3D steerable wavelets and monogenic analysis for bioimaging

ABSTRACT In this paper we introduce a 3D wavelet frame that has the key property of steerability. The proposed wavelet frame relies on the combination of a 3D isotropic wavelet transform with the 3D Riesz operator which brings steerability to the pyramid. The novel transform enjoys self reversibility and exact steering of the basis functions in any 3D direction by linear combination of the primary coefficients. We exploit the link between the Riesz transform and the directional Hilbert transform to define a multiresolution monogenic signal analysis in 3D which achieves multiscale AM/FM signal decomposition. We give an example of application of the 3D monogenic wavelet frame in biological imaging with the enhancement of anisotropic structures in 3D fluorescence microscopy

Continuous Monitoring of Cerebral Autoregulation in Children Supported by Extracorporeal Membrane Oxygenation: A Pilot Study.

OBJECTIVE: Cerebral autoregulation (CA) impairment may pose a risk factor for neurological complications among children supported by extracorporeal membrane oxygenation (ECMO). Our first objective was to investigate the feasibility of CA continuous monitoring during ECMO treatment and to describe its evolution over time. The second objective was to analyze the association between CA impairment and neurological outcome. DESIGN: Observational prospective study. PATIENTS AND SETTING: Twenty-nine children treated with veno-arterial or veno-venous ECMO in the PICU of Nantes University Hospital, France, and the PICU of the IRCCS Giannina Gaslini Institute in Genoa, Italy. MEASUREMENTS: A correlation coefficient between the variations of regional cerebral oxygen saturation and the variations of mean arterial blood pressure (MAP) was calculated as an index of CA (cerebral oxygenation reactivity index, COx). A COx > 0.3 was considered as indicative of autoregulation impairment. COx-MAP plots were investigated allowing determining optimal MAP (MAPopt) and limits of autoregulation: lower (LLA) and upper (ULA). Neurological outcome was assessed by the onset of an acute neurological event (ANE) after ECMO start. RESULTS: We included 29 children (median age 84 days, weight 4.8 kg). MAPopt, LLA, and ULA were detected in 90.8% (84.3-93.3) of monitoring time. Mean COx was significantly higher during day 1 of ECMO compared to day 2 [0.1 (0.02-0.15) vs. 0.01 (- 0.05 to 0.1), p = 0.002]. Twelve children experienced ANE (34.5%). The mean COx and the percentage of time spent with a COx > 0.3 were significantly higher among ANE+ compared to ANE- patients [0.09 (0.01-0.23) vs. 0.04 (- 0.02 to 0.06), p = 0.04 and 33.3% (24.8-62.1) vs. 20.8% (17.3-23.7) p = 0.001]. ANE+ patients spent significantly more time with MAP below LLA [17.2% (6.5-32.9) vs. 5.6% (3.6-9.9), p = 0.02] and above ULA [13% (5.3-38.4) vs. 4.2% (2.7-7.4), p = 0.004], respectively. CONCLUSION: CA assessment is feasible in pediatric ECMO. The first 24 h following ECMO represents the most critical period regarding CA. Impaired autoregulation is significantly more severe among patients who experience ANE

Dynamic interplay between thalamic activity and Cajal-Retzius cells regulates the wiring of cortical layer 1

Cortical wiring relies on guidepost cells and activity-dependent processes that are thought to act sequentially. Here, we show that the construction of layer 1 (L1), a main site of top-down integration, is regulated by crosstalk between transient Cajal-Retzius cells (CRc) and spontaneous activity of the thalamus, a main driver of bottom-up information. While activity was known to regulate CRc migration and elimination, we found that prenatal spontaneous thalamic activity and NMDA receptors selectively control CRc early density, without affecting their demise. CRc density, in turn, regulates the distribution of upper layer interneurons and excitatory synapses, thereby drastically impairing the apical dendrite activity of output pyramidal neurons. In contrast, postnatal sensory-evoked activity had a limited impact on L1 and selectively perturbed basal dendrites synaptogenesis. Collectively, our study highlights a remarkable interplay between thalamic activity and CRc in L1 functional wiring, with major implications for our understanding of cortical development.We thank the IBENS Imaging Facility (France BioImaging, supported by ANR-10-INBS-04, ANR-10-LABX-54 MEMO LIFE, and ANR-11-IDEX-000-02 PSL∗ Research University, “Investments for the Future”). This work was supported by grants from the Spanish Ministry of Science, Innovation, and Universities (PGC2018-096631-B-I00) and the European Research Council (ERC-2014-CoG-647012) to G.L.-B. N.C. received funding from the Marie Skłodowska-Curie individual fellowship under the European Union’s Horizon 2020 research and innovation program (AXO-MATH, grant agreement no. 798326). F.G. received funding from the Agence Nationale de la Recherche (SyTune, ANR-21-CE37-0010), the European Research Council under the European Union’s Horizon 2020 research and innovation program (NEUROGOAL, grant agreement no.677878), the Region Nouvelle-Aquitaine, and the University of Bordeaux. The Garel laboratory is supported by INSERM, CNRS, ANR-15-CE16-0003, ANR-19-CE16-0017-02, Investissements d’Avenir implemented by ANR-10-LABX-54 MEMO LIFE, ANR-11-IDEX-0001-02 PSL∗ Research University, and the European Research Council (ERC-2013-CoG-616080, NImO). I.G. is a recipient of a fellowship from the French Ministry of Research and postdoctoral funding from Labex MemoLife, and S.G. is part of the Ecole des Neurosciences de Paris Ile-de-France network.Peer reviewe

Objective comparison of particle tracking methods

Particle tracking is of key importance for quantitative analysis of intracellular dynamic processes from time-lapse microscopy image data. Because manually detecting and following large numbers of individual particles is not feasible, automated computational methods have been developed for these tasks by many groups. Aiming to perform an objective comparison of methods, we gathered the community and organized an open competition in which participating teams applied their own methods independently to a commonly defined data set including diverse scenarios. Performance was assessed using commonly defined measures. Although no single method performed best across all scenarios, the results revealed clear differences between the various approaches, leading to notable practical conclusions for users and developers

Avancées en suivi probabiliste de particules pour l'imagerie biologique

Particle tracking is a method of choice to understand subcellular mechanisms since it provides a robust and accurate means to characterize the dynamics of moving objects at the micro- and nano-metric scale. This thesis addresses several aspects related to the problem of tracking several hundreds of particles in cluttered conditions. We present novel techniques based on robust mathematical methods which allow us to track subresolutive particles in the wealth of conditions which are met in cellular imaging. Particle detection: we have first addressed the issue of detecting particles in fluorescence images containing a structured background. The key idea of the proposed method is to use a blind source separation technique: the Morphological Component Analysis (MCA) algorithm, to separate the background from the particle signal by exploiting the differences between their morphologies in the image. We have made a number of adaptations to the MCA to comply with the characteristics of biological fluorescence images. For instance, we have proposed to use the curvelet dictionary and a wavelet dictionary with sparsity priors to split the background and the particles signals. After source separation, the background-free image can be reliably analyzed to identify the particle locations and track them through time. Particle tracking problem modeling: we have proposed a global statistical framework which accounts for every aspect of the particle tracking problem in cluttered conditions. The designed probabilistic framework includes several models which are dedicated to biological imaging, such as statistical models of motion of particles. We have also defined the concept of target perceivability for biological particles. By doing so, the existence of particles is explicitly modeled and statistically quantified, thereby addressing the issues of track termination/creation within the statistical framework for tracking. As a result, the proposed framework enjoys a high degree of flexibility since every parameter and model involved finds a simple and intuitive interpretation. The proposed probabilistic framework has consequently allowed us to exhaustively model a wealth of different biological cases. Tracking algorithm design: we have reformulated the Multiple Hypothesis Tracking (MHT) algorithm to include the probabilistic framework for tracking biological particles, and proposed an efficient implementation which allows one to track numerous particles in poor imaging conditions. The Enhanced MHT (E-MHT) we propose takes full advantage of the tracking model by incorporating the knowledge from future frames, whereby the significance of statistical scores is increased. As a result, the E-MHT is able to automatically identify false detections and detect target appearance/disappearance events. We address the complexity of the tracking task by an efficient design of the algorithm which exploits the tree organization of the solutions and the ability to make the computations in a parallel manner. A series of comparative tests between the E-MHT and a number of state-of-the-art techniques have been performed with synthetic 2D image sequences and real 2D and 3D data sets. In every case the E-MHT has proved superior performance over standard techniques, with a remarkable capability to handle very poor imaging conditions. We have applied the proposed tracking techniques in a number of biological projects, leading to novel biological results. The flexibility and robustness of the proposed methods have allowed us to track prions infecting cell, characterize protein transport during the Drosophila oocyte development, and to study the mRNA trafficking in a Drosophila ovocyte.Le suivi de particules est une méthode de choix pour comprendre les mécanismes intra-cellulaires car il fournit des moyens robustes et précis de caractériser la dynamiques des objets mobiles à l'échelle micro et nano métrique. Cette thèse traite de plusieurs aspects liés au problème du suivi de plusieurs centaines de particules dans des conditions bruitées. Nous présentons des techniques nouvelles basée sur des méthodes mathématiques robustes qui nous permettent des suivre des particules sous-résolutives dans les conditions variées qui sont rencontrées en imagerie cellulaire. Détection de particules : nous avons tout d'abord traité le problème de la détection de particules dans les images fluorescentes contenant un fond structuré. L'idée clé de la méthode est l'utilisation d'une technique de séparation de sources : l'algorithme d'Analyse en Composantes Morphologiques (ACM), pour séparer le fond des particules en exploitant leur différence de morphologie dans les images. Nous avons effectué un certain nombre de modifications à l'ACM pour l'adapter aux caractéristiques des images biologiques en fluorescence. Par exemple, nous avons proposé l'utilisation du dictionnaire de Curvelet et d'un dictionnaire de d'ondelettes, avec des à priori de parcimonie différents, afin de séparer le signal des particules du fond. Une fois la séparation de sources effectuée, l'image sans fond peut être analysée pour identifier de manière robuste la position des particules et pour les suivre au cours du temps. Modélisation du problème de suivi : nous avons proposé un cadre de travail statistique global qui tient compte des nombreux aspects du problème de suivi de particules dans des conditions bruitées. Le cadre de travail probabiliste que nous avons mis au point contient de nombreux modèles qui sont dédiés à l'imagerie biologique, tels que des modèles statistiques de mouvement des particules en milieu cellulaire. Nous avons aussi défini la concept de perceiability d'une cible dans le cas des particules biologiques. Grâce à ce modèle l'existence d'une particule est explicitement modélisée et quantifiée, ce qui nous permet de résoudre les problèmes de création et de terminaison des trajectoires au sein même de notre cadre probabiliste de suivi. Le cadre de travail proposé bénéficie d'une grande flexibilité mais reste facile à adapter car chaque paramètre du modèle trouve une interprétation simple et intuitive. Ainsi, notre modèle probabiliste de suivi nous a permis de modéliser de manière exhaustive un grand nombre de systèmes biologiques différents. Mise au point d'un algorithme de suivi : nous avons reformulé l'algorithme de suivi nommé Multiple Hypothesis Tracking (MHT) pour qu'il inclue notre modèle probabiliste de suivi dédié aux particules biologiques, et nous avons proposé une implémentation rapide qui permet de suivre de nombreuses particules dans des conditions d'imagerie dégradées. L'\textit{Enhanced} MHT (E-MHT) que nous avons proposé tire pleinement partie du modèle de suivi en incorporant la connaissance des images futures, ce qui augmente significativement le pouvoir discriminant des critères statistiques. En conséquence, l'E-MHT est capable d'identifier automatiquement les détections erronée et de détecter les événements d'apparition et de disparition des particules. Nous avons résolu le problème de la complexité de la tache de suivi grâce à un design de l'algorithme que exploite la topologie en arbre des solution et à la possibilité d'effectuer les calculs de manière parallèle. Une série de tests comparatifs entre l'E-MHT et des méthodes existantes de suivi a été réalisée avec des séquences d'images synthétiques 2D et avec des jeux de données réels 2D et 3D. Dans chaque cas l'E-MHT a montré des performances supérieures par rapport aux méthodes standards, avec une capacité remarquable à supporter des conditions d'imagerie très dégradées. Nous avons appliqué les méthodes de suivi proposées dans le cadre de plusieurs projets biologiques, ce qui a conduit à des résultats biologiques originaux. La flexibilité et la robustesse de notre méthode nous a notamment permis de suivre des prions infectant des cellules, de caractériser le transport de protéines lors du développement de l'ovocyte de la drosophile, ainsi que d'étudier la trafic d'ARN messager dans l'ovocyte de drosophile

3D Steerable Wavelets in Practice

Abstract — We introduce a systematic and practical design for steerable wavelet frames in 3D. Our steerable wavelets are obtained by applying a 3D version of the generalized Riesz transform to a primary isotropic wavelet frame. The novel transform is self-reversible (tight frame) and its elementary constituents (Riesz wavelets) can be efficiently rotated in any 3D direction by forming appropriate linear combinations. Moreover, the basis functions at a given location can be linearly combined to design custom (and adaptive) steerable wavelets. The features of the proposed method are illustrated with the processing and analysis of 3D biomedical data. In particular, we show how those wavelets can be used to characterize directional patterns and to detect edges by means of a 3D monogenic analysis. We also propose a new inverse-problem formalism along with an optimization algorithm for reconstructing 3D images from a sparse set of wavelet-domain edges. The scheme results in high-quality image reconstructions which demonstrate the feature-reduction ability of the steerable wavelets as well as their potential for solving inverse problems. Index Terms — 3D wavelet transform, edge detection, image reconstruction, monogenic signal, riesz transform, steerability. I

A Unifying Parametric Framework for 2D Steerable Wavelet Transforms

We introduce a complete parameterization of the family of two-dimensional steerable wavelets that are polar-separable in the Fourier domain under the constraint of self-reversibility. These wavelets are constructed by multiorder generalized Riesz transformation of a primary isotropic bandpass pyramid. The backbone of the transform (pyramid) is characterized by a radial frequency profile function h(ω), while the directional wavelet components at each scale are encoded by an M × (2N + 1) shaping matrix U, whereMisthe number of wavelet channels and N the order of the Riesz transform. We provide general conditions on h(ω) andUfor the underlying wavelet system to form a tight frame of L2(R²) (with a redundancy factor 4/3M). The proposed framework ensures that the wavelets are steerable and provides new degrees of freedom (shaping matrix U) that can be exploited for designing specific wavelet systems. It encompasses many known transforms as particular cases: Simoncelli’s steerable pyramid, Marr gradient and Hessian wavelets, monogenic wavelets, and Nth-order Riesz and circular harmonic wavelets. We take advantage of the framework to construct new generalized spheroidal prolate wavelets, whose angular selectivity is maximized, as well as signaladapted detectors based on principal component analysis. We also introduce a curvelet-like steerable wavelet system. Finally, we illustrate the advantages of some of the designs for signal denoising, feature extraction, pattern analysis, and source separation

A new hybrid Bayesian-variational particle filter with application to mitotic cell tracking

Tracking algorithms are traditionally based on either a variational approach or a Bayesian one. In the variational case, a cost function is established between two consecutive frames and minimized by standard optimization algorithms. In the Bayesian case, a stochastic motion model is used to maintain temporal consistency. Among the Bayesian methods we focus on the particle filter, which is especially suited for handling multimodal distributions. In this paper, we present a novel approach to fuse both methodologies in a single tracker where the importance sampling of the particle filter is given implicitly by the optimization algorithm of the variational method. Our technique is capable of outlying nuclei and tracking the lineage of biological cells using different motion models for mitotic and non-mitotic stages of the life of a cell. We validate its ability to track the lineage of HeLa cells in fluorescence microscopy