A Sparse Reduced Rank Framework for Group Analysis of Functional Neuroimaging Data

In spatial-temporal neuroimaging studies, there is an evolving literature on the analysis of functional imaging data in order to learn the intrinsic functional connectivity patterns among different brain regions. However, there are only few efficient approaches for integrating functional connectivity pattern across subjects, while accounting for spatial-temporal functional variation across multiple groups of subjects. The objective of this paper is to develop a new sparse reduced rank (SRR) modeling framework for carrying out functional connectivity analysis across multiple groups of subjects in the frequency domain. Our new framework not only can extract both frequency and spatial factors across subjects, but also imposes sparse constraints on the frequency factors. It thus leads to the identification of important frequencies with high power spectra. In addition, we propose two novel adaptive criteria for automatic selection of sparsity level and model rank. Using simulated data, we demonstrate that SRR outperforms several existing methods. Finally, we apply SRR to detect group differences between controls and two subtypes of attention deficit hyperactivity disorder (ADHD) patients, through analyzing the ADHD-200 data.published_or_final_versio

Image Restoration

This book represents a sample of recent contributions of researchers all around the world in the field of image restoration. The book consists of 15 chapters organized in three main sections (Theory, Applications, Interdisciplinarity). Topics cover some different aspects of the theory of image restoration, but this book is also an occasion to highlight some new topics of research related to the emergence of some original imaging devices. From this arise some real challenging problems related to image reconstruction/restoration that open the way to some new fundamental scientific questions closely related with the world we interact with

System approach to robust acoustic echo cancellation through semi-blind source separation based on independent component analysis

We live in a dynamic world full of noises and interferences. The conventional acoustic echo cancellation (AEC) framework based on the least mean square (LMS) algorithm by itself lacks the ability to handle many secondary signals that interfere with the adaptive filtering process, e.g., local speech and background noise. In this dissertation, we build a foundation for what we refer to as the system approach to signal enhancement as we focus on the AEC problem. We first propose the residual echo enhancement (REE) technique that utilizes the error recovery nonlinearity (ERN) to "enhances" the filter estimation error prior to the filter adaptation. The single-channel AEC problem can be viewed as a special case of semi-blind source separation (SBSS) where one of the source signals is partially known, i.e., the far-end microphone signal that generates the near-end acoustic echo. SBSS optimized via independent component analysis (ICA) leads to the system combination of the LMS algorithm with the ERN that allows for continuous and stable adaptation even during double talk. Second, we extend the system perspective to the decorrelation problem for AEC, where we show that the REE procedure can be applied effectively in a multi-channel AEC (MCAEC) setting to indirectly assist the recovery of lost AEC performance due to inter-channel correlation, known generally as the "non-uniqueness" problem. We develop a novel, computationally efficient technique of frequency-domain resampling (FDR) that effectively alleviates the non-uniqueness problem directly while introducing minimal distortion to signal quality and statistics. We also apply the system approach to the multi-delay filter (MDF) that suffers from the inter-block correlation problem. Finally, we generalize the MCAEC problem in the SBSS framework and discuss many issues related to the implementation of an SBSS system. We propose a constrained batch-online implementation of SBSS that stabilizes the convergence behavior even in the worst case scenario of a single far-end talker along with the non-uniqueness condition on the far-end mixing system. The proposed techniques are developed from a pragmatic standpoint, motivated by real-world problems in acoustic and audio signal processing. Generalization of the orthogonality principle to the system level of an AEC problem allows us to relate AEC to source separation that seeks to maximize the independence, hence implicitly the orthogonality, not only between the error signal and the far-end signal, but rather, among all signals involved. The system approach, for which the REE paradigm is just one realization, enables the encompassing of many traditional signal enhancement techniques in analytically consistent yet practically effective manner for solving the enhancement problem in a very noisy and disruptive acoustic mixing environment.PhDCommittee Chair: Biing-Hwang Juang; Committee Member: Brani Vidakovic; Committee Member: David V. Anderson; Committee Member: Jeff S. Shamma; Committee Member: Xiaoli M

PARALLEL INDEPENDENT COMPONENT ANALYSIS WITH REFERENCE FOR IMAGING GENETICS: A SEMI-BLIND MULTIVARIATE APPROACH

Imaging genetics is an emerging field dedicated to the study of genetic underpinnings of brain structure and function. Over the last decade, brain imaging techniques such as magnetic resonance imaging (MRI) have been increasingly applied to measure morphometry, task-based function and connectivity in living brains. Meanwhile, high-throughput genotyping employing genome-wide techniques has made it feasible to sample the entire genome of a substantial number of individuals. While there is growing interest in image-wide and genome-wide approaches which allow unbiased searches over a large range of variants, one of the most challenging problems is the correction for the huge number of statistical tests used in univariate models. In contrast, a reference-guided multivariate approach shows specific advantage for simultaneously assessing many variables for aggregate effects while leveraging prior information. It can improve the robustness of the results compared to a fully blind approach. In this dissertation we present a semi-blind multivariate approach, parallel independent component analysis with reference (pICA-R), to better reveal relationships between hidden factors of particular attributes. First, a consistency-based order estimation approach is introduced to advance the application of ICA to genotype data. The pICA-R approach is then presented, where independent components are extracted from two modalities in parallel and inter-modality associations are subsequently optimized for pairs of components. In particular, prior information is incorporated to elicit components of particular interests, which helps identify factors carrying small amounts of variance in large complex datasets. The pICA-R approach is further extended to accommodate multiple references whose interrelationships are unknown, allowing the investigation of functional influence on neurobiological traits of potentially related genetic variants implicated in biology. Applied to a schizophrenia study, pICA-R reveals that a complex genetic factor involving multiple pathways underlies schizophrenia-related gray matter deficits in prefrontal and temporal regions. The extended multi-reference approach, when employed to study alcohol dependence, delineates a complex genetic architecture, where the CREB-BDNF pathway plays a key role in the genetic factor underlying a proportion of variation in cue-elicited brain activations, which plays a role in phenotypic symptoms of alcohol dependence. In summary, our work makes several important contributions to advance the application of ICA to imaging genetics studies, which holds the promise to improve our understating of genetics underlying brain structure and function in healthy and disease

A Study of Resting State FMRI Dynamic Functional Network Analysis of MTBI

Mild Traumatic Brain Injury (MTBI) is one of the most common neurological disorders. A subset of patients develop persistent cognitive deficits. A number of the brain studies have been conducted to discover the abnormalities and disruptions in the brain functional networks using similar methods to those employed in more severe brain disorders such as Alzheimer's or Schizophrenia. Static functional network analysis using resting state brain fMRI images has shown some promising results in identifying characteristics of MTBI. However, recent development in the dynamics of functional networks have been able to reveal insightful information about anomalies in brain activities that have not been observed when using traditional static analysis. Our work focuses on both static and dynamic functional analysis of the brain. Our overall analysis pipeline is data-driven using a dataset of 47 MTBI subjects and a demographically matching healthy control group size of 30. The data-driven approach proactively removes noise, focuses on the entire brain functional networks and performs advanced independent component analysis, followed by statistical tests to characterize the functional networks of MTBI patients. A key distinction of our research is the finer labeling of MTBI subject according to their long term 6 months recovery status. Our results suggest that those MTBI subject who suffer prolonged recovery exhibit disturbed functional networks, and slowed dynamism in functional connectivity than those of the healthy control or those MTBI participants who recovered quickly. A number of useful network measurements have been found to capture the states and changes of the brain functional networks for healthy and different types of MTBI subjects in their resting state. We believe that our findings can shed more light into the impact of MTBI on the effectiveness of several functional networks and can contribute to helping clinicians make more informed decisions to aid in the recovery of MTBI patients

Data-Driven Image Restoration

Every day many images are taken by digital cameras, and people are demanding visually accurate and pleasing result. Noise and blur degrade images captured by modern cameras, and high-level vision tasks (such as segmentation, recognition, and tracking) require high-quality images. Therefore, image restoration specifically, image deblurring and image denoising is a critical preprocessing step. A fundamental problem in image deblurring is to recover reliably distinct spatial frequencies that have been suppressed by the blur kernel. Existing image deblurring techniques often rely on generic image priors that only help recover part of the frequency spectrum, such as the frequencies near the high-end. To this end, we pose the following specific questions: (i) Does class-specific information offer an advantage over existing generic priors for image quality restoration? (ii) If a class-specific prior exists, how should it be encoded into a deblurring framework to recover attenuated image frequencies? Throughout this work, we devise a class-specific prior based on the band-pass filter responses and incorporate it into a deblurring strategy. Specifically, we show that the subspace of band-pass filtered images and their intensity distributions serve as useful priors for recovering image frequencies. Next, we present a novel image denoising algorithm that uses external, category specific image database. In contrast to existing noisy image restoration algorithms, our method selects clean image “support patches” similar to the noisy patch from an external database. We employ a content adaptive distribution model for each patch where we derive the parameters of the distribution from the support patches. Our objective function composed of a Gaussian fidelity term that imposes category specific information, and a low-rank term that encourages the similarity between the noisy and the support patches in a robust manner. Finally, we propose to learn a fully-convolutional network model that consists of a Chain of Identity Mapping Modules (CIMM) for image denoising. The CIMM structure possesses two distinctive features that are important for the noise removal task. Firstly, each residual unit employs identity mappings as the skip connections and receives pre-activated input to preserve the gradient magnitude propagated in both the forward and backward directions. Secondly, by utilizing dilated kernels for the convolution layers in the residual branch, each neuron in the last convolution layer of each module can observe the full receptive field of the first layer

Novel multiscale methods for nonlinear speech analysis

Cette thèse présente une recherche exploratoire sur l'application du Formalisme Microcanonique Multiéchelles (FMM) à l'analyse de la parole. Dérivé de principes issus en physique statistique, le FMM permet une analyse géométrique précise de la dynamique non linéaire des signaux complexes. Il est fondé sur l'estimation des paramètres géométriques locaux (les exposants de singularité) qui quantifient le degré de prédictibilité à chaque point du signal. Si correctement définis est estimés, ils fournissent des informations précieuses sur la dynamique locale de signaux complexes. Nous démontrons le potentiel du FMM dans l'analyse de la parole en développant: un algorithme performant pour la segmentation phonétique, un nouveau codeur, un algorithme robuste pour la détection précise des instants de fermeture glottale, un algorithme rapide pour l analyse par prédiction linéaire parcimonieuse et une solution efficace pour l approximation multipulse du signal source d'excitation.This thesis presents an exploratory research on the application of a nonlinear multiscale formalism, called the Microcanonical Multiscale Formalism (the MMF), to the analysis of speech signals. Derived from principles in Statistical Physics, the MMF allows accurate analysis of the nonlinear dynamics of complex signals. It relies on the estimation of local geometrical parameters, the singularity exponents (SE), which quantify the degree of predictability at each point of the signal domain. When correctly defined and estimated, these exponents can provide valuable information about the local dynamics of complex signals and has been successfully used in many applications ranging from signal representation to inference and prediction.We show the relevance of the MMF to speech analysis and develop several applications to show the strength and potential of the formalism. Using the MMF, in this thesis we introduce: a novel and accurate text-independent phonetic segmentation algorithm, a novel waveform coder, a robust accurate algorithm for detection of the Glottal Closure Instants, a closed-form solution for the problem of sparse linear prediction analysis and finally, an efficient algorithm for estimation of the excitation source signal.BORDEAUX1-Bib.electronique (335229901) / SudocSudocFranceF

Constrained Learning And Inference

Data and learning have become core components of the information processing and autonomous systems upon which we increasingly rely on to select job applicants, analyze medical data, and drive cars. As these systems become ubiquitous, so does the need to curtail their behavior. Left untethered, they are susceptible to tampering (adversarial examples) and prone to prejudiced and unsafe actions. Currently, the response of these systems is tailored by leveraging domain expert knowledge to either construct models that embed the desired properties or tune the training objective so as to promote them. While effective, these solutions are often targeted to specific behaviors, contexts, and sometimes even problem instances and are typically not transferable across models and applications. What is more, the growing scale and complexity of modern information processing and autonomous systems renders this manual behavior tuning infeasible. Already today, explainability, interpretability, and transparency combined with human judgment are no longer enough to design systems that perform according to specifications. The present thesis addresses these issues by leveraging constrained statistical optimization. More specifically, it develops the theoretical underpinnings of constrained learning and constrained inference to provide tools that enable solving statistical problems under requirements. Starting with the task of learning under requirements, it develops a generalization theory of constrained learning akin to the existing unconstrained one. By formalizing the concept of probability approximately correct constrained (PACC) learning, it shows that constrained learning is as hard as its unconstrained learning and establishes the constrained counterpart of empirical risk minimization (ERM) as a PACC learner. To overcome challenges involved in solving such non-convex constrained optimization problems, it derives a dual learning rule that enables constrained learning tasks to be tackled by through unconstrained learning problems only. It therefore concludes that if we can deal with classical, unconstrained learning tasks, then we can deal with learning tasks with requirements. The second part of this thesis addresses the issue of constrained inference. In particular, the issue of performing inference using sparse nonlinear function models, combinatorial constrained with quadratic objectives, and risk constraints. Such models arise in nonlinear line spectrum estimation, functional data analysis, sensor selection, actuator scheduling, experimental design, and risk-aware estimation. Although inference problems assume that models and distributions are known, each of these constraints pose serious challenges that hinder their use in practice. Sparse nonlinear functional models lead to infinite dimensional, non-convex optimization programs that cannot be discretized without leading to combinatorial, often NP-hard, problems. Rather than using surrogates and relaxations, this work relies on duality to show that despite their apparent complexity, these models can be fit efficiently, i.e., in polynomial time. While quadratic objectives are typically tractable (often even in closed form), they lead to non-submodular optimization problems when subject to cardinality or matroid constraints. While submodular functions are sometimes used as surrogates, this work instead shows that quadratic functions are close to submodular and can also be optimized near-optimally. The last chapter of this thesis is dedicated to problems involving risk constraints, in particular, bounded predictive mean square error variance estimation. Despite being non-convex, such problems are equivalent to a quadratically constrained quadratic program from which a closed-form estimator can be extracted. These results are used throughout this thesis to tackle problems in signal processing, machine learning, and control, such as fair learning, robust learning, nonlinear line spectrum estimation, actuator scheduling, experimental design, and risk-aware estimation. Yet, they are applicable much beyond these illustrations to perform safe reinforcement learning, sensor selection, multiresolution kernel estimation, and wireless resource allocation, to name a few