An Optimized Algorithm for the Evaluation of Local Singularity Exponents in Digital Signals

Proceedings of the European Conference on Complex Systems 2012

et al. 2013

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Abstract. Transmission of information across the scales of a complex signal has some interesting potential, notably in the derivation of subpixel information, cross-scale inference and data fusion. It follows the structure of complex signals themselves, when they are considered as acquisitions of complex systems. In this work we contemplate the problem of cross-scale information inference through the determination of appropriate multiscale decomposition. Our goal is to derive a generic methodology that can be applied to propagate information across the scales in a wide variety of complex signals. Consequently, we first focus on the determination of appropriate multiscale characteristics, and we show that singularity exponents computed in microcanonical formulations are much better candidates for the characterization of transitions in complex signals : they outperform the classical «linear filtering» approach of the state-of-the-art edge detectors (for the case of 2D signals). This is a fundamental topic as edges are usually considered as important multiscale features in an image. The comparison is done within the formalism of reconstructible systems. Critical exponents, naturally associated to phase transitions and used in complex systems methods in the framework of criticality are key notions in Statistical Physics that can lead to the complete determination of the geometrical cascade properties in complex signals. We study optimal multiresolution analysis associated to critical exponents through the concept of «optimal wavelet». We demonstrate the usefulness of multiresolution analysis associated to critical exponents in two decisive examples : the reconstruction of perturbated optical phase in Adaptive Optics (AO) and the generation of high resolution ocean dynamics from low resolution altimetry data.

Section: Singularity Analysismentioning

confidence: 99%

Inferring Information Across Scales in Acquired Complex Signals

Maji

Proceedings of the European Conference on Complex Systems 2012

et al. 2013

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“…We observe that all the features and their informative degree coincide and furthermore the singularity exponents provide a finer resolution and so a better localization of the information. This paper is presented as an extended version of our previous findings that we have presented at the 14th International Workshop on Combinatorial Image Analysis, IWCIA 2011 held in Madrid in May 2011 [25]. Here we summarise our previous findings, while at the same time we expand them accordingly: we give a deeper description of the analysis performed and the methods used, and we present a more exhaustive evaluation (which includes both signal reconstructibility and illustrating a comparison of information content with multiscale entropy).…”

Section: Introductionmentioning

confidence: 98%

Singularity analysis of digital signals through the evaluation of their unpredictable point manifold

Turiel

International Journal of Computer Mathematics

2013

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The local singularity exponents of a signal are directly related to the distribution of information in it. This fact implies that accurate evaluation of such exponents opens the door to signal reconstruction and characterisation of the dynamical parameters of the process originating the signal. Many practical implications arise in a context of digital signal processing, since the information on singularity exponents is usable for compact encoding, reconstruction and inference. Since singularity exponents are conceptually associated to differential calculus, its evaluation in a digital context is not straightforward and it requires the calculation of the Unpredictable Point Manifold of the signal. In this paper, we present an algorithm for estimating the values of singularity exponents at every point of a digital signal of any dimension. We show that the key ingredient for robust and accurate reconstructibility performance lies on the definition of multiscale measures in the sense that they encode the degree of singularity and the local predictability at the same time.

“…how rare or unreconstructible is the value at that point from the rest of the signal. A reconstruction kernel that is deterministic, linear, isotropic and translational invariant is uniquely defined and its form implies locally evaluated singularities and thus no need to assume any kind of stationarity [14,15,16]. Given a signal s(x), its singularity exponent h(x) can be determined, when the following condition is fulfilled :…”

Section: Singularity Analysis Methodsmentioning

confidence: 99%

Arrhythmic dynamics from singularity analysis of electrocardiographic maps

2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)

2013

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From a point view of nonlinear dynamics, the electrical activity of the heart is a complex dynamical system, whose dynamics reflects the actual state of health of the heart. Nonlinear signal-processing methods are needed in order to accurately characterize these signals and improve understanding of cardiac arrhythmias. Recent developments on reconstructible signals and multiscale information content show that an analysis in terms of singularity exponents provides compact and meaningful descriptors of the structure and dynamics of the system. Such approach gives a compact representation atrial arrhythmic dynamics, which can sharply highlight regime transitions and arrhythmogenic areas.