Signals studied in GEOSTAT belong to two broad classes:

• Acquisitions in Astronomy and Earth Observation.
• Physiological time series.

3.1 General methodology

Every signal conveys, as a measure experiment, information on the physical system whose signal is an acquisition of. As a consequence, it seems natural that signal analysis or compression should make use of physical modelling of phenomena: the goal is to find new methodologies in signal processing that goes beyond the simple problem of interpretation. Physics of disordered systems, and specifically physics of (spin) glasses is putting forward new algorithmic resolution methods in various domains such as optimization, compressive sensing etc. with significant success notably for NP hard problem heuristics. Similarly, physics of turbulence introduces phenomenological approaches involving multifractality. Energy cascades are indeed closely related to geometrical manifolds defined through random processes. At these structures’ scales, information in the process is lost by dissipation (close to the lower bound of inertial range). However, all the cascade is encoded in the geometric manifolds, through long or short distance correlations depending on cases. How do these geometrical manifold structures organize in space and time, in other words, how does the scale entropy cascades itself ? To unify these two notions, a description in term of free energy of a generic physical model is sometimes possible, such as an elastic interface model in a random nonlinear energy landscape : This is for instance the correspondence between compressible stochastic Burgers equation and directed polymers in a disordered medium. Thus, trying to unlock the fingerprints of cascade-like structures in acquired natural signals becomes a fundamental problem, from both theoretical and applicative viewpoints.

3.2 Turbulence in insterstellar clouds and Earth observation data

The research described in this section is a collaboration effort of GEOSTAT, CNRS LEGOS (Toulouse), CNRS LAM (Marseille Laboratory for Astrophysics), MERCATOR (Toulouse), IIT Roorkee, Moroccan Royal Center for Teledetection (CRST), Moroccan Center for Science CNRST, Rabat University, University of Heidelberg. Researchers involved:

• GEOSTAT: H. Yahia, N. Brodu, K. Daoudi, A. El Aouni, A. Tamim
• CNRS LAB: S. Bontemps, N. Schneider
• CNRS LEGOS: V. Garçon, I. Hernandez-Carrasco, J. Sudre, B. Dewitte
• CNRST, CRTS, Rabat University: D. Aboutajdine, A. Atillah, K. Minaoui

The analysis and modeling of natural phenomena, specially those observed in geophysical sciences and in astronomy, are influenced by statistical and multiscale phenomenological descriptions of turbulence; indeed these descriptions are able to explain the partition of energy within a certain range of scales. A particularly important aspect of the statistical theory of turbulence lies in the discovery that the support of the energy transfer is spatially highly non uniform, in other terms it is intermittent47. Because of the absence of localization of the Fourier transform, linear methods are not successful to unlock the multiscale structures and cascading properties of variables which are of primary importance as stated by the physics of the phenomena. This is the reason why new approaches, such as DFA (Detrented Fluctuation Analysis), Time-frequency analysis, variations on curvelets 45 etc. have appeared during the last decades. Recent advances in dimensionality reduction, and notably in Compressive Sensing, go beyond the Nyquist rate in sampling theory using nonlinear reconstruction, but data reduction occur at random places, independently of geometric localization of information content, which can be very useful for acquisition purposes, but of lower impact in signal analysis. We are successfully making use of a microcanonical formulation of the multifractal theory, based on predictability and reconstruction, to study the turbulent nature of interstellar molecular or atomic clouds. Another important result obtained in GEOSTAT is the effective use of multiresolution analysis associated to optimal inference along the scales of a complex system. The multiresolution analysis is performed on dimensionless quantities given by the singularity exponents which encode properly the geometrical structures associated to multiscale organization. This is applied successfully in the derivation of high resolution ocean dynamics, or the high resolution mapping of gaseous exchanges between the ocean and the atmosphere; the latter is of primary importance for a quantitative evaluation of global warming. Understanding the dynamics of complex systems is recognized as a new discipline, which makes use of theoretical and methodological foundations coming from nonlinear physics, the study of dynamical systems and many aspects of computer science. One of the challenges is related to the question of emergence in complex systems: large-scale effects measurable macroscopically from a system made of huge numbers of interactive agents 26, 42. Some quantities related to nonlinearity, such as Lyapunov exponents, Kolmogorov-Sinai entropy etc. can be computed at least in the phase space 27. Consequently, knowledge from acquisitions of complex systems (which include complex signals) could be obtained from information about the phase space. A result from F. Takens 46 about strange attractors in turbulence has motivated the theoretical determination of nonlinear characteristics associated to complex acquisitions. Emergence phenomena can also be traced inside complex signals themselves, by trying to localize information content geometrically. Fundamentally, in the nonlinear analysis of complex signals there are broadly two approaches: characterization by attractors (embedding and bifurcation) and time-frequency, multiscale/multiresolution approaches. In real situations, the phase space associated to the acquisition of a complex phenomenon is unknown. It is however possible to relate, inside the signal's domain, local predictability to local reconstruction 13 and to deduce relevant information associated to multiscale geophysical signals 14. A multiscale organization is a fundamental feature of a complex system, it can be for example related to the cascading properties in turbulent systems. We make use of this kind of description when analyzing turbulent signals: intermittency is observed within the inertial range and is related to the fact that, in the case of FDT (fully developed turbulence), symmetry is restored only in a statistical sense, a fact that has consequences on the quality of any nonlinear signal representation by frames or dictionaries.

The example of FDT as a standard "template" for developing general methods that apply to a vast class of complex systems and signals is of fundamental interest because, in FDT, the existence of a multiscale hierarchy ${ℱ}_h$ which is of multifractal nature and geometrically localized can be derived from physical considerations. This geometric hierarchy of sets is responsible for the shape of the computed singularity spectra, which in turn is related to the statistical organization of information content in a signal. It explains scale invariance, a characteristic feature of complex signals. The analogy from statistical physics comes from the fact that singularity exponents are direct generalizations of critical exponents which explain the macroscopic properties of a system around critical points, and the quantitative characterization of universality classes, which allow the definition of methods and algorithms that apply to general complex signals and systems, and not only turbulent signals: signals which belong to a same universality class share common statistical organization. During the past decades, canonical approaches permitted the development of a well-established analogy taken from thermodynamics in the analysis of complex signals: if $ℱ$ is the free energy, $𝒯$ the temperature measured in energy units, $𝒰$ the internal energy per volume unit $𝒮$ the entropy and $\widehat{\beta }=1/𝒯$, then the scaling exponents associated to moments of intensive variables $p\to {\tau }_p$ corresponds to $\widehat{\beta }ℱ$, $𝒰\left(\widehat{\beta }\right)$ corresponds to the singularity exponents values, and $𝒮\left(𝒰\right)$ to the singularity spectrum 25. The research goal is to be able to determine universality classes associated to acquired signals, independently of microscopic properties in the phase space of various complex systems, and beyond the particular case of turbulent data 40.

We show in figure 1 the result of the computation of singularity exponents on an Herschel astronomical observation map (the Musca galactic cloud) which has been edge-aware filtered using sparse $L^1$ filtering to eliminate the cosmic infrared background (or CIB), a type of noise that can modify the singularity spectrum of a signal.

3.3 Causal modeling

The team is working on a new class of models for modeling physical systems, starting from measured data and accounting for their dynamics 32. The idea is to statistically describe the evolution of a system in terms of causally-equivalent states; states that lead to the same predictions 28. Transitions between these states can be reconstructed from data, leading to a theoretically-optimal predictive model 44. In practice, however, no algorithm is currently able to reconstruct these models from data in a reasonable time and without substantial discrete approximations. Recent progress now allows a continuous formulation of predictive causal models. Within this framework, more efficient algorithms may be found. The broadened class of predictive models promises a new perspective on structural complexity in many applications.

3.4 Speech analysis

Phonetic and sub-phonetic analysis: We developed a novel algorithm for automatic detection of Glottal Closure Instants (GCI) from speech signals using the Microcanonical Multiscale Formalism (MMF). This state of the art algorithm is considered as a reference in this field. We made a Matlab code implementing it available to the community (link). Our approach is based on the Microcanonical Multiscale Formalism. We showed that in the case of clean speech, our algorithm performs almost as well as a recent state-of-the-art method. In presence of different types of noises, we showed that our method is considerably more accurate (particularly for very low SNRs). Moreover, our method has lower computational times does not rely on an estimate of pitch period nor any critical choice of parameters. Using the same MMF, we also developed a method for phonetic segmentation of speech signal. We showed that this method outperforms state of the art ones in term of accuracy and efficiency.

Pathological speech analysis and classification: we made a critical analysis of some widely used methodologies in pathological speech classification. We then introduced some novel methods for extracting some common features used in pathological speech analysis and proposed more robust techniques for classification.

Speech analysis of patients with Parkinsonism: with our collaborators from the Czech Republic, we started preliminary studies of some machine learning issues in the field essentially due the small amount of training data.

3.5 Data-based identification of characteristic scales and automated modeling

Data are often acquired at the highest possible resolution, but that scale is not necessarily the best for modeling and understanding the system from which data was measured. The intrinsic properties of natural processes do not depend on the arbitrary scale at which data is acquired; yet, usual analysis techniques operate at the acquisition resolution. When several processes interact at different scales, the identification of their characteristic scales from empirical data becomes a necessary condition for properly modeling the system. A classical method for identifying characteristic scales is to look at the work done by the physical processes, the energy they dissipate over time. The assumption is that this work matches the most important action of each process on the studied natural system, which is usually a reasonable assumption. In the framework of time-frequency analysis 36, the power of the signal can be easily computed in each frequency band, itself matching a temporal scale.

However, in open and dissipating systems, energy dissipation is a prerequisite and thus not necessarily the most useful metric to investigate. In fact, most natural, physical and industrial systems we deal with fall in this category, while balanced quasi-static assumptions are practical approximation only for scales well below the characteristic scale of the involved processes. Open and dissipative systems are not locally constrained by the inevitable rise in entropy, thus allowing the maintaining through time of mesoscopic ordered structures. And, according to information theory 38, more order and less entropy means that these structures have a higher information content than the rest of the system, which usually gives them a high functional role.

We propose to identify characteristic scales not only with energy dissipation, as usual in signal processing analysis, but most importantly with information content. Information theory can be extended to look at which scales are most informative (e.g. multi-scale entropy 31, $\epsilon$-entropy 30). Complexity measures quantify the presence of structures in the signal (e.g. statistical complexity 33, MPR 41 and others 35). With these notions, it is already possible to discriminate between random fluctuations and hidden order, such as in chaotic systems 32, 41. The theory of how information and structures can be defined through scales is not complete yet, but the state of art is promising 34. Current research in the team focuses on how informative scales can be found using collections of random paths, assumed to capture local structures as they reach out 29.

Building on these notions, it should also possible to fully automate the modeling of a natural system. Once characteristic scales are found, causal relationships can be established empirically. They are then clustered together in internal states of a special kind of Markov models called $ϵ$-machines 33. These are known to be the optimal predictors of a system, with the drawback that it is currently quite complicated to build them properly, except for small system 43. Recent extensions with advanced clustering techniques 28, 37, coupled with the physics of the studied system (e.g. fluid dynamics), have proved that $ϵ$-machines are applicable to large systems, such as global wind patterns in the atmosphere 39. Current research in the team focuses on the use of reproducing kernels, coupled possibly with sparse operators, in order to design better algorithms for $ϵ$-machines reconstruction. In order to help with this long-term project, a collaboration is ongoing with J. Crutchfield lab at UC Davis.

4.1 Sparse signals & optimization

This research topic involves Geostat team and is used to set up an InnovationLab with I2S company

Sparsity can be used in many ways and there exist various sparse models in the literature; for instance minimizing the $l_0$ quasi-norm is known to be an NP-hard problem as one needs to try all the possible combinations of the signal's elements. The $l_1$ norm, which is the convex relation of the $l_0$ quasi-norm results in a tractable optimization problem. The $l_p$ pseudo-norms with $0<p<1$ are particularly interesting as they give closer approximation of $l_0$ but result in a non-convex minimization problem. Thus, finding a global minimum for this kind of problem is not guaranteed. However, using a non-convex penalty instead of the $l_1$ norm has been shown to improve significantly various sparsity-based applications. Nonconvexity has a lot of statistical implications in signal and image processing. Indeed, natural images tend to have a heavy-tailed (kurtotic) distribution in certain domains such as wavelets and gradients. Using the $l_1$ norm comes to consider a Laplacian distribution. More generally, the hyper-Laplacian distribution is related to the $l_p$ pseudo-norm ($0<p<1$) where the value of $p$ controls how the distribution is heavy-tailed. As the hyper-Laplacian distribution for $0<p<1$ represents better the empirical distribution of the transformed images, it makes sense to use the $l_p$ pseudo-norms instead of $l_1$. Other functions that better reflect heavy-tailed distributions of images have been used as well such as Student-t or Gaussian Scale Mixtures. The internal properties of natural images have helped researchers to push the sparsity principle further and develop highly efficient algorithms for restoration, representation and coding. Group sparsity is an extension of the sparsity principle where data is clustered into groups and each group is sparsified differently. More specifically, in many cases, it makes sense to follow a certain structure when sparsifying by forcing similar sets of points to be zeros or non-zeros simultaneously. This is typically true for natural images that represent coherent structures. The concept of group sparsity has been first used for simultaneously shrinking groups of wavelet coefficients because of the relations between wavelet basis elements. Lastly, there is a strong relationship between sparsity, nonpredictability and scale invariance.

We have shown that the two powerful concepts of sparsity and scale invariance can be exploited to design fast and efficient imaging algorithms. A general framework has been set up for using non-convex sparsity by applying a first-order approximation. When using a proximal solver to estimate a solution of a sparsity-based optimization problem, sparse terms are always separated in subproblems that take the form of a proximal operator. Estimating the proximal operator associated to a non-convex term is thus the key component to use efficient solvers for non-convex sparse optimization. Using this strategy, only the shrinkage operator changes and thus the solver has the same complexity for both the convex and non-convex cases. While few previous works have also proposed to use non-convex sparsity, their choice of the sparse penalty is rather limited to functions like the $l_p$ pseudo-norm for certain values of $p\ge 0.5$ or the Minimax Concave (MC) penalty because they admit an analytical solution. Using a first-order approximation only requires calculating the (super)gradient of the function, which makes it possible to use a wide range of penalties for sparse regularization. This is important in various applications where we need a flexible shrinkage function such as in edge-aware processing. Apart from non-convexity, using a first-order approximation makes it easier to verify the optimality condition of proximal operator-based solvers via fixed-point interpretation. Another problem that arises in various imaging applications but has attracted less works is the problem of multi-sparsity, when the minimization problem includes various sparse terms that can be non-convex. This is typically the case when looking for a sparse solution in a certain domain while rejecting outliers in the data-fitting term. By using one intermediate variable per sparse term, we show that proximal-based solvers can be efficient. We give a detailed study of the Alternating Direction Method of Multipliers (ADMM) solver for multi-sparsity and study its properties. The following subjects are addressed and receive new solutions:

1. Edge aware smoothing: given an input image $g$, one seeks a smooth image $u$ "close" to $g$ by minimizing:

   where $\psi$ is a sparcity-inducing non-convex function and $\lambda$ a positive parameter. Splitting and alternate minimization lead to the sub-problems:

   We solve sub-problem $\text{(sp2)}$ through deconvolution and efficient estimation via separable filters and warm-start initialization for fast GPU implementation, and sub-problem $\text{(sp1)}$ through non-convex proximal form.

2. Structure-texture separation: design of an efficient algorithm using non-convex terms on both the data-fitting and the prior. The resulting problem is solved via a combination of Half-Quadratic (HQ) and Maximization-Minimization (MM) methods. We extract challenging texture layers outperforming existing techniques while maintaining a low computational cost. Using spectral sparsity in the framework of low-rank estimation, we propose to use robust Principal Component Analysis (RPCA) to perform robust separation on multi-channel images such as glare and artifacts removal of flash/no-flash photographs. As in this case, the matrix to decompose has much less columns than lines, we propose to use a QR decomposition trick instead of a direct singular value decomposition (SVD) which makes the decomposition faster.
3. Robust integration: in many applications, we need to reconstruct an image from corrupted gradient fields. The corruption can take the form of outliers only when the vector field is the result of transformed gradient fields (low-level vision), or mixed outliers and noise when the field is estimated from corrupted measurements (surface reconstruction, gradient camera, Magnetic Resonance Imaging (MRI) compressed sensing, etc.). We use non-convexity and multi-sparsity to build efficient integrability enforcement algorithms. We present two algorithms : 1) a local algorithm that uses sparsity in the gradient field as a prior together with a sparse data-fitting term, 2) a non-local algorithm that uses sparsity in the spectral domain of non-local patches as a prior together with a sparse data-fitting term. Both methods make use of a multi-sparse version of the Half-Quadratic solver. The proposed methods were the first in the literature to propose a sparse regularization to improve integration. Results produced with these methods significantly outperform previous works that use no regularization or simple $l_1$ minimization. Exact or near-exact recovery of surfaces is possible with the proposed methods from highly corrupted gradient fields with outliers.
4. Learning image denoising: deep convolutional networks that consist in extracting features by repeated convolutions with high-pass filters and pooling/downsampling operators have shown to give near-human recognition rates. Training the filters of a multi-layer network is costly and requires powerful machines. However, visualizing the first layers of the filters shows that they resemble wavelet filters, leading to sparse representations in each layer. We propose to use the concept of scale invariance of multifractals to extract invariant features on each sparse representation. We build a bi-Lipschitz invariant descriptor based on the distribution of the singularities of the sparsified images in each layer. Combining the descriptors of each layer in one feature vector leads to a compact representation of a texture image that is invariant to various transformations. Using this descriptor that is efficient to calculate with learning techniques such as classifiers combination and artificially adding training data, we build a powerful texture recognition system that outperforms previous works on 3 challenging datasets. In fact, this system leads to quite close recognition rates compared to latest advanced deep nets while not requiring any filters training.

5.1 Participation in the Covid-19 Inria mission

GeoStat is participating in the Covid-19 Inria mission: : Vocal biomarkers of respiratory diseases.

6.1 Price

A. El Aouni, PhD student in Geostat receives the "Prix de thèse Systèmes complexes" CNRS ISC-PIF 2020 for his PhD "Lagrangian coherent structures and physical processes of coastal upwelling" defended September 24, 2019.

7.1 New software

8.1 CONCAUST Exploratory Action

Participants: N. Brodu, James P. Crutchfield, L. Bourel, P. Rau, A. Rupe, Y. Li.

Collaboration has also started on the application of this method for:

• The analysis of El Niño patterns, with Luc Bourrel and Pedro Rau. An article was already published with Luc Bourrel and collaborators in a another context (satellite image processing). The logical step was to try the new method on related time series data. Indeed, the method is able to both predict time series, but also to extract relevant parameters that give a physical interpretation to the model. In the case of the El Niño patterns, our goal is to search for relevant data and correct time scales, holding sufficient information so that the causal states can correctly identify and predict the Niño patterns. This would give us an intuition on what are the most relevant factors for these catastrophic natural phenomena, together with a model for their evolution. In particular, the model is already able to extract the strong El Niño patterns of 1982, 1997 and 2016 from data, as seen in Fig. 2.

  

• The analysis of ${\text{CO}}_2$ and latent energy exchanges in ecosystems. This collaboration started on the initiative of Adam Rupe, a colleague already involved in the causal states theory, together with Yao Liu, an ecobiology expert. We are answering a call from the Ecoforecast initiative https://ecoforecast.org, which runs a series of challenges for the prediction and more importantly the analysis and understanding of ecosystems. Our model, by its ability to reconstruct internal states of a physical process from data, is ideally suited for this kind of exploration. Though there is no guarantee we do any better than black box prediction models, this is not our main objective. Our main objective is to better understand how the various biological and physical variables (weather, soil nature, plant types...) interact and extract some of these relations from data. Comparing the output of the CONCAUST theoretical model, a reconstructed model for the physical processes and their interactions, to existing ecobiological models is already instructive. This is a multi-year project and we have just started the collaboration (december 2020) with already interesting results. In particular, we can already reconstruct the system dynamical attractor (Fig. 3), with seasonal cycles, and make realistically looking predictions (Fig. 4). Work is going on for assimilating weather data and improve these predictions, together with making ensemble forecasts.

  

  

  

8.2 Participation in the Covid-19 Inria mission: Vocal biomarkers of respiratory diseases

Participants: K. Daoudi, B. Das, T. Similowski.

In this context, a voice data collection platform, https://dream.inria.fr/vocapnee/, was developed by Inria's SED. This platform is used to collect data from healthy controls. It will then be migrated to the AP-HP servers to collect patient data.

8.3 Turbulent dynamics in the interstellar medium

Participants: H. Yahia, N. Schneider, S. Bontemps, L. Bonne, et al.

Dense molecular filaments are ubiquituous in the interstellar medium, yet their internal physical conditions and the role of gravity, turbulence, the magnetic field, radiation and the ambient cloud during their evolution remain debated. We study the kinematics and physical conditions in the Musca filament, the ambient cloud and the Chamaeleon-Musca complex, to constrain the physics of filament formation.

Publication: Astronomy & Astrophysics, HAL, plus another paper accepted in 2021 in Astronomy & Astrophysics,

8.4 Permuted Spectral and Permuted Spectral-Spatial CNN Models

Participants: G. Phartiyal, N. Brodu, D. Singh, H. Yahia, K. Daoudi.

Publication: International Journal of Remote Sensing, HAL

8.5 Robust Detection of the North-West African Upwelling From SST Images

Participants: A. El Aouni, K. Daoudi, K. Minaoui, H. Yahia.

Publication: IEEE Geoscience and Remote Sensing Letters, HAL

8.6 Defining Lagrangian coherent vortices from their trajectories

Participants: A. El Aouni, K. Daoudi, H. Yahia, H. Kumar Maji, K. Minaoui.

Publication: Physics of Fluids, American Institute of Physics, HAL

8.7 Transparent experiments: releasing data from mechanical tests on three dimensional hydrogel sphere packings

Participants: J. Bares, N. Brodu, H. Zheng, J. A. Dijksman.

Publication: Granular Matter, HAL

8.8 Structure-preserving denoising of SAR images

Participants: S. Kumar Maji, R. Thakur, H. Yahia.

Publication: IEEE Geoscience and Remote Sensing Letters, HAL

8.9 LEFE CNRS IMECO Project: Multiscale intermittence in oceanic fields

Participants: F. Schmitt, H. Yahia, V. Garçon, J. Sudre, B. Dewitte, G. Charria.

The Bay of Biscay and the English Channel, in the Northeastern Atlantic, are considered as a natural laboratory to explore the coastal dynamics at different spatial and temporal scales. In those regions, the coastal circulation is constrained by a complex topography (e.g. varying width of the continental shelf, canyons), river runoffs, strong tides and a seasonally contrasted wind-driven circulation. Based on different numerical model experiments (from 400m to 4km spatial resolution, from 40 to 100 sigma vertical layers using 3D primitive equation ocean models), different features of the Bay of Biscay and English Channel circulation are assessed and explored. Both spatial (submesoscale and mesoscale) and temporal (from hourly to monthly) scales are considered.

Publications: EGU General Assembly 2020, HAL and HAL

8.10 InnovationLab with I2S, sparse signals & optimisation

Participants: A. Zebadua, A. Rashidi, H. Yahia, A. Cherif, J. L. Vallancogne, A. Cailly.

In 2020, one main task was to develop image processing algorithms for 3D stereo imaging. Such algorithms improve the quality of noisy and distorted disparity maps that can be used to reconstruct 3D objects. A. Zebadua was responsible for assisting the two research engineers who implemented the algorithms in C++.

A. Zebadua is also responsible for the co-supervision of the Ph.D. of Arash Rashidi worked with him in the development of fast image deconvolution algorithms.

9.1 Bilateral contracts with industry

InnovationLab with I2S company, starting scheduled after 1st 2019 COPIL in January 2019. This InnovationLab is extended one year starting February 2021.

10.1 International initiatives

10.2 European initiatives

10.3 National initiatives

• CONCAUST Exploratory Action The exploratory action « TRACME » was renamed « CONCAUST » and is going on with good progress. Collaboration with James P. Crutchfield and its laboratory has lead to a first draft of article, “Discovering Causal Structure with Reproducing-Kernel Hilbert Space $\epsilon$-Machines”, available at https://arxiv.org/abs/2011.14821 . That article poses the main theoretical fundations for building a new class of models, able to reconstruct a measured process « causal states » from data.

• Participation in the Covid-19 Inria mission: Vocal biomarkers of respiratory diseases. The CovidVoice project evolved into the VocaPnée project in partnership with AP-HP and co-directed by K. Daoudi and Thomas Similowski, responsible for the pulmonology and resuscitation service at La Pitié-Salpêtrière hospital and UMR-S 1158. The objective of the VocaPnée project is to bring together all the skills available at Inria to develop and validate a vocal biomarker for the remote monitoring of patients at home suffering from an acute respiratory disease (such as Covid) or chronic (such as asthma) . This biomarker will then be integrated into a telemedicine platform, ORTIF or COVIDOM for Covid, to assist the doctors in assessing the patient's respiratory status. VocaPnée is divided into 2 longitudinal pilot clinical studies, a hospital study and another in tele-medicine.

  In this context, a voice data collection platform, https://dream.inria.fr/vocapnee/, was developed by Inria's SED. This platform is used to collect data from healthy controls. It will then be migrated to the AP-HP servers to collect patient data.

• ANR project Voice4PD-MSA, led by K. Daoudi, which targets the differential diagnosis between Parkinson's disease and Multiple System Atrophy. The total amount of the grant is 468555 euros, from which GeoStat has 203078 euros. The duration of the project is 42 months. Partners: CHU Bordeaux (Bordeaux), CHU Toulouse, IRIT, IMT (Toulouse).
• GEOSTAT is a member of ISIS (Information, Image & Vision), AMF (Multifractal Analysis) GDRs.
• GEOSTAT is participating in the CNRS IMECO project Intermittence multi-échelles de champs océaniques : analyse comparative d’images satellitaires et de sorties de modèles numériques. CNRS call AO INSU 2018. PI: F. Schmitt, DR CNRS, UMR LOG 8187. Duration: 2 years.

11.1 Reviewer

H. Yahia is reviewer for the IGARSS conference.

11.2 Invited talks

• H. Yahia gave an invited talk "Description of turbulent dynamics in the interstellar medium: multifractal/microcanonical analysis " for the workshop sftools-bigdata : The close structural connection between gas and young stars, focus on current and new tools of data analysis 27-30 Oct 2020 Grenoble. https://hal.inria.fr/hal-03002810.
• N. Brodu gave a presentation of the concaust method at the “Inference for Dynamical Systems” seminar series, http://csc.ucdavis.edu/Inference_for_Dynamical_Systems.html
• K. Daoudi gave a talk at Vivhealthtech’2020 (https://vivhealthtech.events/FR/), which took place in Bordeaux in November 2020, entitled “Peut-on entendre Parkinson’s ? quid du COVID ?”.

11.3 Supervision

A. Zebadua and H. Yahia are co-supervising A. Rashidi's Phd thesis.

12.1 Major publications

• 1 articleGuillaumeG. Attuel, EvgeniyaE. Gerasimova-Chechkina, FrançoiseF. Argoul, HusseinH. Yahia and AlainA. Arnéodo. Multifractal Desynchronization of the Cardiac Excitable Cell Network During Atrial Fibrillation. II. ModelingFrontiers in Physiology10April 2019, 480 (1-18)
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• 2 articleGuillaumeG. Attuel, Evgeniya GE. Gerasimova-Chechkina, F. Argoul, HusseinH. Yahia and AlainA. Arnéodo. Multifractal desynchronization of the cardiac excitable cell network during atrial fibrillation. I. Multifractal analysis of clinical dataFrontiers in Physiology8March 2018, 1-30
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• 3 articleHichamH. Badri and HusseinH. Yahia. A Non-Local Low-Rank Approach to Enforce IntegrabilityIEEE Transactions on Image ProcessingJune 2016, 10
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• 4 inproceedings HichamH. Badri, HusseinH. Yahia and K. Daoudi. Fast and Accurate Texture Recognition with Multilayer Convolution and Multifractal Analysis European Conference on Computer Vision ECCV 2014 Zürich, Switzerland September 2014
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• 5 articleIsmaelI. Hernandez-Carrasco, VéroniqueV. Garçon, JoelJ. Sudre, ChristophC. Garbe and HusseinH. Yahia. Increasing the Resolution of Ocean pCO₂ Maps in the South Eastern Atlantic Ocean Merging Multifractal Satellite-Derived Ocean VariablesIEEE Transactions on Geoscience and Remote SensingJune 2018, 1 - 15
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• 6 articleII. Hernández-Carrasco, JJ. Sudre, VV. Garçon, HH. Yahia, CC. Garbe, AA. Paulmier, BB. Dewitte, SS. Illig, II. Dadou, MM. González-Dávila and J.M.J. Santana Casiano. Reconstruction of super-resolution ocean pCO 2 and air-sea fluxes of CO 2 from satellite imagery in the Southeastern AtlanticBiogeosciencesSeptember 2015, 20
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• 7 article VahidV. Khanagha, KhalidK. Daoudi and HusseinH. Yahia. Detection of Glottal Closure Instants based on the Microcanonical Multiscale Formalism IEEE Transactions on Audio, Speech and Language Processing December 2014
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• 8 article VahidV. Khanagha, KhalidK. Daoudi and HusseinH. Yahia. Efficient and robust detection of Glottal Closure Instants using Most Singular Manifold of speech signals IEEE Transactions on Acoustics Speech and Signal Processing forthcoming 2014
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• 9 articleSuman KumarS. Maji and HusseinH. Yahia. Edges, Transitions and CriticalityPattern RecognitionJanuary 2014, URL: http://hal.inria.fr/hal-00924137
• 10 articleSumanS. Maji, HusseinH. Yahia and ThierryT. Fusco. A Multifractal-based Wavefront Phase Estimation Technique for Ground-based Astronomical ObservationsIEEE Transactions on Geoscience and Remote SensingNovember 2015, 11
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• 11 articleOriolO. Pont, AntonioA. Turiel and HusseinH. Yahia. Singularity analysis in digital signals through the evaluation of their Unpredictable Point ManifoldInternational Journal of Computer Mathematics2012, URL: http://hal.inria.fr/hal-00688715
• 12 articleJoelJ. Sudre, HusseinH. Yahia, OriolO. Pont and VéroniqueV. Garçon. Ocean Turbulent Dynamics at Superresolution From Optimal Multiresolution Analysis and Multiplicative CascadeIEEE Transactions on Geoscience and Remote Sensing5311June 2015, 12
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• 13 articleAntonioA. Turiel, HusseinH. Yahia and ConradC. Perez-Vicente. Microcanonical multifractal formalism: a geometrical approach to multifractal systems. Part I: singularity analysisJournal of Physics A: Math. Theor412008, URL: http://dx.doi.org/10.1088/1751-8113/41/1/015501
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• 14 articleHusseinH. Yahia, JoëlJ. Sudre, ClaireC. Pottier and VéroniqueV. Garçon. Motion analysis in oceanographic satellite images using multiscale methods and the energy cascadePattern Recognition43102010, 3591-3604URL: http://dx.doi.org/10.1016/j.patcog.2010.04.011
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12.2 Publications of the year

12.3 Cited publications

• 25 book AlainA. Arnéodo, F. Argoul, E. Bacry, J. Elezgaray and J. F.J. Muzy. Ondelettes, multifractales et turbulence Paris, France Diderot Editeur 1995
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• 26 book N. Boccara. Modeling Complex Systems New-York Dordrecht Heidelberg London Springer 2010
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• 27 articleG. Boffetta, M. Cencini, M. Falcioni and A. Vulpiani. Predictability: a way to characterize complexityPhysics Report356arXiv:nlin/0101029v12002, 367--474URL: http://dx.doi.org/10.1016/S0370-1573(01)00025-4
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• 28 articleNicolasN. Brodu. Reconstruction of epsilon-machines in predictive frameworks and decisional statesAdvances in Complex Systems14052011, 761-794URL: https://doi.org/10.1142/S0219525911003347
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• 29 article NicolasN. Brodu and HusseinH. Yahia. Stochastic Texture Difference for Scale-Dependent Data Analysis arXiv preprint arXiv:1503.03278 2015
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• 30 book PatriziaP. Castiglione, MassimoM. Falcioni, AnnickA. Lesne and AngeloA. Vulpiani. Chaos and coarse graining in statistical mechanics Cambridge University Press Cambridge 2008
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• 31 articleMadalenaM. Costa, Ary LA. Goldberger and C-KC.-K. Peng. Multiscale entropy analysis of complex physiologic time seriesPhysical review letters8962002, 068102
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• 32 articleJames PJ. Crutchfield. Between order and chaosNature Physics812012, 17--24
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• 33 articleJames PJ. Crutchfield and KarlK. Young. Inferring statistical complexityPhysical Review Letters6321989, 105
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• 34 articleGianmariaG. Falasco, GuglielmoG. Saggiorato and AngeloA. Vulpiani. About the role of chaos and coarse graining in statistical mechanicsPhysica A: Statistical Mechanics and its Applications4182015, 94--104
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• 35 articleDavid PD. Feldman and James PJ. Crutchfield. Measures of statistical complexity: Why?Physics Letters A2384-51998, 244--252
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• 36 book PatrickP. Flandrin. Time-frequency/time-scale analysis 10 Academic press 1998
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• 37 inproceedingsGeorgG. Goerg and CosmaC. Shalizi. Mixed LICORS: A nonparametric algorithm for predictive state reconstructionArtificial Intelligence and Statistics2013, 289--297
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• 38 book Robert MR. Gray. Entropy and information theory Springer Science & Business Media 2011
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• 39 articleHeikeH. Janicke, AlexanderA. Wiebel, GerikG. Scheuermann and WolfgangW. Kollmann. Multifield visualization using local statistical complexityIEEE Transactions on Visualization and Computer Graphics1362007, 1384--1391
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• 40 book L. P.L. Kadanoff. Statistical physics, statics, dynamics & renormalization World Scie,tific 2000
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• 41 articleMTM. Martin, AA. Plastino and OAO. Rosso. Generalized statistical complexity measures: Geometrical and analytical propertiesPhysica A: Statistical Mechanics and its Applications36922006, 439--462
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• 42 bookJ.P.J. Nadal and P. Eds.P. Grassberger. From Statistical Physics to Statistical Inference and BackNew York Heidelberg BerlinSpringer1994, URL: http://www.springer.com/physics/complexity/book/978-0-7923-2775-2
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• 43 inproceedingsCosma RohillaC. Shalizi and Kristina LisaK. Shalizi. Blind construction of optimal nonlinear recursive predictors for discrete sequencesProceedings of the 20th conference on Uncertainty in artificial intelligenceAUAI Press2004, 504--511
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• 44 articleCosma RohillaC. Shalizi, Kristina LisaK. Shalizi and RobertR. Haslinger. Quantifying Self-Organization with Optimal PredictorsPhys. Rev. Lett.9311Sep 2004, 118701URL: https://link.aps.org/doi/10.1103/PhysRevLett.93.118701
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• 45 book J. L.J. Starck, F. Murthag and J. Fadili. Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity ISBN:9780521119139 Cambridge University Press 2010
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• 46 articleF. Takens. Detecting Strange Attractors in TurbulenceNon Linear Optimization8981981, 366--381URL: http://www.springerlink.com/content/b254x77553874745/
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• 47 article V. Venugopal and et al.. Revisting multifractality of high resolution temporal rainfall using a wavelet-based formalism Water Resources Research 42 2006
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