The paper proposes a method to do so through Lipschitz exponents, relatively efficiently and with many mathematical guarantees.
As far as I could understand (I'm about halfway through), if the function is not rapidly oscillating, this can be done by computing a CWT, then extracting local maxima lines and computing their gradient on a log scale. A wavelet with an appropriate number of moments must be chosen.
Before getting into more details, I looked for existing implementations to play with it, but all I could find were these (rather distorted/vague) mentions to the paper here.
Questions/proposed contribution:
Is anyone aware of an existing implementation?
If I end up implementing it, would it be interesting to include it into pywt? The idea is: given a 1D discrete-time real-valued function, or alternatively its WT, return the minimal pointwise Lipschitz exponent found for each time point. The lower, the more spiky.
I'm only interested in 1D, real-valued signals for the moment. The 1992 work is focused on real-valued signals, but it has been extended to C since then. Also, the 1992 work provides a section for image processing which should allow to extend to 2D.
I'm currently reading the 1992 paper by Mallat and Hwang, Singularity Detection and Processing with Wavelets, because I'm interested in quantifying how "spiky" a 1D function is at given points.
The paper proposes a method to do so through Lipschitz exponents, relatively efficiently and with many mathematical guarantees. As far as I could understand (I'm about halfway through), if the function is not rapidly oscillating, this can be done by computing a CWT, then extracting local maxima lines and computing their gradient on a log scale. A wavelet with an appropriate number of moments must be chosen.
Before getting into more details, I looked for existing implementations to play with it, but all I could find were these (rather distorted/vague) mentions to the paper here.
Questions/proposed contribution:
I'm only interested in 1D, real-valued signals for the moment. The 1992 work is focused on real-valued signals, but it has been extended to C since then. Also, the 1992 work provides a section for image processing which should allow to extend to 2D.
I'd appreciate any thoughts on the matter!