Removing divergences in the negative moments of the multi-fractal parition function with the wavelet transformation

We present a promising technique which is capable of accessing the divergence free component of the partition function for the negative moments of the multi-fractal analysis of data using the wavelet transformation. It is based on implicitly bounding the local logarithmic slope of the wavelet maxima lines between the values of the Holder exponent of the singularities which are accessible for the wavelet used. The method delivers correct and stable results, illustrated using a test example of the Besicovich measure analysed with the Mexican hat wavelet. The performance of the method is then shown as applied to real-life data.