Section: New Results

Optimal wavelets, unpredictable points manifold and the emergence of complexity

Participants : Oriol Pont, Hussein Yahia, Suman Maji.

We have found new theoretical developments that link the optimal wavelet description with the information transfer that characterizes the singularity exponents in complex signals. This fact is particularly relevant when there exists a microcanonical cascade as an effective dynamics for the underlying complex system. The implication of this is that under a multiscale hierarchy, the unpredictable set of a signal can be described in terms of its optimal wavelet coefficients and the multiplicative cascade relations between them, easing the information inference or reconstructability between resolution levels.

A new method for the detection of the unpredictable points manifold has been developed, enhancing previous implementations. The algorithm exploits the basic signal symmetries that can be easily verified and has the advantage of not assuming any underlying model. That work is the result of the collaboration between our team and A. Turiel's team at Institute of Marine Sciences of Barcelona.

Additionally, we have developed a new algorithm that allows for the first time a very robust detection of the optimal wavelet in 2D signals. The main advantage of this new algorithm is that it optimizes the wavelet shape in a totally unconstrained way, therefore not restricting to specific wavelet families.

Related Publications: [7] , [20] .