Fine-scale characterization of the geometry of the folding patterns of the brain is a key processing step in neuroscience, with high impact applications such as for uncovering biomarkers indicative of a neurological pathology. Sulcal graphs constitute relevant representations of the complex and variable geometry of the cortex of individual brains. Comparing sulcal graphs is challenging due to variations across subjects in the number of nodes, graph topology and attributes (on both nodes and edges). Graph matching experiments on real data are limited by the absence of ground truth. In this paper we propose to generate synthetic graphs to benchmark graph matching methods and assess their robustness to noise on attributes and to the presence of un-matchable nodes. Three multi-graph matching methods are compared to one pairwise approach in various simulation settings, showing that good matching performances can be achieved even with highly perturbed sulcal graphs. An experiment on real data from a population of 134 subjects further unveil large performance differences across matching methods.

In neuroscience, understanding inter-individual differences has recently emerged as a major challenge, for which functional magnetic resonance imaging (fMRI) has proven invaluable. For this, neuroscientists rely on basic methods such as univariate linear correlations between single brain features and a score that quantifies either the severity of a disease or the subject's performance in a cognitive task. However, to this date, task-fMRI and resting-state fMRI have been exploited separately for this question, because of the lack of methods to effectively combine them. In this paper, we introduce a novel machine learning method which allows combining the activation- and connectivity-based information respectively measured through these two fMRI protocols to identify markers of individual differences in the functional organization of the brain. It combines a multi-view deep autoencoder which is designed to fuse the two fMRI modalities into a joint representation space within which a predictive model is trained to guess a scalar score that characterizes the patient. Our experimental results demonstrate the ability of the proposed method to outperform competitive approaches and to produce interpretable and biologically plausible results.

We present a generalization of Subspace Pursuit, which seeks the fc-sparse vector that minimizes a generic cost function. We introduce the Restricted Diagonal Property, which much like RIP in the classical setting, enables to control the convergence of Generalized Subspace Pursuit (GSP). To tackle the problem of Poisson denoising, we propose to use GSP together with the Moreau-Yosida approximation of the Poisson likelihood. Experiments were conducted on synthetic, exact sparse and natural images corrupted by Poisson noise. We study the influence of the different parameters and show that our approach performs better than Subspace Pursuit or ℓ1-relaxed methods and compares favorably to state-of-art methods.

We study the problem of learning from multiple views using kernel methods in a supervised setting. We approach this problem from a multi-task learning point of view and illustrate how to capture the interesting multimodal structure of the data using multi-task kernels. Our analysis shows that the multi-task perspective offers the flexibility to design more efficient multiple-source learning algorithms, and hence the ability to exploit multiple descriptions of the data. In particular, we formulate the multimodal learning framework using vector-valued reproducing kernel Hilbert spaces, and we derive specific multi-task kernels that can operate over multiple modalities. Finally, we analyze the vector-valued regularized least squares algorithm in this context, and demonstrate its potential in a series of experiments with a real-world multimodal data set.

The matter density is an important knowledge for today cosmology as many phenomena are linked to matter fluctuations. However, this density is not directly available, but estimated through lensing maps or galaxy surveys. In this article, we focus on galaxy surveys which are incomplete and noisy observations of the galaxy density. Incomplete, as part of the sky is unobserved or unreliable. Noisy as they are count maps degraded by Poisson noise. Using a data augmentation method, we propose a two-step method for recovering the density map, one step for inferring missing data and one for estimating the density. The results show that the missing areas are efficiently inferred and the statistical properties of the maps are preserved.

In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by Poisson noise. A proper data fidelity term (log-likelihood) is introduced to reflect the Poisson statistics of the noise. On the other hand, as a prior, the images to restore are assumed to be positive and sparsely represented in a dictionary of waveforms. Piecing together the data fidelity and the prior terms, the solution to the inverse problem is cast as the minimization of a non-smooth convex functional. We establish the well-posedness of the optimization problem, characterize the corresponding minimizers, and solve it by means of primal and primal-dual proximal splitting algorithms originating from the field of non-smooth convex optimization theory. Experimental results on deconvolution and comparison to prior methods are also reported.

Weighted Graph regularization provides a rich framework that allows to regularize functions defined over the vertices of a weighted graph. Until now, such a framework has been only defined for real or multivalued functions hereby restricting the regularization framework to numerical data. On the other hand, several kernels have been defined on structured objects such as strings or graphs. Using definite positive kernels, each original object is associated by the ``kernel trick'' to one element of an Hilbert space. As a consequence, this paper proposes to extend the weighted graph regularization framework to objects implicitly defined by their kernel hereby performing the regularization within the Hilbert space associated to the kernel. This work opens the door to the regularization of structured objects.

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key contributions are as follows. First, we handle the Poisson noise properly by using the Anscombe variance stabilizing transform leading to a nonlinear degradation equation with additive Gaussian noise. Second, the deconvolution problem is formulated as the minimization of a convex functional with a data-fidelity term reflecting the noise properties, and a nonsmooth sparsity-promoting penalty over the image representation coefficients (e.g., l(1) -norm). An additional term is also included in the functional to ensure positivity of the restored image. Third, a fast iterative forward-backward splitting algorithm is proposed to solve the minimization problem. We derive existence and uniqueness conditions of the solution, and establish convergence of the iterative algorithm. Finally, a GCV-based model selection procedure is proposed to objectively select the regularization parameter. Experimental results are carried out to show the striking benefits gained from taking into account the Poisson statistics of the noise. These results also suggest that using sparse-domain regularization may be tractable in many deconvolution applications with Poisson noise such as astronomy and microscopy.

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transform. Our key innovations are: First, we handle the Poisson noise properly by using the Anscombe variance stabilizing transform leading to a non-linear degradation equation with additive Gaussian noise. Second, the deconvolution problem is formulated as the minimization of a convex functional with a data-fidelity term reflecting the noise properties, and a non-smooth sparsity-promoting penalties over the image representation coefficients (e.g. l1-norm). Third, a fast iterative backward-forward splitting algorithm is proposed to solve the minimization problem. We derive existence and uniqueness conditions of the solution, and establish convergence of the iterative algorithm. Experimental results are carried out to show the striking benefits gained from taking into account the Poisson statistics of the noise. These results also suggest that using sparse-domain regularization may be tractable in many deconvolution applications, e.g. astronomy or microscopy.