On the Determination of Lagrange Multipliers for a Weighted LASSO Problem Using Geometric and Convex Analysis Techniques.

Compressed Sensing (CS) encompasses a broad array of theoretical and applied techniques for recovering signals, given partial knowledge of their coefficients, cf. Candés (C. R. Acad. Sci. Paris, Ser. I 346, 589-592 (2008)), Candés et al. (IEEE Trans. Inf. Theo (2006)), Donoho (IEEE Trans. Inf. Theo. 52(4), (2006)), Donoho et al. (IEEE Trans. Inf. Theo. 52(1), (2006)). Its applications span various fields, including mathematics, physics, engineering, and several medical sciences, cf. Adcock and Hansen (Compressive Imaging: Structure, Sampling, Learning, p. 2021), Berk et al. (2019 13th International conference on Sampling Theory and Applications (SampTA) pp. 1-5. IEEE (2019)), Brady et al. (Opt. Express 17(15), 13040-13049 (2009)), Chan (Terahertz imaging with compressive sensing. Rice University, USA (2010)), Correa et al. (2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) pp. 7789-7793 (2014, May) IEEE), Gao et al. (Nature 516(7529), 74-77 (2014)), Liu and Kang (Opt. Express 18(21), 22010-22019 (2010)), McEwen and Wiaux (Mon. Notices Royal Astron. Soc. 413(2), 1318-1332 (2011)), Marim et al. (Opt. Lett. 35(6), 871-873 (2010)), Yu and Wang (Phys. Med. Biol. 54(9), 2791 (2009)), Yu and Wang (Phys. Med. Biol. 54(9), 2791 (2009)). Motivated by our interest in the mathematics behind Magnetic Resonance Imaging (MRI) and CS, we employ convex analysis techniques to analytically determine equivalents of Lagrange multipliers for optimization problems with inequality constraints, specifically a weighted LASSO with voxel-wise weighting. We investigate this problem under assumptions on the fidelity term Ax-b22, either concerning the sign of its gradient or orthogonality-like conditions of its matrix. To be more precise, we either require the sign of each coordinate of 2(Ax-b)TA to be fixed within a rectangular neighborhood of the origin, with the side lengths of the rectangle dependent on the constraints, or we assume ATA to be diagonal. The objective of this work is to explore the relationship between Lagrange multipliers and the constraints of a weighted variant of LASSO, specifically in the mentioned cases where this relationship can be computed explicitly. As they scale the regularization terms of the weighted LASSO, Lagrange multipliers serve as tuning parameters for the weighted LASSO, prompting the question of their potential effective use as tuning parameters in applications like MR image reconstruction and denoising. This work represents an initial step in this direction.

Learning and navigating digitally rendered haptic spatial layouts.

Learning spatial layouts and navigating through them rely not simply on sight but rather on multisensory processes, including touch. Digital haptics based on ultrasounds are effective for creating and manipulating mental images of individual objects in sighted and visually impaired participants. Here, we tested if this extends to scenes and navigation within them. Using only tactile stimuli conveyed via ultrasonic feedback on a digital touchscreen (i.e., a digital interactive map), 25 sighted, blindfolded participants first learned the basic layout of an apartment based on digital haptics only and then one of two trajectories through it. While still blindfolded, participants successfully reconstructed the haptically learned 2D spaces and navigated these spaces. Digital haptics were thus an effective means to learn and translate, on the one hand, 2D images into 3D reconstructions of layouts and, on the other hand, navigate actions within real spaces. Digital haptics based on ultrasounds represent an alternative learning tool for complex scenes as well as for successful navigation in previously unfamiliar layouts, which can likely be further applied in the rehabilitation of spatial functions and mitigation of visual impairments.

Hi-Fi fMRI: High-resolution, fast-sampled and sub-second whole-brain functional MRI at 3T in humans.

Functional magnetic resonance imaging (fMRI) is a methodological cornerstone of neuroscience. Most studies measure blood-oxygen-level-dependent (BOLD) signal using echo-planar imaging (EPI), Cartesian sampling, and image reconstruction with a one-to-one correspondence between the number of acquired volumes and reconstructed images. However, EPI schemes are subject to trade-offs between spatial and temporal resolutions. We overcome these limitations by measuring BOLD with a gradient recalled echo (GRE) with 3D radial-spiral phyllotaxis trajectory at a high sampling rate (28.24ms) on standard 3T field-strength. The framework enables the reconstruction of 3D signal time courses with whole-brain coverage at simultaneously higher spatial (1mm 3 ) and temporal (up to 250ms) resolutions, as compared to optimized EPI schemes. Additionally, artifacts are corrected before image reconstruction; the desired temporal resolution is chosen after scanning and without assumptions on the shape of the hemodynamic response. By showing activation in the calcarine sulcus of 20 participants performing an ON-OFF visual paradigm, we demonstrate the reliability of our method for cognitive neuroscience research.

Machine learning algorithms on eye tracking trajectories to classify patients with spatial neglect.

BACKGROUND AND OBJECTIVE: Eye-movement trajectories are rich behavioral data, providing a window on how the brain processes information. We address the challenge of characterizing signs of visuo-spatial neglect from saccadic eye trajectories recorded in brain-damaged patients with spatial neglect as well as in healthy controls during a visual search task. METHODS: We establish a standardized pre-processing pipeline adaptable to other task-based eye-tracker measurements. We use traditional machine learning algorithms together with deep convolutional networks (both 1D and 2D) to automatically analyze eye trajectories. RESULTS: Our top-performing machine learning models classified neglect patients vs. healthy individuals with an Area Under the ROC curve (AUC) ranging from 0.83 to 0.86. Moreover, the 1D convolutional neural network scores correlated with the degree of severity of neglect behavior as estimated with standardized paper-and-pencil tests and with the integrity of white matter tracts measured from Diffusion Tensor Imaging (DTI). Interestingly, the latter showed a clear correlation with the third branch of the superior longitudinal fasciculus (SLF), especially damaged in neglect. CONCLUSIONS: The study introduces new methods for both the pre-processing and the classification of eye-movement trajectories in patients with neglect syndrome. The proposed methods can likely be applied to other types of neurological diseases opening the possibility of new computer-aided, precise, sensitive and non-invasive diagnostic tools.

Topological Features of Electroencephalography are Robust to Re-referencing and Preprocessing.

Electroencephalography (EEG) is among the most widely diffused, inexpensive, and adopted neuroimaging techniques. Nonetheless, EEG requires measurements against a reference site(s), which is typically chosen by the experimenter, and specific pre-processing steps precede analyses. It is therefore valuable to obtain quantities that are minimally affected by reference and pre-processing choices. Here, we show that the topological structure of embedding spaces, constructed either from multi-channel EEG timeseries or from their temporal structure, are subject-specific and robust to re-referencing and pre-processing pipelines. By contrast, the shape of correlation spaces, that is, discrete spaces where each point represents an electrode and the distance between them that is in turn related to the correlation between the respective timeseries, was neither significantly subject-specific nor robust to changes of reference. Our results suggest that the shape of spaces describing the observed configurations of EEG signals holds information about the individual specificity of the underlying individual's brain dynamics, and that temporal correlations constrain to a large degree the set of possible dynamics. In turn, these encode the differences between subjects' space of resting state EEG signals. Finally, our results and proposed methodology provide tools to explore the individual topographical landscapes and how they are explored dynamically. We propose therefore to augment conventional topographic analyses with an additional-topological-level of analysis, and to consider them jointly. More generally, these results provide a roadmap for the incorporation of topological analyses within EEG pipelines.

Computational Models in Electroencephalography.

Computational models lie at the intersection of basic neuroscience and healthcare applications because they allow researchers to test hypotheses in silico and predict the outcome of experiments and interactions that are very hard to test in reality. Yet, what is meant by "computational model" is understood in many different ways by researchers in different fields of neuroscience and psychology, hindering communication and collaboration. In this review, we point out the state of the art of computational modeling in Electroencephalography (EEG) and outline how these models can be used to integrate findings from electrophysiology, network-level models, and behavior. On the one hand, computational models serve to investigate the mechanisms that generate brain activity, for example measured with EEG, such as the transient emergence of oscillations at different frequency bands and/or with different spatial topographies. On the other hand, computational models serve to design experiments and test hypotheses in silico. The final purpose of computational models of EEG is to obtain a comprehensive understanding of the mechanisms that underlie the EEG signal. This is crucial for an accurate interpretation of EEG measurements that may ultimately serve in the development of novel clinical applications.

3-Dimensional magnetic resonance imaging of the freely moving human eye.

Eye motion is a major confound for magnetic resonance imaging (MRI) in neuroscience or ophthalmology. Currently, solutions toward eye stabilisation include participants fixating or administration of paralytics/anaesthetics. We developed a novel MRI protocol for acquiring 3-dimensional images while the eye freely moves. Eye motion serves as the basis for image reconstruction, rather than an impediment. We fully reconstruct videos of the moving eye and head. We quantitatively validate data quality with millimetre resolution in two ways for individual participants. First, eye position based on reconstructed images correlated with simultaneous eye-tracking. Second, the reconstructed images preserve anatomical properties; the eye's axial length measured from MRI images matched that obtained with ocular biometry. The technique operates on a standard clinical setup, without necessitating specialized hardware, facilitating wide deployment. In clinical practice, we anticipate that this may help reduce burdens on both patients and infrastructure, by integrating multiple varieties of assessments into a single comprehensive session. More generally, our protocol is a harbinger for removing the necessity of fixation, thereby opening new opportunities for ethologically-valid, naturalistic paradigms, the inclusion of populations typically unable to stably fixate, and increased translational research such as in awake animals whose eye movements constitute an accessible behavioural readout.

Visual illusions via neural dynamics: Wilson-Cowan-type models and the efficient representation principle.

We reproduce suprathreshold perception phenomena, specifically visual illusions, by Wilson-Cowan (WC)-type models of neuronal dynamics. Our findings show that the ability to replicate the illusions considered is related to how well the neural activity equations comply with the efficient representation principle. Our first contribution consists in showing that the WC equations can reproduce a number of brightness and orientation-dependent illusions. Then we formally prove that there cannot be an energy functional that the WC dynamics are minimizing. This leads us to consider an alternative, variational modeling, which has been previously employed for local histogram equalization (LHE) tasks. To adapt our model to the architecture of V1, we perform an extension that has an explicit dependence on local image orientation. Finally, we report several numerical experiments showing that LHE provides a better reproduction of visual illusions than the original WC formulation, and that its cortical extension is capable also to reproduce complex orientation-dependent illusions.NEW & NOTEWORTHY We show that the Wilson-Cowan equations can reproduce a number of brightness and orientation-dependent illusions. Then we formally prove that there cannot be an energy functional that the Wilson-Cowan equations are minimizing, making them suboptimal with respect to the efficient representation principle. We thus propose a slight modification that is consistent with such principle and show that this provides a better reproduction of visual illusions than the original Wilson-Cowan formulation. We also consider the cortical extension of both models to deal with more complex orientation-dependent illusions.

A computational model for grid maps in neural populations.

Grid cells in the entorhinal cortex, together with head direction, place, speed and border cells, are major contributors to the organization of spatial representations in the brain. In this work we introduce a novel theoretical and algorithmic framework able to explain the optimality of hexagonal grid-like response patterns. We show that this pattern is a result of minimal variance encoding of neurons together with maximal robustness to neurons' noise and minimal number of encoding neurons. The novelty lies in the formulation of the encoding problem considering neurons as an overcomplete basis (a frame) where the position information is encoded. Through the modern Frame Theory language, specifically that of tight and equiangular frames, we provide new insights about the optimality of hexagonal grid receptive fields. The proposed model is based on the well-accepted and tested hypothesis of Hebbian learning, providing a simplified cortical-based framework that does not require the presence of velocity-driven oscillations (oscillatory model) or translational symmetries in the synaptic connections (attractor model). We moreover demonstrate that the proposed encoding mechanism naturally explains axis alignment of neighbor grid cells and maps shifts, rotations and scaling of the stimuli onto the shape of grid cells' receptive fields, giving a straightforward explanation of the experimental evidence of grid cells remapping under transformations of environmental cues.

Electroencephalography.

Electroencephalography (EEG) is the non-invasive measurement of the brain's electric fields. Electrodes placed on the scalp record voltage potentials resulting from current flow in and around neurons. EEG is nearly a century old: this long history has afforded EEG a rich and diverse spectrum of applications. On the one hand, foundations of EEG in clinical diagnostics have dovetailed more recently into brain-triggered neurorehabilitation treatments. On the other hand, EEG has not only been a workhorse for providing brain correlates of constructs in the field of experimental psychology, but has also been used as a true neuroimaging method with more recent extensions in translational as well as computational neuroscience. The versatility and accessibility of the technique, in combination with advances in signal processing, allow for this 'old dog' to still deliver new tricks and innovations.