Inferring Information Across Scales in Acquired Complex Signals

Abstract

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.

Spatial and seasonal distributions of frontal activity over the French continental shelf in the Bay of Biscay

“…Following previous studies, this image processing method given by the notion of singularity exponents for edge detection is the most adapted and efficient in the case of natural and turbulent complex signals (Yahia et al, 2010;Kumar Maji & Yahia, 2014;Turiel et al, 2008;Sudre et al, 2015), compared with other classical approaches in image processing (Maji et al, 2013).…”

Pitch-based speech perturbation measures using a novel GCI detection algorithm: application to pathological voice classification

“…It is based on precise computation of local parameters called the Singularity Exponents (SE) at every point in signal domain. When correctly defined and estimated, these exponents alone can provide valuable information about local dynamics of complex signals and has recently proven to be promising in many signal processing applications ranging from signal compression to inference and prediction in a quite diverse set of scientific disciplines such as satellite imaging [18,19,20,21], adaptive optics [22,23], computer graphics [24] and natural image processing [25,26]. In the field of speech processing, besides GCI detection [3] , we have also successfully used MMF in phonetic segmentation [27,28,29].…”

Detection of Glottal Closure Instants Based on the Microcanonical Multiscale Formalism

“…SEs are local quantities that quantify the degree of regularity of the signal at each time instant. When correctly defined and estimated, these exponents alone can provide valuable information about local dynamics of complex signals and have recently proven their strength in many signal processing applications ranging from signal compression to inference and prediction in a quite diverse set of scientific disciplines such as satellite imaging [28], [29], [30], [31], adaptive optics [32], [33], computer graphics [34] and natural image processing [20], [35].…”