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

Improved physiological noise regression in fNIRS: a multimodal extension of the General Linear Model using temporally embedded Canonical Correlation Analysis

For the robust estimation of evoked brain activity from functional Near-Infrared Spectroscopy (fNIRS) signals, it is crucial to reduce nuisance signals from systemic physiology and motion. The current best practice incorporates short-separation (SS) fNIRS measurements as regressors in a General Linear Model (GLM). However, several challenging signal characteristics such as non-instantaneous and non-constant coupling are not yet addressed by this approach and additional auxiliary signals are not optimally exploited. We have recently introduced a new methodological framework for the unsupervised multivariate analysis of fNIRS signals using Blind Source Separation (BSS) methods. Building onto the framework, in this manuscript we show how to incorporate the advantages of regularized temporally embedded Canonical Correlation Analysis (tCCA) into the supervised GLM. This approach allows flexible integration of any number of auxiliary modalities and signals. We provide guidance for the selection of optimal parameters and auxiliary signals for the proposed GLM extension. Its performance in the recovery of evoked HRFs is then evaluated using both simulated ground truth data and real experimental data and compared with the GLM with short-separation regression. Our results show that the GLM with tCCA significantly improves upon the current best practice, yielding significantly better results across all applied metrics: Correlation (HbO max. +45%), Root Mean Squared Error (HbO max. -55%), F-Score (HbO up to 3.25-fold) and p-value as well as power spectral density of the noise floor. The proposed method can be incorporated into the GLM in an easily applicable way that flexibly combines any available auxiliary signals into optimal nuisance regressors. This work has potential significance both for conventional neuroscientific fNIRS experiments as well as for emerging applications of fNIRS in everyday environments, medicine and BCI, where high Contrast to Noise Ratio is of importance for single trial analysis.Published versio

Assisted Dictionary Learning for fMRI Data Analysis

Extracting information from functional magnetic resonance (fMRI) images has been a major area of research for more than two decades. The goal of this work is to present a new method for the analysis of fMRI data sets, that is capable to incorporate a priori available information, via an efficient optimization framework. Tests on synthetic data sets demonstrate significant performance gains over existing methods of this kind.Comment: 5 pages, 2 figure

Early soft and flexible fusion of electroencephalography and functional magnetic resonance imaging via double coupled matrix tensor factorization for multisubject group analysis

Data fusion refers to the joint analysis of multiple datasets that provide different (e.g., complementary) views of the same task. In general, it can extract more information than separate analyses can. Jointly analyzing electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) measurements has been proved to be highly beneficial to the study of the brain function, mainly because these neuroimaging modalities have complementary spatiotemporal resolution: EEG offers good temporal resolution while fMRI is better in its spatial resolution. The EEG–fMRI fusion methods that have been reported so far ignore the underlying multiway nature of the data in at least one of the modalities and/or rely on very strong assumptions concerning the relation of the respective datasets. For example, in multisubject analysis, it is commonly assumed that the hemodynamic response function is a priori known for all subjects and/or the coupling across corresponding modes is assumed to be exact (hard). In this article, these two limitations are overcome by adopting tensor models for both modalities and by following soft and flexible coupling approaches to implement the multimodal fusion. The obtained results are compared against those of parallel independent component analysis and hard coupling alternatives, with both synthetic and real data (epilepsy and visual oddball paradigm). Our results demonstrate the clear advantage of using soft and flexible coupled tensor decompositions in scenarios that do not conform with the hard coupling assumption

Deconvolution of the Functional Ultrasound Response in the Mouse Visual Pathway Using Block-Term Decomposition

Functional ultrasound (fUS) indirectly measures brain activity by recording changes in cerebral blood volume and flow in response to neural activation. Conventional approaches model such functional neuroimaging data as the convolution between an impulse response, known as the hemodynamic response function (HRF), and a binarized representation of the input (i.e., source) signal based on the stimulus onsets, the so-called experimental paradigm (EP). However, the EP may not be enough to characterize the whole complexity of the underlying source signals that evoke the hemodynamic changes, such as in the case of spontaneous resting state activity. Furthermore, the HRF varies across brain areas and stimuli. To achieve an adaptable framework that can capture such dynamics and unknowns of the brain function, we propose a deconvolution method for multivariate fUS time-series that reveals both the region-specific HRFs, and the source signals that induce the hemodynamic responses in the studied regions. We start by modeling the fUS time-series as convolutive mixtures and use a tensor-based approach for deconvolution based on two assumptions: (1) HRFs are parametrizable, and (2) source signals are uncorrelated. We test our approach on fUS data acquired during a visual experiment on a mouse subject, focusing on three regions within the mouse brain's colliculo-cortical, image-forming pathway: the lateral geniculate nucleus, superior colliculus and visual cortex. The estimated HRFs in each region are in agreement with prior works, whereas the estimated source signal is observed to closely follow the EP. Yet, we note a few deviations from the EP in the estimated source signal that most likely arise due to the trial-by-trial variability of the neural response across different repetitions of the stimulus observed in the selected regions