The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICA

We consider the problem of recovering a common latent source with independent components from multiple views. This applies to settings in which a variable is measured with multiple experimental modalities, and where the goal is to synthesize the disparate measurements into a single unified representation. We consider the case that the observed views are a nonlinear mixing of component-wise corruptions of the sources. When the views are considered separately, this reduces to nonlinear Independent Component Analysis (ICA) for which it is provably impossible to undo the mixing. We present novel identifiability proofs that this is possible when the multiple views are considered jointly, showing that the mixing can theoretically be undone using function approximators such as deep neural networks. In contrast to known identifiability results for nonlinear ICA, we prove that independent latent sources with arbitrary mixing can be recovered as long as multiple, sufficiently different noisy views are available

Modelling of the switching behavior of functional connectivity microstates (FCμstates) as a novel biomarker for mild cognitive impairment

It is evident the need for designing and validating novel biomarkers for the detection of mild cognitive impairment (MCI). MCI patients have a high risk of developing Alzheimer’s disease (AD), and for that reason the introduction of novel and reliable biomarkers is of significant clinical importance. Motivated by recent findings about the rich information of dynamic functional connectivity graphs (DFCGs) about brain (dys)function, we introduced a novel approach of identifying MCI based on magnetoencephalographic (MEG) resting state recordings. The activity of different brain rhythms {δ, θ, α1, α2, β1, β2, γ1, γ2} was first beamformed with linear constrained minimum norm variance in the MEG data to determine ninety anatomical regions of interest (ROIs). A dynamic functional connectivity graph (DFCG) was then estimated using the imaginary part of phase lag value (iPLV) for both intra-frequency coupling (8) and also cross-frequency coupling pairs (28). We analysed DFCG profiles of neuromagnetic resting state recordings of 18 Mild Cognitive Impairment (MCI) patients and 20 healthy controls. We followed our model of identifying the dominant intrinsic coupling mode (DICM) across MEG sources and temporal segments that further leads to the construction of an integrated DFCG (iDFCG). We then filtered statistically and topologically every snapshot of the iDFCG with data-driven approaches. Estimation of the normalized Laplacian transformation for every temporal segment of the iDFCG and the related eigenvalues created a 2D map based on the network metric time series of the eigenvalues (NMTSeigs). NMTSeigs preserves the non-stationarity of the fluctuated synchronizability of iDCFG for each subject. Employing the initial set of 20 healthy elders and 20 MCI patients, as training set, we built an overcomplete dictionary set of network microstates (nμstates). Afterward, we tested the whole procedure in an extra blind set of 20 subjects for external validation. We succeeded a high classification accuracy on the blind dataset (85 %) which further supports the proposed Markovian modelling of the evolution of brain states. The adaptation of appropriate neuroinformatic tools that combine advanced signal processing and network neuroscience tools could manipulate properly the non-stationarity of time-resolved FC patterns revealing a robust biomarker for MCI

Distortion-Tolerant Communications with Correlated Information

This dissertation is devoted to the development of distortion-tolerant communication techniques by exploiting the spatial and/or temporal correlation in a broad range of wireless communication systems under various system configurations. Signals observed in wireless communication systems are often correlated in the spatial and/or temporal domains, and the correlation can be used to facilitate system designs and to improve system performance. First, the optimum node density, i.e., the optimum number of nodes in a unit area, is identified by utilizing the spatial data correlation in the one- and two-dimensional wireless sensor networks (WSNs), under the constraint of fixed power per unit area. The WSNs distortion is quantized as the mean square error between the original and the reconstructed signals. Then we extend the analysis into WSNs with spatial-temporally correlated data. The optimum sampling in the space and time domains is derived. The analytical optimum results can provide insights and guidelines on the design of practical WSNs. Second, distributed source coding schemes are developed by exploiting the data correlation in a wireless network with spatially distributed sources. A new symmetric distributed joint source-channel coding scheme (DJSCC) is proposed by utilizing the spatial source correlation. Then the DJSCC code is applied to spatial-temporally correlated sources. The temporal correlated data is modeled as the Markov chain. Correspondingly, two decoding algorithms are proposed. The first multi-codeword message passing algorithm (MCMP) is designed for spatially correlated memoryless sources. In the second algorithm, a hidden Markov decoding process is added to the MCMP decoder to effectively exploit the data correlation in both the space and time domains. Third, we develop distortion-tolerant high mobility wireless communication systems by considering correlated channel state information (CSI) in the time domain, and study the optimum designs with imperfect CSI. The pilot-assisted channel estimation mean square error is expressed as a closed-form expression of various system parameters through asymptotic analysis. Based on the statistical properties of the channel estimation error, we quantify the impacts of imperfect CSI on system performance by developing the analytical symbol error rate and a spectral efficiency lower bound of the communication system

Reduced Complexity Sequential Monte Carlo Algorithms for Blind Receivers

Monte Carlo algorithms can be used to estimate the state of a system given relative observations. In this dissertation, these algorithms are applied to physical layer communications system models to estimate channel state information, to obtain soft information about transmitted symbols or multiple access interference, or to obtain estimates of all of these by joint estimation. Initially, we develop and analyze a multiple access technique utilizing mutually orthogonal complementary sets (MOCS) of sequences. These codes deliberately introduce inter-chip interference, which is naturally eliminated during processing at the receiver. However, channel impairments can destroy their orthogonality properties and additional processing becomes necessary. We utilize Monte Carlo algorithms to perform joint channel and symbol estimation for systems utilizing MOCS sequences as spreading codes. We apply Rao-Blackwellization to reduce the required number of particles. However, dense signaling constellations, multiuser environments, and the interchannel interference introduced by the spreading codes all increase the dimensionality of the symbol state space significantly. A full maximum likelihood solution is computationally expensive and generally not practical. However, obtaining the optimum solution is critical, and looking at only a part of the symbol space is generally not a good solution. We have sought algorithms that would guarantee that the correct transmitted symbol is considered, while only sampling a portion of the full symbol space. The performance of the proposed method is comparable to the Maximum Likelihood (ML) algorithm. While the computational complexity of ML increases exponentially with the dimensionality of the problem, the complexity of our approach increases only quadratically. Markovian structures such as the one imposed by MOCS spreading sequences can be seen in other physical layer structures as well. We have applied this partitioning approach with some modification to blind equalization of frequency selective fading channel and to multiple-input multiple output receivers that track channel changes. Additionally, we develop a method that obtains a metric for quantifying the convergence rate of Monte Carlo algorithms. Our approach yields an eigenvalue based method that is useful in identifying sources of slow convergence and estimation inaccuracy.Ph.D.Committee Chair: Douglas B. Williams; Committee Member: Brani Vidakovic; Committee Member: G. Tong zhou; Committee Member: Gordon Stuber; Committee Member: James H. McClella

ERP source tracking and localization from single trial EEG MEG signals

Electroencephalography (EEG) and magnetoencephalography (MEG), which are two of a number of neuroimaging techniques, are scalp recordings of the electrical activity of the brain. EEG and MEG (E/MEG) have excellent temporal resolution, they are easy to acquire, and have a wide range of applications in science, medicine and engineering. These valuable signals, however, suffer from poor spatial resolution and in many cases from very low signal to noise ratios. In this study, new computational methods for analyzing and improving the quality of E/MEG signals are presented. We mainly focus on single trial event-related potential (ERP) estimation and E/MEG dipole source localization. Several methods basically based on particle filtering (PF) are proposed. First, a method using PF for single trial estimation of ERP signals is considered. In this method, the wavelet coefficients of each ERP are assumed to be a Markovian process and do not change extensively across trials. The wavelet coefficients are then estimated recursively using PF. The results both for simulations and real data are compared with those of the well known Kalman Filtering (KF) approach. In the next method we move from single trial estimation to source localization of E/MEG signals. The beamforming (BF) approach for dipole source localization is generalized based on prior information about the noise. BF is in fact a spatial filter that minimizes the power of all the signals at the output of the filter except those that come from the locations of interest. In the proposed method, using two more constraints than in the classical BF formulation, the output noise powers are minimized and the interference activities are stopped.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Signal separation of musical instruments: simulation-based methods for musical signal decomposition and transcription

This thesis presents techniques for the modelling of musical signals, with particular regard to monophonic and polyphonic pitch estimation. Musical signals are modelled as a set of notes, each comprising of a set of harmonically-related sinusoids. An hierarchical model is presented that is very general and applicable to any signal that can be decomposed as the sum of basis functions. Parameter estimation is posed within a Bayesian framework, allowing for the incorporation of prior information about model parameters. The resulting posterior distribution is of variable dimension and so reversible jump MCMC simulation techniques are employed for the parameter estimation task. The extension of the model to time-varying signals with high posterior correlations between model parameters is described. The parameters and hyperparameters of several frames of data are estimated jointly to achieve a more robust detection. A general model for the description of time-varying homogeneous and heterogeneous multiple component signals is developed, and then applied to the analysis of musical signals. The importance of high level musical and perceptual psychological knowledge in the formulation of the model is highlighted, and attention is drawn to the limitation of pure signal processing techniques for dealing with musical signals. Gestalt psychological grouping principles motivate the hierarchical signal model, and component identifiability is considered in terms of perceptual streaming where each component establishes its own context. A major emphasis of this thesis is the practical application of MCMC techniques, which are generally deemed to be too slow for many applications. Through the design of efficient transition kernels highly optimised for harmonic models, and by careful choice of assumptions and approximations, implementations approaching the order of realtime are viable.Engineering and Physical Sciences Research Counci

ERP source tracking and localization from single trial EEG MEG signals

Electroencephalography (EEG) and magnetoencephalography (MEG), which are two of a number of neuroimaging techniques, are scalp recordings of the electrical activity of the brain. EEG and MEG (E/MEG) have excellent temporal resolution, they are easy to acquire, and have a wide range of applications in science, medicine and engineering. These valuable signals, however, suffer from poor spatial resolution and in many cases from very low signal to noise ratios. In this study, new computational methods for analyzing and improving the quality of E/MEG signals are presented. We mainly focus on single trial event-related potential (ERP) estimation and E/MEG dipole source localization. Several methods basically based on particle filtering (PF) are proposed. First, a method using PF for single trial estimation of ERP signals is considered. In this method, the wavelet coefficients of each ERP are assumed to be a Markovian process and do not change extensively across trials. The wavelet coefficients are then estimated recursively using PF. The results both for simulations and real data are compared with those of the well known Kalman Filtering (KF) approach. In the next method we move from single trial estimation to source localization of E/MEG signals. The beamforming (BF) approach for dipole source localization is generalized based on prior information about the noise. BF is in fact a spatial filter that minimizes the power of all the signals at the output of the filter except those that come from the locations of interest. In the proposed method, using two more constraints than in the classical BF formulation, the output noise powers are minimized and the interference activities are stopped