An Information Theoretic Condition for Perfect Reconstruction.

A new information theoretic condition is presented for reconstructing a discrete random variable X based on the knowledge of a set of discrete functions of X. The reconstruction condition is derived from Shannon's 1953 lattice theory with two entropic metrics of Shannon and Rajski. Because such a theoretical material is relatively unknown and appears quite dispersed in different references, we first provide a synthetic description (with complete proofs) of its concepts, such as total, common, and complementary information. The definitions and properties of the two entropic metrics are also fully detailed and shown to be compatible with the lattice structure. A new geometric interpretation of such a lattice structure is then investigated, which leads to a necessary (and sometimes sufficient) condition for reconstructing the discrete random variable X given a set {X1,…,Xn} of elements in the lattice generated by X. Intuitively, the components X1,…,Xn of the original source of information X should not be globally "too far away" from X in the entropic distance in order that X is reconstructable. In other words, these components should not overall have too low of a dependence on X; otherwise, reconstruction is impossible. These geometric considerations constitute a starting point for a possible novel "perfect reconstruction theory", which needs to be further investigated and improved along these lines. Finally, this condition is illustrated in five specific examples of perfect reconstruction problems: the reconstruction of a symmetric random variable from the knowledge of its sign and absolute value, the reconstruction of a word from a set of linear combinations, the reconstruction of an integer from its prime signature (fundamental theorem of arithmetic) and from its remainders modulo a set of coprime integers (Chinese remainder theorem), and the reconstruction of the sorting permutation of a list from a minimal set of pairwise comparisons.

Impact of dataset size and long-term ECoG-based BCI usage on deep learning decoders performance.

Introduction: In brain-computer interfaces (BCI) research, recording data is time-consuming and expensive, which limits access to big datasets. This may influence the BCI system performance as machine learning methods depend strongly on the training dataset size. Important questions arise: taking into account neuronal signal characteristics (e.g., non-stationarity), can we achieve higher decoding performance with more data to train decoders? What is the perspective for further improvement with time in the case of long-term BCI studies? In this study, we investigated the impact of long-term recordings on motor imagery decoding from two main perspectives: model requirements regarding dataset size and potential for patient adaptation. Methods: We evaluated the multilinear model and two deep learning (DL) models on a long-term BCI & Tetraplegia (ClinicalTrials.gov identifier: NCT02550522) clinical trial dataset containing 43 sessions of ECoG recordings performed with a tetraplegic patient. In the experiment, a participant executed 3D virtual hand translation using motor imagery patterns. We designed multiple computational experiments in which training datasets were increased or translated to investigate the relationship between models' performance and different factors influencing recordings. Results: Our results showed that DL decoders showed similar requirements regarding the dataset size compared to the multilinear model while demonstrating higher decoding performance. Moreover, high decoding performance was obtained with relatively small datasets recorded later in the experiment, suggesting motor imagery patterns improvement and patient adaptation during the long-term experiment. Finally, we proposed UMAP embeddings and local intrinsic dimensionality as a way to visualize the data and potentially evaluate data quality. Discussion: DL-based decoding is a prospective approach in BCI which may be efficiently applied with real-life dataset size. Patient-decoder co-adaptation is an important factor to consider in long-term clinical BCI.

Decoding ECoG signal into 3D hand translation using deep learning.

Objective.Motor brain-computer interfaces (BCIs) are a promising technology that may enable motor-impaired people to interact with their environment. BCIs would potentially compensate for arm and hand function loss, which is the top priority for individuals with tetraplegia. Designing real-time and accurate BCI is crucial to make such devices useful, safe, and easy to use by patients in a real-life environment. Electrocorticography (ECoG)-based BCIs emerge as a good compromise between invasiveness of the recording device and good spatial and temporal resolution of the recorded signal. However, most ECoG signal decoders used to predict continuous hand movements are linear models. These models have a limited representational capacity and may fail to capture the relationship between ECoG signal features and continuous hand movements. Deep learning (DL) models, which are state-of-the-art in many problems, could be a solution to better capture this relationship.Approach.In this study, we tested several DL-based architectures to predict imagined 3D continuous hand translation using time-frequency features extracted from ECoG signals. The dataset used in the analysis is a part of a long-term clinical trial (ClinicalTrials.gov identifier: NCT02550522) and was acquired during a closed-loop experiment with a tetraplegic subject. The proposed architectures include multilayer perceptron, convolutional neural networks (CNNs), and long short-term memory networks (LSTM). The accuracy of the DL-based and multilinear models was compared offline using cosine similarity.Main results.Our results show that CNN-based architectures outperform the current state-of-the-art multilinear model. The best architecture exploited the spatial correlation between neighboring electrodes with CNN and benefited from the sequential character of the desired hand trajectory by using LSTMs. Overall, DL increased the average cosine similarity, compared to the multilinear model, by up to 60%, from 0.189 to 0.302 and from 0.157 to 0.249 for the left and right hand, respectively.Significance.This study shows that DL-based models could increase the accuracy of BCI systems in the case of 3D hand translation prediction in a tetraplegic subject.

A corrected likelihood approach for the nonlinear transformation model with application to fluorescence lifetime measurements using exponential mixtures.

A fast and efficient estimation method is proposed that compensates the distortion in nonlinear transformation models. A likelihood-based estimator is developed that can be computed by an EM-type algorithm. The consistency of the estimator is shown and its limit distribution is provided. The new estimator is particularly well suited for fluorescence lifetime measurements, where only the shortest arrival time of a random number of emitted fluorescence photons can be detected and where arrival times are often modeled by a mixture of exponential distributions. The method is evaluated on real and synthetic data. Compared to currently used methods in fluorescence, the new estimator should allow a reduction of the acquisition time of an order of magnitude.

Comparison of eight methods for the estimation of the image-derived input function in dynamic [(18)F]-FDG PET human brain studies.

The aim of this study was to compare eight methods for the estimation of the image-derived input function (IDIF) in [(18)F]-FDG positron emission tomography (PET) dynamic brain studies. The methods were tested on two digital phantoms and on four healthy volunteers. Image-derived input functions obtained with each method were compared with the reference input functions, that is, the activity in the carotid labels of the phantoms and arterial blood samples for the volunteers, in terms of visual inspection, areas under the curve, cerebral metabolic rates of glucose (CMRglc), and individual rate constants. Blood-sample-free methods provided less reliable results as compared with those obtained using the methods that require the use of blood samples. For some of the blood-sample-free methods, CMRglc estimations considerably improved when the IDIF was calibrated with a single blood sample. Only one of the methods tested in this study, and only in phantom studies, allowed a reliable calculation of the individual rate constants. For the estimation of CMRglc values using an IDIF in [(18)F]-FDG PET brain studies, a reliable absolute blood-sample-free procedure is not available yet.

xDAWN algorithm to enhance evoked potentials: application to brain-computer interface.

A brain-computer interface (BCI) is a communication system that allows to control a computer or any other device thanks to the brain activity. The BCI described in this paper is based on the P300 speller BCI paradigm introduced by Farwell and Donchin . An unsupervised algorithm is proposed to enhance P300 evoked potentials by estimating spatial filters; the raw EEG signals are then projected into the estimated signal subspace. Data recorded on three subjects were used to evaluate the proposed method. The results, which are presented using a Bayesian linear discriminant analysis classifier , show that the proposed method is efficient and accurate.

Subspace estimation approach to P300 detection and application to brain-computer interface.

Brain-computer interface (BCI) is a system for direct communication between brain and computer. In this work, a new unsupervised algorithm is introduced for P300 subspace estimation: the raw EEG are thus enhanced by projection on the estimated subspace. Moreover a simple scheme to detect the P300 potentials in the human EEG by dimension reduction and linear support vector machine (SVM) is proposed to build a BCI based on the P300 speller. The proposed algorithm is finally tested with dataset from the BCI Competition 2003 and gives results that compare favourably to the state of the art.

Topographical dynamics of brain connections for the design of asynchronous brain-computer interfaces.

This article presents a new processing method to design brain-computer interfaces (BCIs). It shows how to use the perturbations of the communication between different cortical areas due to a cognitive task. For this, the network of the cerebral connections is built from correlations between cortical areas at specific frequencies and is analyzed using graph theory. This allows us to describe the topological organisation of the networks using quantitative measures. This method is applied to an auditive steady-state evoked potentials experiment (dichotic binaural listening) and compared to a more classical method based on spectral filtering.