, Gang
  • Zhao, Huichang
  • Yang, Yonghong

Abstract

There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross-correlations. This paper presents two-dimensional multifractal cross-correlation analysis based on the partition function (2D-MFXPF), two-dimensional multifractal cross-correlation analysis based on the detrended fluctuation analysis (2D-MFXDFA) and two-dimensional multifractal cross-correlation analysis based on the detrended moving average analysis (2D-MFXDMA). We apply these methods to pairs of two-dimensional multiplicative cascades (2D-MC) to do a comparative study. Then, we apply the two-dimensional multifractal cross-correlation analysis based on the detrended fluctuation analysis (2D-MFXDFA) to real images and unveil intriguing multifractality in the cross correlations of the material structures. At last, we give the main conclusions and provide a valuable reference on how to choose the multifractal algorithms in the potential applications in the field of SAR image classification and detection.

Suggested Citation

  • Xi, Caiping & Zhang, Shuning & Xiong, Gang & Zhao, Huichang & Yang, Yonghong, 2017. "Two-dimensional multifractal cross-correlation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 59-69.
    • Handle: RePEc:eee:chsofr:v:96:y:2017:i:c:p:59-69
    DOI: 10.1016/j.chaos.2017.01.004
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    References listed on IDEAS

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    1. Kong, Xiangguo & Wang, Enyuan & He, Xueqiu & Li, Dexing & Liu, Quanlin, 2017. "Time-varying multifractal of acoustic emission about coal samples subjected to uniaxial compression," Chaos, Solitons & Fractals, Elsevier, vol. 103(C), pages 571-577.
    2. Xiong, Gang & Xiong, Ziqin & Jia, Liqiong & Truong, Trieu-Kien, 2023. "Spatial multifractal spectrum distribution method for breast ultrasonic image classification," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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