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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. [ABSTRACT FROM AUTHOR]

Abstract: The time-singularity multifractal spectrum distribution (MFSD) has been proposed recently as a generalized singularity spectrum in a time varying framework. In this paper, we aim at putting forward a new algorithm i.e. MFSD based on detrending moving average (DMA-MFSD) to determine MFSD, which is also a generalization of multifractal detrending moving average (MF-DMA) method. We relate DMA-MFSD method to the MFSD based on the standard partition function, and prove that both approaches are equivalent for fractal time series with compact support. The performance of the DMA-MFSD methods with different moving windows is studied using synthetic fractional Gaussian noise (fGn), binomial multiplicative cascades (BMC) with analytical solutions and real sea clutter data. We find that the estimated DMA-MFSD is in good accordance with the detrended fluctuation analysis based multifractal spectrum distribution (DFA-MFSD) and the theoretical analysis. Overall, the backward DMA-MFSD method has the best performance, which provides the most accurate estimates of the time-singularity MFSD, while the centered DMA-MFSD method performs worse. In addition we find that the backward DMA-MFSD algorithm even outperforms the DFA-MFSD method in the computational complexity and precision. [Copyright &y& Elsevier]

Fractal reconstruction (FR) and multifractal reconstruction (MFR) can be considered as the inverse problem of singularity spectrum analysis, and it is challenging to reconstruct fractal signal in accord with multifractal spectrum (MFS). Due to the multiple solutions of fractal reconstruction, the traditional methods of FR/MFR, such as FBM based method, wavelet based method, random wavelet series, fail to reconstruct fractal signal deterministically, and besides, those methods neglect the power spectral distribution in the singular domain. In this paper, we propose a novel MFR method based singularity power spectrum (SPS). Supposing the consistent uniform covering of multifractal measurement, we control the traditional power law of each scale of wavelet coefficients based on the instantaneous singularity exponents (ISE) or MFS, simultaneously control the singularity power law based on the SPS, and deduce the principle and algorithm of MFR based on SPS. Reconstruction simulation and error analysis of estimated ISE, MFS and SPS show the effectiveness and the improvement of the proposed methods compared to those obtained by the Fraclab package. [ABSTRACT FROM AUTHOR]