![]() īayesian estimation for multifractal analysisīayesian univariate and multivariate models and estimators for multifractal analysis for Signals (1D) and Images (2D) ![]() "Wavelet leaders and bootstrap for multifractal analysis of images". Relations to Detrended Fluctuation Analysis" "p-exponent and p-leaders, Part II: Multifractal Analysis. "Bootstrap for empirical multifractal analysis" If you use the code in your work, please cite the following references: You may also want to have a look at my thesis, which includes a synthetic overview of wavelet-based multifractal analysis, and collects material on a large number of theoretical and practical issues in empirical multifractal analysis. Another useful reference can be found in this review article. Specific aspects and particularities in the multifractal analysis of images are treated in this reference. You can find a brief overview on (discrete) wavelet transform and leaders based multifractal analysis in this reference, and in this tutorial article on wavelet-based multifractal analysis (with main focus on continuous wavelet transform). Further details may be found in reference , The theoretical and practical aspects of the renewing of multifractal analysis through the use of p-leaders are discussed in reference and reference, respectively (which also establishes connections with the wavelet leaders and MFDFA). Several demo files are included and use of the toolbox should be straightforward. The toolbox is self-contained and entirely written in MATLAB (with the exception of one function that can be replaced with a mex C file that is provided in the release). automatic selection of scaling range (see this reference) test for the null hypothesis of time constancy of multifractal attributes (1d only) tests for null hypotheses on the precise value of multifractal attributes several confidence intervals for structure functions and multifractal attributes time- (space-) block, and time-scale- (space-scale-) block bootstrap Wavelet-domain block bootstrap for multifractal analysis preliminary wavelet domain fractional integration multifractal attributes (scaling exponents, log-cumulants, multifractal spectrum) Wavelet p-leader and dyadic wavelet coefficient based multifractal analysis The following functionalities are implemented: The toolbox is a generalization (to p-leaders based analysis) and significant update (to a more efficient code) of the wavelet leader based WLBMF toolbox. This toolbox for MATLAB enables the (discrete) wavelet domain based multifractal analysis of (1d) signals and (2d) images, with bootstrap confidence intervals and significance tests, using wavelet p-leaders and wavelet leaders. ![]() Wavelet p-Leader and Bootstrap based MultiFractal analysis (PLBMF) toolbox ![]()
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