Quantifying and containing the curse of high resolution coronal imaging

Future missions such as Solar Orbiter (SO), InterHelioprobe, or Solar Probe aim at approaching the Sun closer than ever before, with on board some high resolution imagers (HRI) having a subsecond cadence and a pixel area of about $(80km)^2$ at the Sun during perihelion. In order to guarantee their scientific success, it is necessary to evaluate if the photon counts available at these resolution and cadence will provide a sufficient signal-to-noise ratio (SNR). We perform a first step in this direction by analyzing and characterizing the spatial intermittency of Quiet Sun images thanks to a multifractal analysis. We identify the parameters that specify the scale-invariance behavior. This identification allows next to select a family of multifractal processes, namely the Compound Poisson Cascades, that can synthesize artificial images having some of the scale-invariance properties observed on the recorded images. The prevalence of self-similarity in Quiet Sun coronal images makes it relevant to study the ratio between the SNR present at SoHO/EIT images and in coarsened images. SoHO/EIT images thus play the role of 'high resolution' images, whereas the 'low-resolution' coarsened images are rebinned so as to simulate a smaller angular resolution and/or a larger distance to the Sun. For a fixed difference in angular resolution and in Spacecraft-Sun distance, we determine the proportion of pixels having a SNR preserved at high resolution given a particular increase in effective area. If scale-invariance continues to prevail at smaller scales, the conclusion reached with SoHO/EIT images can be transposed to the situation where the resolution is increased from SoHO/EIT to SO/HRI resolution at perihelion.Comment: 25 pages, 1 table, 7 figure

Comprehensive Multifractal Analysis of Turbulent Velocity Using the Wavelet Leaders

The multifractal framework relates the scaling properties of turbulence to its local regularity properties through a statistical description as a collection of local singularities. The multifractal properties are moreover linked to the multiplicative cascade process that creates the peculiar properties of turbulence such as intermittency. A comprehensive estimation of the multifractal properties of turbulence from data analysis, using a tool valid for all kind of singularities (including oscillating singularities) and mathematically well-founded, is thus of first importance in order to extract a reliable information on the underlying physical processes. The wavelet leaders yield a new multifractal formalism which meets all these requests. This paper aims at describing it and at applying it to experimental turbulent velocity data. After a detailed discussion of the practical use of the wavelet leader based multifractal formalism, the following questions are carefully investigated: (1) What is the dependence of multifractal properties on the Reynolds number? (2) Are oscillating singularities present in turbulent velocity data? (3) Which multifractal model does correctly account for the observed multifractal properties? Results from several data set analysis are used to discuss the dependence of the computed multifractal properties on the Reynolds number but also to assess their common or universal component. An exact though partial answer (no oscillating singularities are detected) to the issue of the presence of oscillating singularities is provided for the first time. Eventually an accurate parameterization with cumulants exponents up to order 4 confirms that the log-normal model (with $c_2 = -0.025\pm 0.002$) correctly accounts for the universal multifractal properties of turbulent velocity

Large deviations estimates for the multiscale analysis of heart rate variability

International audienceIn the realm of multiscale signal analysis, multifractal analysis provides with a natural and rich framework to measure the roughness of a time series. As such, it has drawn special attention of both mathematicians and practitioners, and led them to characterize relevant physiological factors impacting the heart rate variability. Notwithstanding these considerable progresses, multifractal analysis almost exclusively developed around the concept of Legendre singularity spectrum, for which efficient and elaborate estimators exist, but which are structurally blind to subtle features like non-concavity or, to a certain extent, non scaling of the distributions. Large deviations theory allows bypassing these limitations but it is only very recently that performing estimators were proposed to reliably compute the corresponding large deviations singularity spectrum. In this article, we illustrate the relevance of this approach, on both theoretical objects and on human heart rate signals from the Physionet public database. As conjectured, we verify that large deviations principles reveal significant information that otherwise remains hidden with classical approaches, and which can be reminiscent of some physiological characteristics. In particular we quantify the presence/absence of scale invariance of RR signals

Computer-aided detection and diagnosis of breast cancer in 2D and 3D medical imaging through multifractal analysis

This Thesis describes the research work performed in the scope of a doctoral research program and presents its conclusions and contributions. The research activities were carried on in the industry with Siemens S.A. Healthcare Sector, in integration with a research team. Siemens S.A. Healthcare Sector is one of the world biggest suppliers of products, services and complete solutions in the medical sector. The company offers a wide selection of diagnostic and therapeutic equipment and information systems. Siemens products for medical imaging and in vivo diagnostics include: ultrasound, computer tomography, mammography, digital breast tomosynthesis, magnetic resonance, equipment to angiography and coronary angiography, nuclear imaging, and many others. Siemens has a vast experience in Healthcare and at the beginning of this project it was strategically interested in solutions to improve the detection of Breast Cancer, to increase its competitiveness in the sector. The company owns several patents related with self-similarity analysis, which formed the background of this Thesis. Furthermore, Siemens intended to explore commercially the computer- aided automatic detection and diagnosis eld for portfolio integration. Therefore, with the high knowledge acquired by University of Beira Interior in this area together with this Thesis, will allow Siemens to apply the most recent scienti c progress in the detection of the breast cancer, and it is foreseeable that together we can develop a new technology with high potential. The project resulted in the submission of two invention disclosures for evaluation in Siemens A.G., two articles published in peer-reviewed journals indexed in ISI Science Citation Index, two other articles submitted in peer-reviewed journals, and several international conference papers. This work on computer-aided-diagnosis in breast led to innovative software and novel processes of research and development, for which the project received the Siemens Innovation Award in 2012. It was very rewarding to carry on such technological and innovative project in a socially sensitive area as Breast Cancer.No cancro da mama a deteção precoce e o diagnóstico correto são de extrema importância na prescrição terapêutica e caz e e ciente, que potencie o aumento da taxa de sobrevivência à doença. A teoria multifractal foi inicialmente introduzida no contexto da análise de sinal e a sua utilidade foi demonstrada na descrição de comportamentos siológicos de bio-sinais e até na deteção e predição de patologias. Nesta Tese, três métodos multifractais foram estendidos para imagens bi-dimensionais (2D) e comparados na deteção de microcalci cações em mamogramas. Um destes métodos foi também adaptado para a classi cação de massas da mama, em cortes transversais 2D obtidos por ressonância magnética (RM) de mama, em grupos de massas provavelmente benignas e com suspeição de malignidade. Um novo método de análise multifractal usando a lacunaridade tri-dimensional (3D) foi proposto para classi cação de massas da mama em imagens volumétricas 3D de RM de mama. A análise multifractal revelou diferenças na complexidade subjacente às localizações das microcalci cações em relação aos tecidos normais, permitindo uma boa exatidão da sua deteção em mamogramas. Adicionalmente, foram extraídas por análise multifractal características dos tecidos que permitiram identi car os casos tipicamente recomendados para biópsia em imagens 2D de RM de mama. A análise multifractal 3D foi e caz na classi cação de lesões mamárias benignas e malignas em imagens 3D de RM de mama. Este método foi mais exato para esta classi cação do que o método 2D ou o método padrão de análise de contraste cinético tumoral. Em conclusão, a análise multifractal fornece informação útil para deteção auxiliada por computador em mamogra a e diagnóstico auxiliado por computador em imagens 2D e 3D de RM de mama, tendo o potencial de complementar a interpretação dos radiologistas

Investigation of neural activity in Schizophrenia during resting-state MEG : using non-linear dynamics and machine-learning to shed light on information disruption in the brain

Environ 25% de la population mondiale est atteinte de troubles psychiatriques qui sont typiquement associés à des problèmes comportementaux, fonctionnels et/ou cognitifs et dont les corrélats neurophysiologiques sont encore très mal compris. Non seulement ces dysfonctionnements réduisent la qualité de vie des individus touchés, mais ils peuvent aussi devenir un fardeau pour les proches et peser lourd dans l’économie d’une société. Cibler les mécanismes responsables du fonctionnement atypique du cerveau en identifiant des biomarqueurs plus robustes permettrait le développement de traitements plus efficaces. Ainsi, le premier objectif de cette thèse est de contribuer à une meilleure caractérisation des changements dynamiques cérébraux impliqués dans les troubles mentaux, plus précisément dans la schizophrénie et les troubles d’humeur. Pour ce faire, les premiers chapitres de cette thèse présentent, en intégral, deux revues de littératures systématiques que nous avons menées sur les altérations de connectivité cérébrale, au repos, chez les patients schizophrènes, dépressifs et bipolaires. Ces revues révèlent que, malgré des avancées scientifiques considérables dans l’étude de l’altération de la connectivité cérébrale fonctionnelle, la dimension temporelle des mécanismes cérébraux à l’origine de l’atteinte de l’intégration de l’information dans ces maladies, particulièrement de la schizophrénie, est encore mal comprise. Par conséquent, le deuxième objectif de cette thèse est de caractériser les changements cérébraux associés à la schizophrénie dans le domaine temporel. Nous présentons deux études dans lesquelles nous testons l’hypothèse que la « disconnectivité temporelle » serait un biomarqueur important en schizophrénie. Ces études explorent les déficits d’intégration temporelle en schizophrénie, en quantifiant les changements de la dynamique neuronale dite invariante d’échelle à partir des données magnétoencéphalographiques (MEG) enregistrés au repos chez des patients et des sujets contrôles. En particulier, nous utilisons (1) la LRTCs (long-range temporal correlation, ou corrélation temporelle à longue-distance) calculée à partir des oscillations neuronales et (2) des analyses multifractales pour caractériser des modifications de l’activité cérébrale arythmique. Par ailleurs, nous développons des modèles de classification (en apprentissage-machine supervisé) pour mieux cerner les attributs corticaux et sous-corticaux permettant une distinction robuste entre les patients et les sujets sains. Vu que ces études se basent sur des données MEG spontanées enregistrées au repos soit avec les yeux ouvert, ou les yeux fermées, nous nous sommes par la suite intéressés à la possibilité de trouver un marqueur qui combinerait ces enregistrements. La troisième étude originale explore donc l’utilité des modulations de l’amplitude spectrale entre yeux ouverts et fermées comme prédicteur de schizophrénie. Les résultats de ces études démontrent des changements cérébraux importants chez les patients schizophrènes au niveau de la dynamique d’invariance d’échelle. Elles suggèrent une dégradation du traitement temporel de l’information chez les patients, qui pourrait être liée à leurs symptômes cognitifs et comportementaux. L’approche multimodale de cette thèse, combinant la magétoencéphalographie, analyses non-linéaires et apprentissage machine, permet de mieux caractériser l’organisation spatio-temporelle du signal cérébrale au repos chez les patients atteints de schizophrénie et chez des individus sains. Les résultats fournissent de nouvelles preuves supportant l’hypothèse d’une « disconnectivité temporelle » en schizophrénie, et étendent les recherches antérieures, en explorant la contribution des structures cérébrales profondes et en employant des mesures non-linéaires avancées encore sous-exploitées dans ce domaine. L’ensemble des résultats de cette thèse apporte une contribution significative à la quête de nouveaux biomarqueurs de la schizophrénie et démontre l’importance d’élucider les altérations des propriétés temporelles de l’activité cérébrales intrinsèque en psychiatrie. Les études présentées offrent également un cadre méthodologique pouvant être étendu à d’autres psychopathologie, telles que la dépression.Psychiatric disorders affect nearly a quarter of the world’s population. These typically bring about debilitating behavioural, functional and/or cognitive problems, for which the underlying neural mechanisms are poorly understood. These symptoms can significantly reduce the quality of life of affected individuals, impact those close to them, and bring on an economic burden on society. Hence, targeting the baseline neurophysiology associated with psychopathologies, by identifying more robust biomarkers, would improve the development of effective treatments. The first goal of this thesis is thus to contribute to a better characterization of neural dynamic alterations in mental health illnesses, specifically in schizophrenia and mood disorders. Accordingly, the first chapter of this thesis presents two systematic literature reviews, which investigate the resting-state changes in brain connectivity in schizophrenia, depression and bipolar disorder patients. Great strides have been made in neuroimaging research in identifying alterations in functional connectivity. However, these two reviews reveal a gap in the knowledge about the temporal basis of the neural mechanisms involved in the disruption of information integration in these pathologies, particularly in schizophrenia. Therefore, the second goal of this thesis is to characterize the baseline temporal neural alterations of schizophrenia. We present two studies for which we hypothesize that the resting temporal dysconnectivity could serve as a key biomarker in schizophrenia. These studies explore temporal integration deficits in schizophrenia by quantifying neural alterations of scale-free dynamics using resting-state magnetoencephalography (MEG) data. Specifically, we use (1) long-range temporal correlation (LRTC) analysis on oscillatory activity and (2) multifractal analysis on arrhythmic brain activity. In addition, we develop classification models (based on supervised machine-learning) to detect the cortical and sub-cortical features that allow for a robust division of patients and healthy controls. Given that these studies are based on MEG spontaneous brain activity, recorded at rest with either eyes-open or eyes-closed, we then explored the possibility of finding a distinctive feature that would combine both types of resting-state recordings. Thus, the third study investigates whether alterations in spectral amplitude between eyes-open and eyes-closed conditions can be used as a possible marker for schizophrenia. Overall, the three studies show changes in the scale-free dynamics of schizophrenia patients at rest that suggest a deterioration of the temporal processing of information in patients, which might relate to their cognitive and behavioural symptoms. The multimodal approach of this thesis, combining MEG, non-linear analyses and machine-learning, improves the characterization of the resting spatiotemporal neural organization of schizophrenia patients and healthy controls. Our findings provide new evidence for the temporal dysconnectivity hypothesis in schizophrenia. The results extend on previous studies by characterizing scale-free properties of deep brain structures and applying advanced non-linear metrics that are underused in the field of psychiatry. The results of this thesis contribute significantly to the identification of novel biomarkers in schizophrenia and show the importance of clarifying the temporal properties of altered intrinsic neural dynamics. Moreover, the presented studies offer a methodological framework that can be extended to other psychopathologies, such as depression

Decomposing multifractal crossovers

Physiological processes-such as, the brain's resting-state electrical activity or hemodynamic fluctuations-exhibit scale-free temporal structuring. However, impacts common in biological systems such as, noise, multiple signal generators, or filtering by transport function, result in multimodal scaling that cannot be reliably assessed by standard analytical tools that assume unimodal scaling. Here, we present two methods to identify breakpoints or crossovers in multimodal multifractal scaling functions. These methods incorporate the robust iterative fitting approach of the focus-based multifractal formalism (FMF). The first approach (moment-wise scaling range adaptivity) allows for a breakpoint-based adaptive treatment that analyzes segregated scale-invariant ranges. The second method (scaling function decomposition method, SFD) is a crossover-based design aimed at decomposing signal constituents from multimodal scaling functions resulting from signal addition or co-sampling, such as, contamination by uncorrelated fractals. We demonstrated that these methods could handle multimodal, mono- or multifractal, and exact or empirical signals alike. Their precision was numerically characterized on ideal signals, and a robust performance was demonstrated on exemplary empirical signals capturing resting-state brain dynamics by near infrared spectroscopy (NIRS), electroencephalography (EEG), and blood oxygen level-dependent functional magnetic resonance imaging (fMRI-BOLD). The NIRS and fMRI-BOLD low-frequency fluctuations were dominated by a multifractal component over an underlying biologically relevant random noise, thus forming a bimodal signal. The crossover between the EEG signal components was found at the boundary between the δ and θ bands, suggesting an independent generator for the multifractal d rhythm. The robust implementation of the SFD method should be regarded as essential in the seamless processing of large volumes of bimodal fMRI-BOLD imaging data for the topology of multifractal metrics free of the masking effect of the underlying random noise. © 2017 Nagy, Mukli, Herman and Eke