Hyperbolic Wavelet-Fisz denoising for a model arising in Ultrasound Imaging

International audienceWe present an algorithm and its fully data-driven extension for noise reduction in ultrasound imaging. Our proposed method computes the hyperbolic wavelet transform of the image, before applying a multiscale variance stabilization technique, via a Fisz transformation. This adapts the wavelet coefficients statistics to the wavelet thresholding paradigm. The aim of the hyperbolic setting is to recover the image while respecting the anisotropic nature of structural details. The data-driven extension removes the need for any prior knowledge of the noise model parameters by estimating the noise variance using an isotonic Nadaraya-Watson estimator. Experiments on synthetic and real data, and comparisons with other noise reduction methods demonstrate the potential of our method at recovering ultrasound images while preserving tissue details. Finally, we emphasize the noise model we consider by applying our variance estimation procedure on real images

Large-scale functional network dynamics in human callosal agenesis:Increased subcortical involvement and preserved laterality

In the human brain, the corpus callosum is the major white-matter commissural tract enabling the transmission of sensory-motor, and higher level cognitive information between homotopic regions of the two cerebral hemispheres. Despite developmental absence (i.e., agenesis) of the corpus callosum (AgCC), functional connectivity is preserved, including interhemispheric connectivity. Subcortical structures have been hypothesised to provide alternative pathways to enable this preservation. To test this hypothesis, we used functional Magnetic Resonance Imaging (fMRI) recordings in children with AgCC and typically developing children, and a time-resolved approach to retrieve temporal characteristics of whole-brain functional networks. We observed an increased engagement of the cerebellum and amygdala/hippocampus networks in children with AgCC compared to typically developing children. There was little evidence that laterality of activation networks was affected in AgCC. Our findings support the hypothesis that subcortical structures play an essential role in the functional reconfiguration of the brain in the absence of a corpus callosum

Parcimonie structurée anisotrope pour l'estimation non paramétrique

Le problème d'estimer une fonction de plusieurs variables à partir d'une observation corrompue surgit dans de nombreux domaines d'ingénierie. Par exemple, en imagerie médicale cette tâche a attiré une attention particulière et a, même, motivé l'introduction de nouveaux concepts qui ont trouvé des applications dans de nombreux autres domaines. Cet intérêt est principalement du au fait que l'analyse des données médicales est souvent effectuée dans des conditions difficiles car on doit faire face au bruit, au faible contraste et aux transformations indésirables inhérents aux systèmes d'acquisition. D'autre part , le concept de parcimonie a eu un fort impact sur la reconstruction et la restauration d'images au cours des deux dernières décennies. La parcimonie stipule que certains signaux et images ont des représentations impliquant seulement quelques coefficients non nuls. Cela est avéré être vérifiable dans de nombreux problèmes pratiques. La thèse introduit de nouvelles constructions d'a priori de parcimonie dans le cas des ondelettes et de la variation totale. Ces constructions utilisent une notion d'anisotopie généralisée qui permet de regrouper des variables ayant des comportements similaires : ces comportement peuvent peut être liée à la régularité de la fonction, au sens physique des variables ou bien au modèle d'observation. Nous utilisons ces constructions pour l'estimation non-paramétriques de fonctions. Dans le cas des ondelettes, nous montrons l'optimalité de l'approche sur les espaces fonctionnelles habituels avant de présenter quelques exemples d’applications en débruitage de séquences d'images, de données spectrales et hyper-spectrales, écoulements incompressibles ou encore des images ultrasonores. En suite, nous modélisons un problème déconvolution de données d'imagerie par résonance magnétique fonctionnelle comme un problème de minimisation faisant apparaître un a priori de variation totale structuré en espace-temps. Nous adaptons une généralisation de l'éclatement explicite-implicite pour trouver une solution au problème de minimisation.The problem of estimating a multivariate function from corrupted observations arises throughout many areas of engineering. For instance, in the particular field of medical signal and image processing, this task has attracted special attention and even triggered new concepts and notions that have found applications in many other fields. This interest is mainly due to the fact that the medical data analysis pipeline is often carried out in challenging conditions, since one has to deal with noise, low contrast and undesirable transformations operated by acquisition systems. On the other hand, the concept of sparsity had a tremendous impact on data reconstruction and restoration in the last two decades. Sparsity stipulates that some signals and images have representations involving only a few non-zero coefficients. The present PhD dissertation introduces new constructions of sparsity priors for wavelets and total variation. These construction harness notions of generalized anisotropy that enables grouping variables into sub-sets having similar behaviour; this behaviour can be related to the regularity of the unknown function, the physical meaning of the variables or the observation model. We use these constructions for non-parametric estimation of multivariate functions. In the case of wavelet thresholding, we show the optimality of the procedure over usual functional spaces before presenting some applications on denoising of image sequence, spectral and hyperspectral data, incompressible flows and ultrasound images. Afterwards, we study the problem of retrieving activity patterns from functional Magnetic Resonance Imaging data without incorporating priors on the timing, durations and atlas-based spatial structure of the activation. We model this challenge as a spatio-temporal deconvolution problem. We propose the corresponding variational formulation and we adapt the generalized forward-backward splitting algorithm to solve it

Parcimonie structurée anisotrope pour l'estimation non paramétrique

The problem of estimating a multivariate function from corrupted observations arises throughout many areas of engineering. For instance, in the particular field of medical signal and image processing, this task has attracted special attention and even triggered new concepts and notions that have found applications in many other fields. This interest is mainly due to the fact that the medical data analysis pipeline is often carried out in challenging conditions, since one has to deal with noise, low contrast and undesirable transformations operated by acquisition systems. On the other hand, the concept of sparsity had a tremendous impact on data reconstruction and restoration in the last two decades. Sparsity stipulates that some signals and images have representations involving only a few non-zero coefficients. The present PhD dissertation introduces new constructions of sparsity priors for wavelets and total variation. These construction harness notions of generalized anisotropy that enables grouping variables into sub-sets having similar behaviour; this behaviour can be related to the regularity of the unknown function, the physical meaning of the variables or the observation model. We use these constructions for non-parametric estimation of multivariate functions. In the case of wavelet thresholding, we show the optimality of the procedure over usual functional spaces before presenting some applications on denoising of image sequence, spectral and hyperspectral data, incompressible flows and ultrasound images. Afterwards, we study the problem of retrieving activity patterns from functional Magnetic Resonance Imaging data without incorporating priors on the timing, durations and atlas-based spatial structure of the activation. We model this challenge as a spatio-temporal deconvolution problem. We propose the corresponding variational formulation and we adapt the generalized forward-backward splitting algorithm to solve it.Le problème d'estimer une fonction de plusieurs variables à partir d'une observation corrompue surgit dans de nombreux domaines d'ingénierie. Par exemple, en imagerie médicale cette tâche a attiré une attention particulière et a, même, motivé l'introduction de nouveaux concepts qui ont trouvé des applications dans de nombreux autres domaines. Cet intérêt est principalement du au fait que l'analyse des données médicales est souvent effectuée dans des conditions difficiles car on doit faire face au bruit, au faible contraste et aux transformations indésirables inhérents aux systèmes d'acquisition. D'autre part , le concept de parcimonie a eu un fort impact sur la reconstruction et la restauration d'images au cours des deux dernières décennies. La parcimonie stipule que certains signaux et images ont des représentations impliquant seulement quelques coefficients non nuls. Cela est avéré être vérifiable dans de nombreux problèmes pratiques. La thèse introduit de nouvelles constructions d'a priori de parcimonie dans le cas des ondelettes et de la variation totale. Ces constructions utilisent une notion d'anisotopie généralisée qui permet de regrouper des variables ayant des comportements similaires : ces comportement peuvent peut être liée à la régularité de la fonction, au sens physique des variables ou bien au modèle d'observation. Nous utilisons ces constructions pour l'estimation non-paramétriques de fonctions. Dans le cas des ondelettes, nous montrons l'optimalité de l'approche sur les espaces fonctionnelles habituels avant de présenter quelques exemples d’applications en débruitage de séquences d'images, de données spectrales et hyper-spectrales, écoulements incompressibles ou encore des images ultrasonores. En suite, nous modélisons un problème déconvolution de données d'imagerie par résonance magnétique fonctionnelle comme un problème de minimisation faisant apparaître un a priori de variation totale structuré en espace-temps. Nous adaptons une généralisation de l'éclatement explicite-implicite pour trouver une solution au problème de minimisation

A variational Shearlet-based model for aortic stent detection

International audienceIn medical applications, stent segmentation in the abdominal aorta has to be carried out in challenging conditions, since one has to deal with noise, low contrast, objects having similar appearances and missing or blurred edges. Variational segmentation methods eases this task by carrying prior information on the target region or on the regularity of its boundaries. In this paper, we propose a new approach based on the global minimization of the Active Contour model using the L1-norm of the Shearlet Transform instead of Total Variation (TV -norm). One of the distinctive features of such a regularization is that it allows the detection of anisotropic structures in images like stents boundaries. The sparsity imposed by the minimization provides piecewise smooth solutions with C2-singularities. We also use the shearlet coefficients to construct an edge function for more faithful contour detection. Performances of our algorithm are evaluated on a stent segmentation from post-operative CT data. Results show that the proposed method drastically improves the detection of the stent placement compared to the TV based approach

Deconvolution of sustained neural activity from large-scale calcium imaging data

Recent technological advances in light-sheet microscopy make it possible to perform whole-brain functional imaging at the cellular level with the use of Ca2+ indicators. The outstanding spatial extent and resolution of this type of data open unique opportunities for understanding the complex organization of neuronal circuits across the brain. However, the analysis of this data remains challenging because the observed variations in fluorescence are, in fact, noisy indirect measures of the neuronal activity. [...

BOLD Signal Deconvolution Under Uncertain Haemodynamics: A Semi-Blind Approach

The investigation of spontaneous and evoked neuronal activity from functional Magnetic Resonance Imaging (fMRI) data has come to play a significant role in deepening our understanding of brain function. As this research trend continues, activity detection metthat can adapt to different activation scenarios must be developed. The present work describes a new method for temporal semi-blind deconvolution of fMRI data; i.e., undo temporal signals from the effect of the Hæmodynamic Response Function (HRF), in the absence of information about the timing and duration of neuronal events and under uncertain characterization of cerebral hæmodynamics. A sequential minimization of two functionals is deployed: the first functional recovers activity signals with sparse transients while the second exploits the retrieved activity moments to estimate the Taylor expansion coefficients of the HRF. These coefficients are inherently linked to two values of interests that characterize the hæmodynamics: time-to-peak and the width of the response. We evaluate the performances of the method on synthetic signals before demonstrating its potential on experimental measurements from the visual cortex

Ultrasound spatiotemporal despeckling via Kronecker wavelet-Fisz thresholding

International audienceWe propose a novel framework for despeckling ultrasound image sequences while respecting the structural details. More precisely, we use thresholding in an adapted wavelet domain that jointly takes into account for the non-Gaussian statistics of the noise and the differences in spatial and temporal regularities. The spatiotemporal wavelet is obtained via the Kronecker product of two sparsifying wavelet bases acting, respectively, on the spatial and temporal domains. Besides enabling a structured sparse representation of the time–space plan, it also makes it possible to perform a variance stabilization routine on the spatial domain through a Fisz transformation. The proposed method enjoys adaptability, easy tuning and theoretical guaranties. We propose the corresponding algorithm together with results that demonstrate the benefits of the proposed spatiotemporal approach over the successive spatial treatment. Finally, we describe a data-driven extension of the proposed method that is based on temporal pre-filtering

Graph Slepians To Strike A Balance Between Local And Global Network Interactions: Application To Functional Brain Imaging

Brain function exhibits coordinated activity patterns that are also reflected in anatomy, a finding that can be harnessed to constrain the dynamics of functional time series to the underlying structure while performing various signal processing operations. Graph signal processing (GSP) is such a framework, which we here equip with a new tool to uncover localised functional brain interactions. The functional magnetic resonance imaging (fMRI) signal is projected onto a collection of Slepian vectors defined on a graph extracted from structural and diffusion MRI data. This decomposition allows a multi-bandwidth description of signals that are maximally concentrated within a subset of nodes, as is often the case for neural activity. On simulated data, we compare this technique to classical Laplacian and localised Laplacian filtering. We then present, on real fMRI data, an illustration of the Slepians potential to retrieve localised interaction patterns in the context of a visual stimulation task