Tensor Analysis and Fusion of Multimodal Brain Images

Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data fusion. A case in point is the attempt to parse out the brain structures and networks that underpin human cognitive processes by analysis of different neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the multimodal, multi-scale nature of neuroimaging data is well reflected by a multi-way (tensor) structure where the underlying processes can be summarized by a relatively small number of components or "atoms". We introduce Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network notation in order to analyze these models. These diagrams not only clarify matrix and tensor EEG and fMRI time/frequency analysis and inverse problems, but also help understand multimodal fusion via Multiway Partial Least Squares and Coupled Matrix-Tensor Factorization. We show here, for the first time, that Granger causal analysis of brain networks is a tensor regression problem, thus allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI recordings shows the potential of the methods and suggests their use in other scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE

Non-negative data-driven mapping of structural connections with application to the neonatal brain

© 2020 Mapping connections in the neonatal brain can provide insight into the crucial early stages of neurodevelopment that shape brain organisation and lay the foundations for cognition and behaviour. Diffusion MRI and tractography provide unique opportunities for such explorations, through estimation of white matter bundles and brain connectivity. Atlas-based tractography protocols, i.e. a priori defined sets of masks and logical operations in a template space, have been commonly used in the adult brain to drive such explorations. However, rapid growth and maturation of the brain during early development make it challenging to ensure correspondence and validity of such atlas-based tractography approaches in the developing brain. An alternative can be provided by data-driven methods, which do not depend on predefined regions of interest. Here, we develop a novel data-driven framework to extract white matter bundles and their associated grey matter networks from neonatal tractography data, based on non-negative matrix factorisation that is inherently suited to the non-negative nature of structural connectivity data. We also develop a non-negative dual regression framework to map group-level components to individual subjects. Using in-silico simulations, we evaluate the accuracy of our approach in extracting connectivity components and compare with an alternative data-driven method, independent component analysis. We apply non-negative matrix factorisation to whole-brain connectivity obtained from publicly available datasets from the Developing Human Connectome Project, yielding grey matter components and their corresponding white matter bundles. We assess the validity and interpretability of these components against traditional tractography results and grey matter networks obtained from resting-state fMRI in the same subjects. We subsequently use them to generate a parcellation of the neonatal cortex using data from 323 new-born babies and we assess the robustness and reproducibility of this connectivity-driven parcellation

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field