A Bridge Between Geometric Measure Theory and Signal Processing: Multifractal Analysis

We describe the main features of wavelet techniques in multifractal analysis, using wavelet bases both as a tool for analysis, and for synthesis. We focus on two promising developments: We introduce the quantile leader method, which allows to put into light nonconcave multifractal spectra; we also test recent extensions of multifractal techniques fitted to functions that are not locally bounded but only belong to an L q space (determination of the q-spectrum).

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