Signals studied in Geostat belong to two broad classes:

• Acquisitions in astronomy and earth observation.
• Physiological time series.

3.1 General methodology

Geostat is a research project which investigates the analysis of some classes of natural complex signals (physiological time series, turbulent universe and earth observation data sets) by determining, in acquired signals, the properties that are predicted by commonly admitted or new physical models best fitting the phenomenon. The team makes fundamental and applied research in the analysis of complex natural signals using paradigms and methods from statistical physics such as: scale invariance, predictability, universality classes. We study the parameters related to common statistical organization in different complex signals and systems, we derive new types of sparse and compact representations, and machine learning approaches. We are also developing tools for the analysis of complex signals that better match the statistical and geometrical organisation inside these data: as a typical example, we cite the evaluation of cascading properties of physical variables inside complex signals.

When statistical properties discovered in the signals do not match closely enough those predicted by accepted physical models, we question the validity of existing models or propose, whenever possible, modifications or extensions of existing models. Also, a direction of research, based on the Concaust exploratory action and the newly accepted (in February 2021) associated team Comcausa proposed by N. Brodu with USA / UC Davis, Complexity Sciences Center, Physics Department is developped in the team.

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.

An important aspect of the methodological approach is that we don't rely on a predetermined "universal" signal processing model to analyze natural complex signals. Instead, we take into consideration existing approaches in nonlinear signal processing (wavelets, multifractal analysis tools such as log-cumulants or micro-canonical multifractal formalism, time frequency analysis etc.) which are used to determine the micro structures or other micro features inside the acquired signals. Then, statistical analysis of these micro data are determined and compared to expected behavior from theoretical physical models used to describe the phenomenon from which the data is acquired. From there different possibilities can be contemplated:

• -
  The statistics match behaviour predicted by the model: complexity parameters predicted by the model are extracted from signals to analyze the dynamics of underlying phenomena. Examples: analysis of turbulent data sets in Oceanography and Astronomy.
• -
  The signals displays statistics that cannot be attainable by the common lore of accepted models: how to extend or modify the models according to the behaviour of observed signals? Example: audio speech signals.

We focus on the following theoretical developments:

1. Signal processing using methods from complex systems and statistical physics,
2. Sparse and compact representations, signal reconstruction, machine learning,
3. Predictability in complex systems,
4. Analysis, classification, detection in complex signals.

The team conducts research in nonlinear signal processing on these considerations: we consider the signals as the realizations of complex extended dynamical systems. The driving approach is to describe the relations between complexity (or information content) and the geometric organization of information in a signal. For instance, for signals which are acquisitions of turbulent fluids, the organization of information may be related to the effective presence of a multiscale hierarchy of coherent structures, of multifractal nature, which is strongly related to intermittency and multiplicative cascade phenomena ; the determination of this geometric organization unlocks key nonlinear parameters and features associated to these signals; it helps understand their dynamical properties and their analysis. We use this approach to derive novel solution methods for super-resolution and data fusion in Universe Sciences acquisitions. Specific advances are obtained in using this type of statistical/geometric approach to get validated dynamical information of signals acquired in Universe Sciences, e.g. Oceanography or Astronomy. The approach encompasses nonlinear signal processing and the study of emergence in complex systems, with a strong emphasis on geometric approaches to complexity. Consequently, research is oriented towards the determination, in real signals, of quantities or phenomena, usually unattainable through linear methods, that are known to play an important role both in the evolution of dynamical systems whose acquisitions are the signals under study, and in the compact representations of the signals themselves.

Signals under study belong to two broad classes:

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

3.2 Turbulence in insterstellar clouds and Earth observation data

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 intermittent46. 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 43 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 20, 40. Some quantities related to nonlinearity, such as Lyapunov exponents, Kolmogorov-Sinai entropy etc. can be computed at least in the phase space 21. 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 44 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 19. 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 35.

We show in figure 1 the result of the computation of singularity exponents on an Herschel astronomical observation map (Aquila galactic cloud, sub-region) which has been edge-aware filtered using sparse $l^2$-$l^p$ filtering to eliminate the cosmic infrared background (or CIB), a type of noise that can modify the singularity spectrum of a signal.

3.3 Data analysis, causal modeling, application to earth sciences

Generally speaking, we are interested in developing new methods for inferring models of physical systems from data. The key questions are: What are the important objects of study at each description level? What are the patterns of their interactions? How to detect them in the first place? How to describe them using relevant variables? How to recover and formalize their dynamics, with analytical formula or via a computer program? Powerful mathematical tools and conceptual frameworks have been developed over years of research on complex systems and nonlinear dynamics  26, 32 ; yet the arousal of big data and regain in machine learning popularity have recently stimulated this domain of research  37, 38, 23. Our approach is to focus on how information is produced (emergence of patterns, of large-scale structures) and on how that information is maintained and transformed at different scales  25. We operate on states of similar information content, in the same way that thermodynamics operate on states of similar energy levels. Our goal is to search for the analog of Hamiltonian dynamics, but that describes information transformations instead of energy transformations. This approach would be particularly useful for modeling steady-state systems, which operate far from thermodynamic equilibrium. In these, energy dissipation is a prerequisite for maintaining the observed patterns, 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 ordered structures. And, according to information theory, 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 (power spectrum 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  36, $\epsilon$-entropy  24). Multiple complexity measures can quantify the presence of structures in the signal (e.g. statistical complexity  27, MPR  39 and others  31). With these notions, it is already possible to discriminate between random fluctuations and hidden order, such as in chaotic systems  25, 39. The theory of how information and structures can be defined through scales is not complete yet, but the state of art is promising  30. 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 $\epsilon$-machines  27. 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  42. Recent extensions with advanced clustering techniques  22, 33, coupled with the physics of the studied system (e.g. fluid dynamics), have proved that $\epsilon$-machines are applicable to large systems, such as global wind patterns in the atmosphere  34. Current research in the team focuses on the use of reproducing kernels, coupled possibly with sparse operators, in order to design better algorithms for $\epsilon$-machines reconstruction.

3.4 Vocal biomarkers

Speech convey valuable information about the health (and emotional) state of the speaker. A disturbance in this state can affect some or all the speech production subsystems: respiratory, phonatory, articulatory, nasalic and prosodic. A vocal biomarker is thus a digital signature of a speech signal that is associated with a clinical finding/observation and can be used to assist in: diagnose a disease, monitor patients, assess the severity or stage of a disease, assess response to treatment. Vocal biomarkers could provide attractive solutions in (tele)medicine which are non- invasive, cost-effective and rapidly deployable on large scales. Consequently, during this century, there has been an ever increasing interest in the development of objective vocal biomarkers with a major peak since the Covid-19 pandemic  29, with the emergence of several start- ups in the area (www.sondehealth.com, www.evocalhealth.com,...). Traditionally, most of the research has been carried out on neurodegenerative diseases, particularly on dysarthria, a class of motor speech disorders 28. There is however now a growing contribution in mental, cognitive, respiratory, cardiovascular and other diseases. While there has been definitely a progress in understanding how some pathologies alter speech, the field is still in its early development. One reason is the domination of pure-IA research in this area, while the clinical involvement is crucial unlock the clinical, scientific and technological challenges. In GeoStat, the core strategy of research in this area is to conduct R&D with a close partnership with (top) clinician experts of the pathologies under study, in the form of clinical trials. Our main research has been on differential diagnosis of Parkinsonism. We have thus been conducting an ANR project, Voice4PD-MSA, with the neurology and ENT departments of the university hospitals of Bordeaux and Toulouse. We have been also closely collaborating in a clinical study with Czech partners in Charles university and Technical university of Prague. In these two partnerships, we address the difficult problem of early discrimination between Parkinson’s disease (PD) and atypical Parkinsonian disorders (APD) such as Progressive Supranuclear Palsy (PSP) and Multiple System Atrophy (MSA). Since the Covid-19 pandemic, we started 3 projects with different hospitals of Paris (AP-HP). The first one, VocaPnée, on the remote monitoring of patients with respiratory diseases. The second one, Respeak, on the dispatch assistance of emergency calls. The third (recent) one, AcroVox, on the diagnosis of a rare hormonal disease, acromegalia. All the projects with AP-HP are accompanied by the recently created Bernoulli lab (see). From the methodological perspective, our main goal is to develop a signal processing framework which can be more appropriate to handle the specificities of pathological voices than the classical framework. Indeed, most of the research in this area rely on methods and tools developed for healthy speech, mainly based on the linear and independent source-filter speech production model. In the presence of an impairment, many of the underlying assumptions and models can fail to capture the disease specific alteration(s). This makes it necessary to adapt existing techniques and/or to develop new ones in order to extract the useful features and cues and to achieve the classification or regression targets. Besides following this approach, our ambition is to provide a theoretical framework which can “unify” healthy and pathological speech analysis. We have been recently investigating that “Probabilistic time-frequency analysis (PTFA)” 45 under the framework of Gaussian processes 41 as a promising candidate to achieve this goal. This framework is appealing because it makes it easier and natural to provide adaptive time- frequency representations, control representation sparsity, propagate uncertainty, quantify noise, reveal non-linearity, sampling/synthesis (for data augmentation for instance). As an example, classical spectrograms, wavelets or (a class of) filter-banks become probabilistic inference in this framework. PTFA was introduced in 45 but did not attract a lot of attention from the community, mainly because of the significant computational complexity load of the approach. We are investigating low-rank covariance approximation techniques to overcome this issue. We underline that we chose not to follow (for the moment) the dominating deep learning flow (even in this area which is a small-data problem), because interpretability at the acoustico-phonetic and clinical level is crucial in our setting. We are also putting a significant effort on software development. There exists indeed no publicly available tool for the analysis of pathological speech. We have been thus developing a Python library, VocaPy, where we integrate confirmed, adapted and new algorithms, after solid validation on speech datasets altered by different pathologies. Such a software would be very beneficial to the community and would contribute considerably to the R&D progress in the field (as Praat does in healthy speech analysis).

3.5 InnovationLab, sparse and non-convex methods in image processing

This research topic involves Geostat team and is used to set up an InnovationLab with I2S company. In 2022, the theoretical efforts have been concentrated in super-resolution thematics (PhD of A. Rashidi, defended in March 2022) while setting up the InnovationLab resulted in a very successful INRIA transfer operation (link to INRIA article). The results obtained in the InnovationLab have been used in the research described in section 3.2. See also section 4.

5.1 Startup Bits2Beat

Startup co-founded by G. Attuel on predictive heart rate analysis. Bits2Beat aims to facilitate the early detection of some of the most common cardiovascular diseases, notably atrial fibrillation, using the research made by G. Attuel in Geostat. National INRIA article link.

5.2 Comcausa

N. Brodu set up the Comcausa associated team with the Complexity center at UC Davis and the Concaust exploratory action.

6.1 New software

6.2 New platforms

Participants: N. Brodu, K. Daoudi.

• Concaust
• Web site:
  https://team.inria.fr/comcausa/continuous-causal-states/.

  • Software Family:
    research
  • Audience:
    team
  • Evolution and maintenance:
    proto
  • Duration of the Development:
    2 years
  • Scientific description:
    This software implements the algorithm resulting from the Concaust Exploratory Action, published in  15. Despite considerable time being spent on its development, the code itself is not that large. Indeed, the difficulty lies in the theoretical and algorithmic work. Once we know what to compute and how the implementation follows, but there were many rounds of developement with different theoretical approaches. Some of these points are still not stabilized, which reflects in the API and the code performances. These are regularly tested and updated as the code is run against concrete data sets. For these reasons, the code is constantly evolving and is actively being developped within the team, but it not ready yet for diffusion to the community at large. The code is open source (MIT licence) and shared with close partners from the Comcausa Associate Team.
• VocaPy
  • Software family:
    vehicle
  • Audience:
    community
  • Evolution and maintenance:
    basic (still under development)
  • Duration of the Development:
    1 year (still 1 year left)
  • Scientific description:
    VocaPy is an interface and a Python library implementing pathological speech analysis algorithms and vocal biomarkers for one clinical applications at the moment, differential diagnosis of Parkinsonism, but it will evolve to include other clinical targets, particularly the monitoring of respiratory diseases. VocaPy works in synergy with the ADT VocaPnée-Infra dedicated to the development of an infrastructure to interact with protected health data.

7.1 Discovering Causal Structure with Reproducing-Kernel Hilbert Space $\epsilon$-Machines

Participants: N. Brodu, J. P. Crutchfield.

Publication: Chaos, an Interdisciplinary Journal of Nonlinear Science , HAL.

7.2 CONCAUST Exploratory Action

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

The article detailing the exploratory action core method “Discovering Causal Structure with Reproducing-Kernel Hilbert Space $\epsilon$-Machines”, has been accepted for publication in the Chaos journal. The remaining budget was reallocated into 2 years of post-doctorate positions: - 1 year for working on the core methodology - 1 year for researching the applicability of the method on real data, in particular the study of El Niño phenomena. Due to covid constraints, the postdoctorate candidate (Alexandra Jurgens) that was selected for the core methodology could not come to France in fall 2021. She may come again in fall 2022, if the situation allows, so the corresponding post-doc is reserved for her. The second post-doctorate offer on El Niño is currently opened for applications.

7.3 COMCAUSA Associated team

Participants: N. Brodu, J. P. Crutchfield, et al. (see Website).

7.4 Speech acoustic indices for differential diagnosis between Parkinson's disease, multiple system atrophy and progressive supranuclear palsy

Participants: K. Daoudi, B. Das, T. Tykalova, J. Klempir, J. Rusz.

Publication: HAL), Nature npj, parkinson's disease).

7.5 A comparative study on vowel articulation in Parkinson's disease and multiple system atrophy

Participants: K. Daoudi, B. Das, S. Milhé de Saint Victor, A. Foubert Samier, M. Fabbri, A. Pavy-Le Traon, O. Rascol, V. Woisard, W. G. Meissner.

Publication: HAL), Interspeech 2022).

7.6 Advanced super-resolution

Participants: A. Rashidi, H. Yahia, A. Cherif [I2S], J. L. Vallancogne [I2S], A. Cailly [I2S].

Publication: A. Rashidi PhD's thesis, HAL.

8.1 International initiatives

Associate Teams in the framework of an Inria International Lab or in the framework of an Inria International Program

8.2 International research visitors

Visits of international scientists:

• Sarah Marzen, assistant professor at Keck Science Department, Pitzer, Scripps, and Claremont McKenna Colleges, participant in Comcausa associated team, visited Geostat in December 2022 during one week.
• Alexandra Jürgens, Post-doctoral researcher in the domains of stochastic modeling, information theory, stochastic thermodynamics, and member of the Comcausa associated team, visited Geostat in April-May 2022. Duration: 2 weeks.

8.3 European initiatives

Other european programs/initiatives:

• GENESIS:
  blackGENESIS : (GENreration and Evolution of Structure in the ISm). Funding: 385728 euros.

  1. Deutsch-franzosische Projekte in den - Natur - Lebens - Ingenieurwissenschaften. Duration: 3 ans, exrtended in 2022.
  2. Geostat, Laboratoire d'Astrophysique de Bordeaux, Institut de Physique de l'Université de Cologne (KOSMA)
  3. Precise evaluation of the multiscale MHD (magneto hydrodynamic) properties of ISMs (interstellar molecular clouds) acquisitions of Herschel data and their correlations with star formation process.
  4. https://astro.uni-koeln.de/stutzki/research/genesis.

8.4 National initiatives

• PEPR:
  with AgroParisTech. Title: Modeling the global states and dynamics of ecosystems - Applications to carbon flux and stock in ecosystems modified by agricultural activities. This project is supporting research on causality presently in Geostat and in the post-Geostat being currently set up by N. Brodu. PIs: N. Brodu, E. Vaudour. Duration: 60 months. Funding: 1,5 M euros.

• CONCAUST Exploratory Action The exploratory action « TRACME » was renamed « CONCAUST » and is going on with good progress. Collaboration with J. P. Crutchfield and its laboratory has lead to a first article, “Discovering Causal Structure with Reproducing-Kernel Hilbert Space $\epsilon$-Machines”, available here. That article poses the main theoretical fundations for building a new class of models, able to reconstruct a measured process « causal states » from data.
• CovidVoice project: Inria Coind-19 mission. 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.
• Vocapy. The ADT (IA Plan) project VocaPy, led by K. Daoudi, started in November 2021 for a 2 years duration. The goal of VocaPy is to develop a Python library dedicated to pathological speech analysis and vocal biomarkers conception. In case of success, our R&D on vocal biomarkers would obviously have a non-negligible impact at the clinical, scientific, technological and socio-economical levels. VocaPy and VocaPnée-Infra will serve a kernel for the development of disease-specific IA solutions to achieve the clinical targets and for their technological transfer to the clinical (and/or future industrial) partners.
• 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. Initial duration of the project was 42 months, and has been extended until January 2023. 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.

9.1 Promoting scientific activities

9.2 Teaching - Supervision - Juries

10.1 Major publications

• 1 articleG.Guillaume Attuel, E.Evgeniya Gerasimova-Chechkina, F.Françoise Argoul, H.Hussein Yahia and A.Alain Arnéodo. Multifractal Desynchronization of the Cardiac Excitable Cell Network During Atrial Fibrillation. II. Modeling.Frontiers in Physiology10April 2019, 480 (1-18)
  HALDOI
• 2 articleG.Guillaume Attuel, E. G.Evgeniya G Gerasimova-Chechkina, F.F. Argoul, H.Hussein Yahia and A.Alain Arnéodo. Multifractal desynchronization of the cardiac excitable cell network during atrial fibrillation. I. Multifractal analysis of clinical data.Frontiers in Physiology8March 2018, 1-30
  HALDOI
• 3 articleH.Hicham Badri and H.Hussein Yahia. A Non-Local Low-Rank Approach to Enforce Integrability.IEEE Transactions on Image ProcessingJune 2016, 10
  HAL
• 4 inproceedingsH.Hicham Badri, H.Hussein Yahia and K.K. Daoudi. Fast and Accurate Texture Recognition with Multilayer Convolution and Multifractal Analysis.European Conference on Computer VisionECCV 2014Zürich, SwitzerlandSeptember 2014
  HAL
• 5 articleI.Ismael Hernandez-Carrasco, V.Véronique Garçon, J.Joel Sudre, C.Christoph Garbe and H.Hussein Yahia. Increasing the Resolution of Ocean pCO₂ Maps in the South Eastern Atlantic Ocean Merging Multifractal Satellite-Derived Ocean Variables.IEEE Transactions on Geoscience and Remote SensingJune 2018, 1 - 15
  HALDOI
• 6 articleI.I Hernández-Carrasco, J.J Sudre, V.V Garçon, H.H Yahia, C.C Garbe, A.A Paulmier, B.B Dewitte, S.S Illig, I.I Dadou, M.M González-Dávila and J.J.M. Santana Casiano. Reconstruction of super-resolution ocean pCO 2 and air-sea fluxes of CO 2 from satellite imagery in the Southeastern Atlantic.BiogeosciencesSeptember 2015, 20
  HAL
• 7 articleV.Vahid Khanagha, K.Khalid Daoudi and H.Hussein Yahia. Detection of Glottal Closure Instants based on the Microcanonical Multiscale Formalism.IEEE Transactions on Audio, Speech and Language ProcessingDecember 2014
  HAL
• 8 articleV.Vahid Khanagha, K.Khalid Daoudi and H.Hussein Yahia. Efficient and robust detection of Glottal Closure Instants using Most Singular Manifold of speech signals.IEEE Transactions on Acoustics Speech and Signal Processingforthcoming2014
  HAL
• 9 articleS. K.Suman Kumar Maji and H.Hussein Yahia. Edges, Transitions and Criticality.Pattern RecognitionJanuary 2014, URL: http://hal.inria.fr/hal-00924137
• 10 articleS.Suman Maji, H.Hussein Yahia and T.Thierry Fusco. A Multifractal-based Wavefront Phase Estimation Technique for Ground-based Astronomical Observations.IEEE Transactions on Geoscience and Remote SensingNovember 2015, 11
  HALDOI
• 11 articleO.Oriol Pont, A.Antonio Turiel and H.Hussein Yahia. Singularity analysis in digital signals through the evaluation of their Unpredictable Point Manifold.International Journal of Computer Mathematics2012, URL: http://hal.inria.fr/hal-00688715
• 12 articleJ.Joel Sudre, H.Hussein Yahia, O.Oriol Pont and V.Véronique Garçon. Ocean Turbulent Dynamics at Superresolution From Optimal Multiresolution Analysis and Multiplicative Cascade.IEEE Transactions on Geoscience and Remote Sensing5311June 2015, 12
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• 13 articleA.Antonio Turiel, H.Hussein Yahia and C.Conrad Perez-Vicente. Microcanonical multifractal formalism: a geometrical approach to multifractal systems. Part I: singularity analysis.Journal of Physics A: Math. Theor412008, URL: http://dx.doi.org/10.1088/1751-8113/41/1/015501
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• 14 articleH.Hussein Yahia, J.Joël Sudre, C.Claire Pottier and V.Véronique Garçon. Motion analysis in oceanographic satellite images using multiscale methods and the energy cascade.Pattern Recognition43102010, 3591-3604URL: http://dx.doi.org/10.1016/j.patcog.2010.04.011
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10.2 Publications of the year

10.3 Cited publications

• 19 bookA.Alain Arnéodo, F.F. Argoul, E.E. Bacry, J.J. Elezgaray and J. F.J. F. Muzy. Ondelettes, multifractales et turbulence.Paris, FranceDiderot Editeur1995
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• 20 bookN.N. Boccara. Modeling Complex Systems.New-York Dordrecht Heidelberg LondonSpringer2010
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• 21 articleG.G. Boffetta, M.M. Cencini, M.M. Falcioni and A.A. Vulpiani. Predictability: a way to characterize complexity.Physics Report356arXiv:nlin/0101029v12002, 367--474URL: http://dx.doi.org/10.1016/S0370-1573(01)00025-4
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• 22 articleN.Nicolas Brodu. RECONSTRUCTION OF EPSILON-MACHINES IN PREDICTIVE FRAMEWORKS AND DECISIONAL STATES.Advances in Complex Systems14052011, 761-794URL: https://doi.org/10.1142/S0219525911003347
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• 23 articleS. L.Steven L. Brunton, M.Marko Budišić, E.Eurika Kaiser and J. N.J. Nathan Kutz. Modern Koopman Theory for Dynamical Systems.SIAM Review6422022, 229-340URL: https://doi.org/10.1137/21M1401243
  DOIback to text
• 24 bookP.Patrizia Castiglione, M.Massimo Falcioni, A.Annick Lesne and A.Angelo Vulpiani. Chaos and Coarse Graining in Statistical Mechanics.Cambridge University Press2008
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• 28 bookJ.J. Duffy. Motor Speech Disorders Substrates, Differential Diagnosis, and Management.Elsevier2013
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• 33 articleG. M.Georg M. Goerg and C. R.Cosma Rohilla Shalizi. Mixed LICORS: A Nonparametric Algorithm for Predictive State Reconstruction.2012, URL: https://arxiv.org/abs/1211.3760
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• 35 bookL. P.L. P. Kadanoff. Statistical physics, statics, dynamics & renormalization.World Scie,tific2000
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• 41 bookC. E.Carl Edward Rasmussen and C. K.Christopher K. I. Williams. Gaussian Processes for Machine Learning.The MIT Press11 2005, URL: https://doi.org/10.7551/mitpress/3206.001.0001
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• 43 bookJ. L.J. L. Starck, F.F. Murthag and J.J. Fadili. Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity.ISBN:9780521119139Cambridge University Press2010
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