Oriol Pont

An optimized algorithm for the evaluation of local singularity exponents in digital signals

Recent works show that the determination of singularity exponents in images can be useful to assess their information content, and in some cases they can cast additional information about underlying physical processes. However, the concept of singularity exponent is associated to differential calculus and thus cannot be easily translated to a digital context, even using wavelets. In this work we show that a recently patented algorithm allows obtaining precise, meaningful values of singularity exponents at every point in the image by the use of a discretized combinatorial mask, which is an extension of a particular wavelet basis. This mask is defined under the hypothesis that singularity exponents are a measure not only of the degree of regularity of the image, but also of the reconstructibility of a signal from their points.

Phonetic segmentation of speech signal using local singularity analysis

This paper presents the application of a radically novel approach, called the Microcanonical Multiscale Formalism (MMF) to speech analysis. MMF is based on precise estimation of local scaling parameters that describe the inter-scale correlations at each point in the signal domain and provides efficient means for studying local non-linear dynamics of complex signals. In this paper we introduce an efficient way for estimation of these parameters and then, we show that they convey relevant information about local dynamics of the speech signal that can be used for the task of phonetic segmentation. We thus develop a two-stage segmentation algorithm: for the first step, we introduce a new dynamic programming technique to efficiently generate an initial list of phoneme-boundary candidates and in the second step, we use hypothesis testing to refine the initial list of candidates. We present extensive experiments on the full TIMIT database. The results show that our algorithm is significantly more accurate than state-of-the-art ones.

Improving text-independent phonetic segmentation based on the Microcanonical Multiscale Formalism

In an earlier work, we proposed a novel phonetic segmentation method based on speech analysis under the Microcanonical Multiscale Formalism (MMF). The latter relies on the computation of local geometrical parameters, singularity exponents (SE). We showed that SE convey valuable information about the local dynamics of speech that can readily and simply used to detect phoneme boundaries. By performing error analysis of our original algorithm, in this paper we propose a 2-steps technique which better exploits SE to improve the segmentation accuracy. In the first step, we detect the boundaries of the original signal and of a low-pass filtred version, and we consider the union of all detected boundaries as candidates. In the second step, we use a hypothesis test over the local SE distribution of the original signal to select the final boundaries. We carry out a detailed evaluation and comparison over the full training set of the TIMIT database which could be useful to other researchers for comparison purposes. The results show that the new algorithm not only outperforms the original one, but also is significantly much more accurate than state-of-the-art ones.

Ocean Turbulent Dynamics at Superresolution From Optimal Multiresolution Analysis and Multiplicative Cascade

The synoptic determination of ocean circulation using the data acquired from space, with a coherent depiction of its turbulent characteristics, remains a fundamental challenge in oceanography. This determination has the potential of revealing all aspects of the ocean dynamic variability on a wide range of spatiotemporal scales and will enhance our understanding of ocean-atmosphere exchanges at superresolution, as required in the present context of climate change. Here, we show a four-year time series of spatial superresolution (4 km) turbulent ocean dynamics generated from satellite data using emerging ideas in signal processing coming from nonlinear physics, low-resolution dynamics, and superresolution oceanic sea surface temperature data acquired from optical sensors. The method at its core consists in propagating across the scales the low-resolution dynamics in a multiresolution analysis computed on adimensional critical transition information.

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

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 characterization 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 with 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.

Towards multiscale reconstruction of perturbated phase from Hartmann-Shack acquisitions

Atmospheric turbulence perturbates to a great extent the optical path of incoming light from outer space thereby limiting the resolution power of capturing devices. One of the most common techniques used in astronomical imaging to compensate for this perturbation is Adaptive Optics (AO). In this paper we explore the potential of Microcanonical Multiscale Formalism (MMF) for the reconstruction of the perturbated wavefront, from the low-resolution acquisition of the turbulent phase by a Hartmann-Shack wavefront sensor used in AO. In fact, turbulent flows, although chaotic in nature, are characterised by scale hierarchy and develop cascade like structures where transfer of energy takes place from one scale to the other. We make use of MMF to infer properties along the scales of the complex signal consisting of optical phase perturbation and perform reconstruction using an appropriate wavelet decomposition associated to the cascading properties of the turbulent flow.

Reconstruction of speech signals from their unpredictable points manifold

This paper shows that a microcanonical approach to complexity, such as the Microcanonical Multiscale Formalism, provides new insights to analyze non-linear dynamics of speech, specifically in relation to the problem of speech samples classification according to their information content. Central to the approach is the precise computation of Local Predictability Exponents (LPEs) according to a procedure based on the evaluation of the degree of reconstructibility around a given point. We show that LPEs are key quantities related to predictability in the framework of reconstructible systems: it is possible to reconstruct the whole speech signal by applying a reconstruction kernel to a small subset of points selected according to their LPE value. This provides a strong indication of the importance of the Unpredictable Points Manifold (UPM), already demonstrated for other types of complex signals. Experiments show that a UPM containing around 12% of the points provides very good perceptual reconstruction quality.

Non-linear speech representation based on local predictability exponents

Looking for new perspectives to analyze non-linear dynamics of speech, this paper presents a novel approach based on a microcanonical multiscale formulation which allows the geometric and statistical description of multiscale properties of the complex dynamics. Speech is a complex system whose dynamics can be, to some extent, geometrically and statistically accessed by the computation of Local Predictability Exponents (LPEs) unlocking the determination of the most informative subset (Most Singular Manifold or MSM), leading to associated compact representation and reconstruction. But the complex intertwining of different dynamics in speech (added to purely turbulent descriptions) suggests the definition of appropriate multiscale functionals that might influence the evaluation of LPEs, hence leading to more compact MSM. Consequently, by using the classical and generic Sauer/Allebach algorithm for signal reconstruction from irregularly spaced samples, we show that speech reconstruction of good quality can be achieved using MSM of low cardinality. Moreover, in order to further show the potential of the new methodology, we develop a simple and efficient waveform coder which achieves almost the same level of perceptual quality as a standard coder, while having a lower bit-rate.

Parameters Analysis of FitzHugh-Nagumo Model for a Reliable Simulation

Derived from the pioneer ionic Hodgkin-Huxley model and due to its simplicity and richness from a point view of nonlinear dynamics, the FitzHugh-Nagumo model (FHN) is one of the most successful simplified neuron / cardiac cell model. There exist many variations of the original FHN model. Though these FHN type models help to enrich the dynamics of the FHN model, the parameters used in these models are often in biased conditions. The related results would be questionable. So, in this study, the aim is to find the parameter thresholds for one of the commonly used FHN model in order to provide a better simulation environment. The results showed at first that inappropriate time step and integration tolerance in numerical solution of FHN model can give some biased results which would make some publications questionable. Then the thresholds of parameters α, γ and ε are presented. α controls the global dynamics of FHN. α > 0, the cell is in refractory mode; α <; 0, the cell is excitable. ε controls the main morphology of the action potential generated and has a relation with the period (P = 3.065 × αα,γ-0.8275+ 4.397). To show oscillations of relaxation with FHN, ε should be smaller than 0.0085. 7 influences barely action potential, it showed linear relationship with the period and duration of action potential. Even though α <; 0.1, ε <; 0.0085, there is no definite threshold for γ, smaller values are recommended.

Arrhythmic dynamics from singularity analysis of electrocardiographic maps

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.