Impact of Data Quantization on Empirical Multifractal Analysis

Multifractal analysis is nowadays commonly used in real-life data analyses and involved in standard signal processing tasks such as detection, identification or classification. In a number of situations, mostly in image processing, the data are available for the analyses only in (possibly severely) quantized versions. The present contribution aims at analyzing the robustness of standard multifractal estimation procedures against quantization. To this end, we analyze the behaviors and statistical performance of these procedures when applied to a large number of realizations of known synthetic multifractal processes subject to various quantization levels. Our study shows that immunity against quantization can be obtained by restricting the range of scales involved in multifractal parameter estimation to the largest ones. Comparing multifractal analyses based on different multiresolution quantities, increments, wavelet coefficients and leaders, we show that wavelets, thanks to their good frequency localization, bring robustness against quantization when increments do not. This study provides the practitioner with a clear guide line to perform multifractal analysis over quantized data.