To characterize the geometry of a measure, its so-called generalized dimensions D(<i>q</i>) have been introduced recently. The mathematically precise definition given by Falconer turns out to be unsatisfactory for reasons ...

Usual fixed-size box-counting algorithms are inefficient for computing generalized fractal dimensions D(<i>q</i>) in the range of <i>q</i><0. In this Letter we describe a new numerical algorithm specifically devised to ...

This paper evaluates the performance of the recently published wavelet based algorithm for speckle reduction of SAR images. The original algorithm, based on the theory of wavelet thresholding due to Donoho and Johnstone, ...

There are strong reasons to believe that the multifractal spectrum of DLA shows anomalies which have been termed left sided. In order to show that this is compatible with strictly multiplicative structures Mandelbrot et ...

Joint signal representations (JSRs) of arbitrary variables generalize time-frequency representations (TFRs) to a much broader class of nonstationary signal characteristics. Two main distributional approaches to JSRs of ...

In the study of the involved geometry of singular distributions the use of fractal and multifractal analysis has shown results of outstanding significance. So far, the investigation has focused on structures produced by ...

In an earlier paper the authors introduced the <i>inverse measure</i> <i>µ</i>^â(<i>dt</i>) of a given measure <i>µ</i>(<i>dt</i>) on [0,1] and presented the 'inversion formula' <i>f</i>^â(<i>a</i>) ...

The present paper is part I of a series of three closely related papers in which the inverse measure m' of a given measure m on [0,1] is introduced. In the first case discussed in detail, both these measures are multifractal ...

We introduce a new method for the time-scale analysis of non-stationary signals. Our work leverages the success of the "time-frequency distribution series / cross-term deleted representations" into the time-scale domain ...

Nonlinearities are often encountered in the analysis and processing of real-world signals. In this paper, we introduce two new structures for nonlinear signal processing. The new structures simplify the analysis, design, ...