arXiv subjects

Dimitri Van De Ville

Publications and source records attributed to Dimitri Van De Ville.

At least 19 recordsLinked to original sources

arXiv2026

Graph Signal Surrogate Generation for Statistical Testing of Covariance Structure on Directed Graphs

Non-parametric statistical testing is based on surrogate data generation that randomizes chosen features in the empirical data. In the graph setting, graph signal processing (GSP) brings forward versatile schemes; e.g., to preserve smoothness of graph signals as measured by the Dirichlet energy. However, how to deal with directed graphs remains an active area of research. We begin by revisiting the definition of directed graph wide-sense stationarity. The surrogate signals preserve covariance under the stationary assumption. We demonstrate the feasibility of the scheme to detect irregular node covariance and benchmark our method against conventional schemes using the symmetrized graph. We also investigate how the level of asymmetry affects the detection performance, thus assessing the advantages of the presented approach. Finally, we show results for a real-world graph extracted from the Freeman EIES social network dataset.

stat.ME↗

arXiv2026

Optimal Wiener-Filter Solutions for Denoising of Graph Signals on Directed Graphs

Graph signal processing has opened new avenues to the canonical denoising problem in interesting settings. Specifically, here we propose a Wiener-filter solution for graph signals on directed graphs. Under various stationarity assumptions combining uncorrelated and correlated noise conditions, we show optimal solutions, including a successful proof-of-concept for temperature graph.

eess.SP↗

arXiv2026

Statistical Testing on Directed Graphs by Surrogate Data Generation

In recent years, graph signal processing has emerged as a powerful framework at the intersection of signal processing and graph theory, providing tools for the analysis of signals defined on nodes while accounting for their relationships represented by edges. These tools have been successfully applied to various settings, including statistical hypothesis testing. In particular, non-parametric approaches based on surrogate generation have been proposed for signals on undirected graphs. However, they are yet to be extended to directed graphs. In this work, we first revisit the notion of stationary graph signals on directed graphs. Specifically, and through the eigendecomposition of the graph shift operator, we define directed graph wide-sense stationary signals. Then, we propose a new framework to generate surrogate graph signals that preserve covariance structure under stationarity assumptions. Null distributions of the test metric can then be constructed from these surrogates and serve as a reference for the empirical data. Finally, we provide guiding examples and an application on real data, in which we compare the performance of our framework with existing techniques for undirected graphs or based on naive permutation, demonstrating feasibility and superiority of the proposed approach.

stat.ML↗

arXiv2026

Topological Signal Processing: An Application-Oriented Tutorial

Many modern datasets are large and carry complex structural relationships. Graph-based methods have traditionally been used to represent networked data, modeling individual elements as nodes and pairwise interactions as edges. Furthermore, Graph Signal Processing (GSP) has been developed to analyze signals on graph nodes, such as temperature measurements (node signals) across different regions of a country represented as a graph. Topological Signal Processing (TSP) is an emerging field that generalizes GSP, enabling the analysis of signals defined not only on nodes but also on edges, triangles, and higher-dimensional network elements, modeled as simplicial complexes and related topological structures. This makes TSP naturally well-suited for studying higher-order interactions in complex systems by extending classical signal processing concepts, such as filtering and Fourier transforms, to the topological level. Despite its versatility, TSP remains challenging for many practitioners. Therefore, we present an accessible overview of TSP foundations while drawing connections with application-oriented settings. We focus on processing techniques based on the combinatorial Hodge Laplacian, which generalizes the graph Laplacian to simplicial complexes. In particular, we review key TSP concepts, relate them to real-world examples, and discuss how higher-order structures and signals can be derived from datasets. For instance, we introduce an edge-level signal capturing lagged interactions between nodal signals, and demonstrate its use in a case study on TSP-based analysis of brain imaging data, revealing nontrivial interactions between sets of brain regions. Overall, we aim to promote a broader adoption of TSP by bridging methodological developments with applications, fostering its use among a wide community of theoretical and applied researchers.

eess.SP↗

arXiv2025

Monitoring morphometric drift in lifelong learning segmentation of the spinal cord

Morphometric measures derived from spinal cord segmentations can serve as diagnostic and prognostic biomarkers in neurological diseases and injuries affecting the spinal cord. While robust, automatic segmentation methods to a wide variety of contrasts and pathologies have been developed over the past few years, whether their predictions are stable as the model is updated using new datasets has not been assessed. This is particularly important for deriving normative values from healthy participants. In this study, we present a spinal cord segmentation model trained on a multisite $(n=75)$ dataset, including 9 different MRI contrasts and several spinal cord pathologies. We also introduce a lifelong learning framework to automatically monitor the morphometric drift as the model is updated using additional datasets. The framework is triggered by an automatic GitHub Actions workflow every time a new model is created, recording the morphometric values derived from the model's predictions over time. As a real-world application of the proposed framework, we employed the spinal cord segmentation model to update a recently-introduced normative database of healthy participants containing commonly used measures of spinal cord morphometry. Results showed that: (i) our model outperforms previous versions and pathology-specific models on challenging lumbar spinal cord cases, achieving an average Dice score of $0.95 \pm 0.03$; (ii) the automatic workflow for monitoring morphometric drift provides a quick feedback loop for developing future segmentation models; and (iii) the scaling factor required to update the database of morphometric measures is nearly constant among slices across the given vertebral levels, showing minimum drift between the current and previous versions of the model monitored by the framework. The code and model are open-source and accessible via Spinal Cord Toolbox v7.0.

cs.CV↗

arXiv2025

Community detection for directed networks revisited using bimodularity

Community structure is a key feature omnipresent in real-world network data. Plethora of methods have been proposed to reveal subsets of densely interconnected nodes using criteria such as the modularity index. These approaches have been successful for undirected graphs, but directed edge information has not yet been dealt with in a satisfactory way. Here, we revisit the concept of directed communities as a mapping between sending and receiving communities. This translates into a new definition that we term bimodularity. Using convex relaxation, bimodularity can be optimized with the singular value decomposition of the directed modularity matrix. Subsequently, we propose an edge-based clustering approach to reveal the directed communities including their mappings. The feasibility of the new framework is illustrated on a synthetic model and further applied to the neuronal wiring diagram of the \textit{C. elegans}, for which it yields meaningful feedforward loops of the head and body motion systems. This framework sets the ground for the understanding and detection of community structures in directed networks.

cs.SI↗

arXiv2025

Deep Neural Encoder-Decoder Model to Relate fMRI Brain Activity with Naturalistic Stimuli

We propose an end-to-end deep neural encoder-decoder model to encode and decode brain activity in response to naturalistic stimuli using functional magnetic resonance imaging (fMRI) data. Leveraging temporally correlated input from consecutive film frames, we employ temporal convolutional layers in our architecture, which effectively allows to bridge the temporal resolution gap between natural movie stimuli and fMRI acquisitions. Our model predicts activity of voxels in and around the visual cortex and performs reconstruction of corresponding visual inputs from neural activity. Finally, we investigate brain regions contributing to visual decoding through saliency maps. We find that the most contributing regions are the middle occipital area, the fusiform area, and the calcarine, respectively employed in shape perception, complex recognition (in particular face perception), and basic visual features such as edges and contrasts. These functions being strongly solicited are in line with the decoder's capability to reconstruct edges, faces, and contrasts. All in all, this suggests the possibility to probe our understanding of visual processing in films using as a proxy the behaviour of deep learning models such as the one proposed in this paper.

cs.CV↗

arXiv2025

Hilbert Transform on Graphs: Let There Be Phase

In the past years, many signal processing operations have been successfully adapted to the graph setting. One elegant and effective approach is to exploit the eigendecomposition of a graph shift operator (GSO), such as the adjacency or Laplacian operator, to define a graph Fourier transform when projecting graph signals on the corresponding basis. However, the extension of this scheme to directed graphs is challenging since the associated GSO is non-symmetric and, in general, not diagonalizable. Here, we build upon a recent framework that adds a minimal number of edges to allow diagonalization of the GSO and thus provide a proper graph Fourier transform. Furthermore, we show that such minimal addition of edges creates a cycle cover and that it is essential for the phase analysis of a signal throughout the graph. Concurrently, we propose a generalization of the Hilbert transform interpreted over the newfound cycle cover, which re-establishes intuitions from traditional Hilbert Transform, equivalent to the generalized Hilbert Transform on a single cycle. This generalization leads to a number of simple and elegant recipes to effectively exploit the phase information of graph signals provided by the graph Fourier transform. The feasibility of the approach is demonstrated on several examples.

eess.SP↗

arXiv2025

Signal-adapted decomposition of graph signals

Analysis of signals defined on complex topologies modeled by graphs is a topic of increasing interest. Signal decomposition plays a crucial role in the representation and processing of such information, in particular, to process graph signals based on notions of scale (e.g., coarse to fine). The graph spectrum is more irregular than for conventional domains; i.e., it is influenced by graph topology, and, therefore, assumptions about spectral representations of graph signals are not easy to make. Here, we propose a tight frame design that is adapted to the graph Laplacian spectral content of given classes of graph signals. The design is based on using the ensemble energy spectral density, a notion of spectral content of given signal sets that we determine either directly using the graph Fourier transform or indirectly through a polynomial-based approximation scheme. The approximation scheme has the benefit that (i) it does not require eigendecomposition of the Laplacian matrix making the method feasible for large graphs, and (ii) it leads to a smooth estimate of the spectral content. A prototype system of spectral kernels each capturing an equal amount of energy is initially defined and subsequently warped using the signal set's ensemble energy spectral density such that the resulting subbands each capture an equal amount of ensemble energy. This approach accounts at the same time for graph topology and signal features, and it provides a meaningful interpretation of subbands in terms of coarse-to-fine representations. We also show how more simplified designs of signal-adapted decomposition of graph signals can be adopted based on ensemble energy estimates. We show the application of proposed methods on the Minnesota road graph and three different designs of brain graphs derived from neuroimaging data.

eess.SP↗

arXiv2023

From Nano to Macro: Overview of the IEEE Bio Image and Signal Processing Technical Committee

The Bio Image and Signal Processing (BISP) Technical Committee (TC) of the IEEE Signal Processing Society (SPS) promotes activities within the broad technical field of biomedical image and signal processing. Areas of interest include medical and biological imaging, digital pathology, molecular imaging, microscopy, and associated computational imaging, image analysis, and image-guided treatment, alongside physiological signal processing, computational biology, and bioinformatics. BISP has 40 members and covers a wide range of EDICS, including CIS-MI: Medical Imaging, BIO-MIA: Medical Image Analysis, BIO-BI: Biological Imaging, BIO: Biomedical Signal Processing, BIO-BCI: Brain/Human-Computer Interfaces, and BIO-INFR: Bioinformatics. BISP plays a central role in the organization of the IEEE International Symposium on Biomedical Imaging (ISBI) and contributes to the technical sessions at the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), and the IEEE International Conference on Image Processing (ICIP). In this paper, we provide a brief history of the TC, review the technological and methodological contributions its community delivered, and highlight promising new directions we anticipate.

eess.SP↗

arXiv2022

Hemodynamic Deconvolution Demystified: Sparsity-Driven Regularization at Work

Deconvolution of the hemodynamic response is an important step to access short timescales of brain activity recorded by functional magnetic resonance imaging (fMRI). Albeit conventional deconvolution algorithms have been around for a long time (e.g., Wiener deconvolution), recent state-of-the-art methods based on sparsity-pursuing regularization are attracting increasing interest to investigate brain dynamics and connectivity with fMRI. This technical note revisits the main concepts underlying two main methods, Paradigm Free Mapping and Total Activation, in the most accessible way. Despite their apparent differences in the formulation, these methods are theoretically equivalent as they represent the synthesis and analysis sides of the same problem, respectively. We demonstrate this equivalence in practice with their best-available implementations using both simulations, with different signal-to-noise ratios, and experimental fMRI data acquired during a motor task and resting-state. We evaluate the parameter settings that lead to equivalent results, and showcase the potential of these algorithms compared to other common approaches. This note is useful for practitioners interested in gaining a better understanding of state-of-the-art hemodynamic deconvolution, and aims to answer questions that practitioners often have regarding the differences between the two methods.

q-bio.NC↗

arXiv2020

Community-Aware Graph Signal Processing

The emerging field of graph signal processing (GSP) allows to transpose classical signal processing operations (e.g., filtering) to signals on graphs. The GSP framework is generally built upon the graph Laplacian, which plays a crucial role to study graph properties and measure graph signal smoothness. Here instead, we propose the graph modularity matrix as the centerpiece of GSP, in order to incorporate knowledge about graph community structure when processing signals on the graph, but without the need for community detection. We study this approach in several generic settings such as filtering, optimal sampling and reconstruction, surrogate data generation, and denoising. Feasibility is illustrated by a small-scale example and a transportation network dataset, as well as one application in human neuroimaging where community-aware GSP reveals relationships between behavior and brain features that are not shown by Laplacian-based GSP. This work demonstrates how concepts from network science can lead to new meaningful operations on graph signals.

eess.SP↗

arXiv2019

TbCAPs: A ToolBox for Co-Activation Pattern Analysis

Functional magnetic resonance imaging provides rich spatio-temporal data of human brain activity during task and rest. Many recent efforts have focussed on characterising dynamics of brain activity. One notable instance is co-activation pattern (CAP) analysis, a frame-wise analytical approach that disentangles the different functional brain networks interacting with a user-defined seed region. While promising applications in various clinical settings have been demonstrated, there is not yet any centralised, publicly accessible resource to facilitate the deployment of the technique. Here, we release a working version of TbCAPs, a new toolbox for CAP analysis, which includes all steps of the analytical pipeline, introduces new methodological developments that build on already existing concepts, and enables a facilitated inspection of CAPs and resulting metrics of brain dynamics. The toolbox is available on a public academic repository (https://c4science.ch/source/CAP_Toolbox.git). In addition, to illustrate the feasibility and usefulness of our pipeline, we describe an application to the study of human cognition. CAPs are constructed from resting-state fMRI using as seed the right dorsolateral prefrontal cortex, and, in a separate sample, we successfully predict a behavioural measure of continuous attentional performance from the metrics of CAP dynamics (R=0.59).

q-bio.QM↗

arXiv2019

Decoupling of brain function from structure reveals regional behavioral specialization in humans

The brain is an assembly of neuronal populations interconnected by structural pathways. Brain activity is expressed on and constrained by this substrate. Therefore, statistical dependencies between functional signals in directly connected areas can be expected higher. However, the degree to which brain function is bound by the underlying wiring diagram remains a complex question that has been only partially answered. Here, we introduce the structural-decoupling index to quantify the coupling strength between structure and function, and we reveal a macroscale gradient from brain regions more strongly coupled, to regions more strongly decoupled, than expected by realistic surrogate data. This gradient spans behavioral domains from lower-level sensory function to high-level cognitive ones and shows for the first time that the strength of structure-function coupling is spatially varying in line with evidence derived from other modalities, such as functional connectivity, gene expression, microstructural properties and temporal hierarchy.

q-bio.NC↗

arXiv2019

Structural mediation of human brain activity revealed by white-matter interpolation of fMRI

Anatomy of the human brain constrains the formation of large-scale functional networks. Here, given measured brain activity in gray matter, we interpolate these functional signals into the white matter on a structurally-informed high-resolution voxel-level brain grid. The interpolated volumes reflect the underlying anatomical information, revealing white matter structures that mediate functional signal flow between temporally coherent gray matter regions. Functional connectivity analyses of the interpolated volumes reveal an enriched picture of the default mode network (DMN) and its subcomponents, including how white matter bundles support their formation, thus transcending currently known spatial patterns that are limited within the gray matter only. These subcomponents have distinct structure-function patterns, each of which are differentially recruited during tasks, demonstrating plausible structural mechanisms for functional switching between task-positive and -negative components. This work opens new avenues for integration of brain structure and function and demonstrates how global patterns of activity arise from a collective interplay of signal propagation along different white matter pathways.

q-bio.NC↗

arXiv2019

Domain-Informed Spline Interpolation

Standard interpolation techniques are implicitly based on the assumption that the signal lies on a single homogeneous domain. In contrast, many naturally occurring signals lie on an inhomogeneous domain, such as brain activity associated to different brain tissue. We propose an interpolation method that instead exploits prior information about domain inhomogeneity, characterized by different, potentially overlapping, subdomains. As proof of concept, the focus is put on extending conventional shift-invariant B-spline interpolation. Given a known inhomogeneous domain, B-spline interpolation of a given order is extended to a domain-informed, shift-variant interpolation. This is done by constructing a domain-informed generating basis that satisfies stability properties. We illustrate example constructions of domain-informed generating basis, and show their property in increasing the coherence between the generating basis and the given inhomogeneous domain. By advantageously exploiting domain knowledge, we demonstrate the benefit of domain-informed interpolation over standard B-spline interpolation through Monte Carlo simulations across a range of B-spline orders. We also demonstrate the feasibility of domain-informed interpolation in a neuroimaging application where the domain information is available by a complementary image contrast. The results show the benefit of incorporating domain knowledge so that an interpolant consistent to the anatomy of the brain is obtained.

eess.SP↗

arXiv2019

Agito ergo sum: correlates of spatiotemporal motion characteristics during fMRI

The impact of in-scanner motion on functional magnetic resonance imaging (fMRI) data has a notorious reputation in the neuroimaging community. State-ofthe-art guidelines advise to scrub out excessively corrupted frames as assessed by a composite framewise displacement (FD) score, to regress out models of nuisance variables, and to include average FD as a covariate in group-level analyses. Here, we studied individual motion time courses at time points typically retained in fMRI analyses. We observed that even in this set of putatively clean time points, motion exhibited a very clear spatiotemporal structure, so that we could distinguish subjects into four groups of movers with varying characteristics Then, we showed that this spatiotemporal motion cartography tightly relates to a broad array of anthropometric, behavioral and clinical factors. Convergent results were obtained from two different analytical perspectives: univariate assessment of behavioral differences across mover subgroups unraveled defining markers, while subsequent multivariate analysis broadened the range of involved factors and clarified that multiple motion/behavior modes of covariance overlap in the data. Our results demonstrate that even the smaller episodes of motion typically retained in fMRI analyses carry structured, behaviorally relevant information. They call for further examinations of possible biases in current regression-based motion correction strategies.

q-bio.NC↗

arXiv2019

Guided Graph Spectral Embedding: Application to the C. elegans Connectome

Graph spectral analysis can yield meaningful embeddings of graphs by providing insight into distributed features not directly accessible in nodal domain. Recent efforts in graph signal processing have proposed new decompositions-e.g., based on wavelets and Slepians-that can be applied to filter signals defined on the graph. In this work, we take inspiration from these constructions to define a new guided spectral embedding that combines maximizing energy concentration with minimizing modified embedded distance for a given importance weighting of the nodes. We show these optimization goals are intrinsically opposite, leading to a well-defined and stable spectral decomposition. The importance weighting allows to put the focus on particular nodes and tune the trade-off between global and local effects. Following the derivation of our new optimization criterion and its linear approximation, we exemplify the methodology on the C. elegans structural connectome. The results of our analyses confirm known observations on the nematode's neural network in terms of functionality and importance of cells. Compared to Laplacian embedding, the guided approach, focused on a certain class of cells (sensory, inter- and motoneurons), provides more biological insights, such as the distinction between somatic positions of cells, and their involvement in low or high order processing functions.

cs.LG↗