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Understanding the organizational principles of human brain activity at the systems level remains a major challenge in network neuroscience. Here, we introduce a fully data-driven approach based on graph learning to extract meaningful repeating network patterns from regionally-averaged time-courses. We use the Graph Laplacian Mixture Model (GLMM), a generative model that treats functional data as a collection of signals expressed on multiple underlying graphs. By exploiting covariance between activity of brain regions, these graphs can be learned without resorting to structural information. To validate the proposed technique, we first apply it to task fMRI with a known experimental paradigm. The probability of each graph to occur at each time-point is found to be consistent with the task timing, while the spatial patterns associated to each epoch of the task are in line with previously established activation patterns using classical regression analysis. We further on apply the technique to resting state data, which leads to extracted graphs that correspond to well-known brain functional activation patterns. The GLMM allows to learn graphs entirely from the functional activity that, in practice, turn out to reveal high degrees of similarity to the structural connectome. We compared similarity of the default mode network estimated from different task data and comparing them to each other and to structure. Using different metrics, a similar distinction between high- and low-level cognitive tasks arises.Overall, this method allows us to infer relevant functional brain networks without the need of structural connectome information. Moreover, we find that these networks correspond better to structure compared to traditional methods.

Brain signatures of functional activity have shown promising results in both decoding brain states, meaning distinguishing between different tasks, and fingerprinting, that is identifying individuals within a large group. Importantly, these brain signatures do not account for the underlying brain anatomy on which brain function takes place. Structure-function coupling based on graph signal processing (GSP) has recently revealed a meaningful spatial gradient from unimodal to transmodal regions, on average in healthy subjects during resting-state. Here, we explore the potential of GSP to introduce new imaging-based biomarkers to characterize tasks and individuals. We used multimodal magnetic resonance imaging of 100 unrelated healthy subjects from the Human Connectome Project both during rest and seven different tasks and adopted a support vector machine classification approach for both decoding and fingerprinting, with various cross-validation settings. We found that structurefunction coupling measures allow accurate classifications for both task decoding and fingerprinting. In particular, key information for fingerprinting is found in the more liberal portion of functional signals, that is the one decoupled from structure. A network mainly involving cortico-subcortical connections showed the strongest correlation with cognitive traits, assessed with partial least square analysis, corroborating its relevance for fingerprinting. By introducing a new perspective on GSP-based signal filtering and FC decomposition, these results show that brain structure-function coupling provides a new class of signatures of cognition and individual brain organization at rest and during tasks. Further, they provide insights on clarifying the role of low and high spatial frequencies of the structural connectome, leading to new understanding of where key structure-function information for characterizing individuals can be found across the structural connectome graph spectrum.Highlights-The relation of brain function with the underlying structural wiring is complex-We propose new structure-informed graph signal processing (GSP) of functional data-GSP-derived features allow accurate task decoding and individual fingerprinting-Functional connectivity from filtered data is more unique to subject and cognition-The role of structurally aligned and liberal graph frequencies is elucidated

Functional magnetic resonance imaging (fMRI) has been widely employed to study stroke pathophysiology. In particular, analyses of fMRI signals at rest were directed at quantifying the impact of stroke on spatial features of brain networks. However, brain networks have intrinsic time features that were, so far, disregarded in these analyses. In consequence, standard fMRI analysis failed to capture temporal imbalance resulting from stroke lesions, hence restricting their ability to reveal the interdependent pathological changes in structural and temporal network features following stroke. Here, we longitudinally analyzed hemodynamic-informed transient activity in a large cohort of stroke patients (n = 103) to assess spatial and temporal changes of brain networks after stroke. While large-scale spatial patterns of these networks were preserved after stroke, their durations were altered, with stroke subjects exhibiting a varied pattern of longer and shorter network activations compared to healthy individuals. These temporal alterations were associated with white matter damage and were behavior-specific. Specifically, restoration of healthy brain dynamics paralleled recovery of cognitive functions, but was not significantly correlated to motor recovery. These findings underscore the critical importance of network temporal properties in dissecting the pathophysiology of brain changes after stroke, thus shedding new light on the clinical potential of time-resolved methods for fMRI analysis.Significance StatementUnderstanding the pathophysiology of a disorder is pivotal to design effective treatment. In this regard, recent advances in stroke research settled a new clinical concept: connectional diaschisis, which suggested that post-stroke impairments arise from both focal structural changes (tied to the injury) and widespread alterations in functional connectivity. fMRI time-resolved methods consider structural and temporal properties of brain networks as interdependent features. They are, thus, better suited to capture the intertwine between structural and functional changes. Here we leveraged a dynamic functional connectivity framework based on the clustering of hemodynamic-informed transients in a large and heterogeneous stroke population assessed longitudinally. We showed that lesions led to an unbalance in the brain dynamics that was associated with white matter fibers disruption and was restored as deficits recovered. Our work showed the potential of a time-resolved method to reveal clinically relevant dynamics of large-scale brain networks.

As a consequence of recent technological advances in the field of functional magnetic resonance imaging (fMRI), results can now be made available in real-time. This allows for novel applications such as online quality assurance of the acquisition, intra-operative fMRI, brain-computer-interfaces, and neurofeedback. To that aim, signal processing algorithms for real-time fMRI must reliably correct signal contaminations due to physiological noise, head motion, and scanner drift. The aim of this study was to compare performance of the commonly used online detrending algorithms exponential moving average (EMA), incremental general linear model (iGLM) and sliding window iGLM (iGLM(window)). For comparison, we also included offline detrending algorithms (i.e., MATLAB's and SPM8's native detrending functions). Additionally, we optimized the EMA control parameter, by assessing the algorithm's performance on a simulated data set with an exhaustive set of realistic experimental design parameters. First, we optimized the free parameters of the online and offline detrending algorithms. Next, using simulated data, we systematically compared the performance of the algorithms with respect to varying levels of Gaussian and colored noise, linear and non-linear drifts, spikes, and step function artifacts. Additionally, using in vivo data from an actual rte-fMRI experiment, we validated our results in a post hoc offline comparison of the different detrending algorithms. Quantitative measures show that all algorithms perform well, even though they are differently affected by the different artifact types. The iGLM approach outperforms the other online algorithms and achieves online detrending performance that is as good as that of offline procedures. These results may guide developers and users of real-time fMRI analyses tools to best account for the problem of signal drifts in real-time fMRI.

International audience

Publication in the conference proceedings of SampTA, Bremen, Germany, 2013

Recently, we have proposed a novel family of bivariate, non-separable splines. These splines, called "hexsplines" have been designed to deal with hexagonally sampled data. Incorporating the shape of the Voronoi cell of a hexagonal lattice, they preserve the twelve-fold symmetry of the hexagon tiling cell. Similar to B-splines, we can use them to provide a link between the discrete and the continuous domain, which is required for many fundamental operations such as interpolation and resampling. The question we answer in this paper is "How well do the hex-splines approximate a given function in the continuous domain?" and more specifically "How do they compare to separable B-splines deployed on a lattice with the same sampling density?"

Based on the class of complex gradient-Laplace operators, we show the design of a non-separable two-dimensional wavelet basis from a single and analytically defined generator wavelet function. The wavelet decomposition is implemented by an efficient FFT-based filterbank. By allowing for slight redundancy, we obtain the Marr wavelet pyramid decomposition that features improved translation-invariance and steerability. The link with Marr's theory of early vision is due to the replication of the essential processing steps (Gaussian smoothing, Laplacian, orientation detection). Finally, we show how to find a compact multiscale primal sketch of the image, and how to reconstruct an image from it.

Background: A neurocognitive phenotype of post-COVID-19 infection has recently been described that is characterized by a lack of awareness of memory impairment (i.e., anosognosia), altered functional connectivity in the brain's default mode and limbic networks, and an elevated monocyte count. However, the relationship between these cognitive and brain functional connectivity alterations in the chronic phase with the level of cytokines during the acute phase has yet to be identified.Aim: Determine whether acute cytokine type and levels is associated with anosognosia and functional patterns of brain connectivity 6-9 months after infection.Methods: We analyzed the predictive value of the concentration of acute cytokines (IL-1RA, IL-1 beta, IL-6, IL-8, IFN beta, G-CSF, GM-CSF) (cytokine panel by multiplex immunoassay) in the plasma of 39 patients (mean age 59 yrs, 38-78) in relation to their anosognosia scores for memory deficits via stepwise linear regression. Then, associations between the different cytokines and brain functional connectivity patterns were analyzed by MRI and multivariate partial least squares correlations for the whole group. Results: Stepwise regression modeling allowed us to show that acute TNFa levels predicted (R-2 = 0.145; beta =-0.38; p = .017) and were associated (r =-0.587; p < .001) with scores of anosognosia for memory deficits observed 6-9 months post-infection. Finally, high TNFa levels were associated with hippocampal, temporal pole, accumbens nucleus, amygdala, and cerebellum connectivity. Conclusion: Increased plasma TNFa levels in the acute phase of COVID-19 predict the presence of long-term anosognosia scores and changes in limbic system functional connectivity.

In this work, we propose a new grid conversion algorithm between the hexagonal lattice and the orthogonal (a.k.a. Cartesian) lattice. The conversion process, named $ H _{ 2 } $ O, is easy to implement and is perfectly reversible using the same algorithm to return from one lattice to the other. The key observation of our approach is a decomposition of the lattice conversion as a sequence of shearing operations along three well-chosen directions. Hence, only 1-D fractional sample delay operators are required, which can be implemented by simple convolutions. The proposed algorithm combines reversibility and fast 1-D operations, together with high-quality resampled images.

One very influential method for texture synthesis is based on the steerable pyramid by alternately imposing marginal statistics on the image and the pyramid's subbands. In this work, we investigate two extensions to this framework. First, we exploit the steerability of the transform to obtain histograms of the subbands independent of the local orientation; i.e., we select the direction of maximal response as the reference orientation. Second, we explore the option of multidimensional histogram matching. The distribution of the responses to various orientations is expected to capture better the local geometric structure. Experimental results show how the proposed approach improves the performance of the original pyramid-based synthesis method.

Magnetic resonance spectroscopy imaging (MRSI) is an attractive tool for medical imaging. However, its practical use is often limited by the intrinsic low spatial resolution and long acquisition time. Spectral localization by imaging (SLIM) has been proposed as a non-Fourier reconstruction algorithm that incorporates spatial a priori information about spectroscopically uniform compartments. Unfortunately, the influence of the magnetic field inhomogeneity—in particular, the susceptibility effects at tissues' boundaries—undermines the validity of the compartmental model. Therefore, we propose BSLIM as an extension of SLIM with field inhomogeneity compensation. A $ B _{ 0 } $ -field inhomogeneity map, which can be acquired rapidly and at high resolution, is used by the new algorithm as additional a priori information. We show that the proposed method is distinct from the generalized SLIM (GSLIM) framework. Experimental results of a two-compartment phantom demonstrate the feasibility of the method and the importance of inhomogeneity compensation.

Motivated by the fractal-like behavior of natural images, we propose a new smoothing technique that uses a regularization functional which is a fractional iterate of the Laplacian. This type of functional has previously been introduced by Duchon in the context of radial basis functions (RBFs) for the approximation of non-uniform data. Here, we introduce a new solution to Duchon's smoothing problem in multiple dimensions using non-separable fractional polyharmonic B-splines. The smoothing is performed in the Fourier domain by filtering, thereby making the algorithm fast enough for most multi-dimensional real-time applications.

We present a functional imaging method based on triplet state kinetics. The triplet state of many known fluorophores show a triplet lifetime typically in the order of ~10e-6 – 10e-3 s, 3-6 orders of magnitude longer than the associated fluorescence singlet lifetime. As a consequence triplet state sensing is more exposed to the microenvironment of fluorophores and can be used as a functional molecular antenna. Using an adaptive modulated excitation scheme, these long living triplet state dynamics are accessible by standard CCD detector technology. We built an imaging setup allowing extraction of triplet lifetime maps. Effective correction of the competitive bleaching component is achieved by simultaneous monitoring of bleaching. The signal processing is based on a linear regressor analysis enabling extraction of the triplet state lifetime. As a first proof of principle, we investigated oxygen as a triplet state quencher on a sample of Tetramethylrhodamine (TMR) printed on a glass cover slide by soft lithography. First bioassays will be presented indicating the high potential for functional and metabolic imaging in life cell applications.

Conference of Wavelets and Sparsity XVII 2017 ; Conference Date: 6 August 2017 Through 9 August 2017; Conference Code:131333; International audience; We introduce a novel design for analyzing and approximating functions defined on the vertices of a directed graph Γ in a multi-scale fashion. The starting point of our construction is the setting-up of a frequency notion through the study of the Dirichlet energy of random walk operator's eigenfunctions. By this alluring frequency interpretation, the set of random walk's eigenfunctions is considered as the Fourier basis for functions over directed graphs. We are thus able to construct a multi-scale frame based on the bi-orthogonal basis of the random walk on directed graphs. This multi-resolution frame paves thus the way to a generalization of the diffusion wavelet framework to the directed scope.

Recently, new programming paradigms have emerged that combine parallelism and numerical computations with algorithmic differentiation. This approach allows for the hybridization of neural network techniques for inverse imaging problems with more traditional methods such as wavelet-based sparsity modelling techniques. The benefits are twofold: on the one hand traditional methods with well-known properties can be integrated in neural networks, either as separate layers or tightly integrated in the network, on the other hand, parameters in traditional methods can be trained end-to-end from datasets in a neural network "fashion" (e.g., using Adagrad or Adam optimizers). In this paper, we explore these hybrid neural networks in the context of shearlet-based regularization for the purpose of biomedical image restoration. Due to the reduced number of parameters, this approach seems a promising strategy especially when dealing with small training data sets.

It is believed by many that three-dimensional (3D) television will be the next logical development toward a more natural and vivid home entertaiment experience. While classical 3D approach requires the transmission of two video streams, one for each view, 3D TV systems based on depth image rendering (DIBR) require a single stream of monoscopic images and a second stream of associated images usually termed depth images or depth maps, that contain per-pixel depth information. Depth map is a two-dimensional function that contains information about distance from camera to a certain point of the object as a function of the image coordinates. By using this depth information and the original image it is possible to reconstruct a virtual image of a nearby viewpoint by projecting the pixels of available image to their locations in 3D space and finding their position in the desired view plane. One of the most significant advantages of the DIBR is that depth maps can be coded more efficiently than two streams corresponding to left and right view of the scene, thereby reducing the bandwidth required for transmission, which makes it possible to reuse existing transmission channels for the transmission of 3D TV. This technique can also be applied for other 3D technologies such as multimedia systems. In this paper we propose an advanced wavelet domain scheme for the reconstruction of stereoscopic images, which solves some of the shortcommings of the existing methods discussed above. We perform the wavelet transform of both the luminance and depth images in order to obtain significant geometric features, which enable more sensible reconstruction of the virtual view. Motion estimation employed in our approach uses Markov random field smoothness prior for regularization of the estimated motion field. The evaluation of the proposed reconstruction method is done on two video sequences which are typically used for comparison of stereo reconstruction algorithms. The results demonstrate advantages of the proposed approach with respect to the state-of-the-art methods, in terms of both objective and subjective performance measures.

Physiological Brain connectivity and spontaneous interaction between regions of interest of the brain can be represented by a matrix (full or sparse) or equivalently by a complex network called connectome. This representation of brain connectivity is adopted when comparing different patterns of structural and functional connectivity to null models or between groups of individuals. Two levels of comparison could be considered when analyzing brain connectivity: the global level and the local level. In the global level, the whole brain information is summarized by one summary statistic, whereas in the local analysis, each region of interest of the brain is summarized by a specific statistic. We show that these levels are mutually informatively integrative in some extent. We present different methods of analysis at both levels, the most relevant global and local network measures. We discuss as well the assumptions to be satisfied for each method; the error rates controlled by each method, and the challenges to overcome, especially, in the local case. We also highlight the possible factors that could influence the statistical results and the questions that have to be addressed in such analyses.

We consider the problem of reconstruction of astrophysical signals probed by radio interferometers with baselines bearing a non-negligible component in the pointing direction. The visibilities measured essentially identify with a noisy and incomplete Fourier coverage of the product of the planar signals with a linear chirp modulation. We analyze the related spread spectrum phenomenon and suggest its universality relative to the sparsity dictionary, in terms of the achievable quality of reconstruction through the Basis Pursuit problem. The present manuscript represents a summary of recent work by the authors.