abstract: Spotlight mode synthetic aperture radar (SAR) imaging involves a tomo- graphic reconstruction from projections, necessitating acquisition of large amounts of data in order to form a moderately sized image. Since typical SAR sensors are hosted on mobile platforms, it is common to have limitations on SAR data acquisi- tion, storage and communication that can lead to data corruption and a resulting degradation of image quality. It is convenient to consider corrupted samples as missing, creating a sparsely sampled aperture. A sparse aperture would also result from compressive sensing, which is a very attractive concept for data intensive sen- sors such as SAR. Recent developments in sparse decomposition algorithms can be applied to the problem of SAR image formation from a sparsely sampled aperture. Two modified sparse decomposition algorithms are developed, based on well known existing algorithms, modified to be practical in application on modest computa- tional resources. The two algorithms are demonstrated on real-world SAR images. Algorithm performance with respect to super-resolution, noise, coherent speckle and target/clutter decomposition is explored. These algorithms yield more accu- rate image reconstruction from sparsely sampled apertures than classical spectral estimators. At the current state of development, sparse image reconstruction using these two algorithms require about two orders of magnitude greater processing time than classical SAR image formation. / Dissertation/Thesis / M.S. Electrical Engineering 2011

L’électroencéphalographie permet de mesurer l’activité du cerveau à partir des variations du champ électrique à la surface du crâne. Cette mesure est utilisée pour le diagnostic médical, la compréhension du fonctionnement du cerveau ou dans les systèmes d’interface cerveau-machine. De nombreux travaux se sont attachés au développement de méthodes d’analyse de ces signaux en vue d’en extraire différentes composantes d’intérêt, néanmoins leur traitement pose encore de nombreux problèmes. Cette thèse s’intéresse à la mise en place de méthodes permettant l’obtention de représentations redondantes pour ces signaux. Ces représentations se sont avérées particulièrement efficaces ces dernières années pour la description de nombreuses classes de signaux grâce à leur grande flexibilité. L’obtention de telles représentations pour les mesures EEG présente certaines difficultés du fait d’un faible rapport signal à bruit des composantes recherchées. Nous proposons dans cette thèse de les surmonter en guidant les méthodes considérées vers des représentations physiologiquement plausibles des signaux EEG à l’aide de régularisations. Ces dernières sont construites à partir de connaissances a priori sur les propriétés spatiales et temporelles de ces signaux. Pour chacune d’entre elles, des algorithmes sont proposés afin de résoudre les problèmes d’optimisation associés à l’obtention de ces représentations. L’évaluation des approches proposées sur des signaux EEG souligne l’efficacité des régularisations proposées et l’intérêt des représentations obtenues. / The electroencephalography measures the brain activity by recording variations of the electric field on the surface of the skull. This measurement is usefull in various applications like medical diagnosis, analysis of brain functionning or whithin brain-computer interfaces. Numerous studies have tried to develop methods for analyzing these signals in order to extract various components of interest, however, none of them allows to extract them with sufficient reliabilty. This thesis focuses on the development of approaches considering redundant (overcomoplete) representations for these signals. During the last years, these representations have been shown particularly efficient to describe various classes of signals due to their flexibility. Obtaining such representations for EEG presents some difficuties due to the low signal-to-noise ratio of these signals. We propose in this study to overcome them by guiding the methods considered to physiologically plausible representations thanks to well-suited regularizations. These regularizations are built from prior knowledge about the spatial and temporal properties of these signals. For each regularization, an algorithm is proposed to solve the optimization problem allowing to obtain the targeted representations. The evaluation of the proposed EEG signals approaches highlights their effectiveness in representing them.

Esta tese apresenta um novo método para analisar dados de ressonância magnética funcional (FMRI) durante o estado de repouso denominado Análise de Componentes Esparsos Locais (LSCA). A LSCA é uma especialização da Análise de Componentes Esparsos (SCA) que leva em consideração a informação espacial dos dados para reconstruir a informação temporal de fontes bem localizadas, ou seja, fontes que representam a atividade de regiões corticais conectadas. Este estudo contém dados de simulação e dados reais. Os dados simulados foram preparados para avaliar a LSCA em diferentes cenários. Em um primeiro cenário, a LSCA é comparada com a Análise de Componentes Principais (PCA) em relação a capacidade de detectar fontes locais sob ruído branco e gaussiano. Em seguida, a LSCA é comparada com o algoritmo de Maximização da Expectativa (EM) no quesito detecção de fontes dinâmicas locais. Os dados reais foram coletados para fins comparativos e ilustrativos. Imagens de FMRI de onze voluntários sadios foram adquiridas utilizando um equipamento de ressonância magnética de 3T durante um protocolo de estado de repouso. As imagens foram pré-processadas e analisadas por dois métodos: a LSCA e a Análise de Componentes Independentes (ICA). Os componentes identificados pela LSCA foram comparados com componentes comumente reportados na literatura utilizando a ICA. Além da comparação direta com a ICA, a LSCA foi aplicada com o propósito único de caracterizar a dinâmica das redes de estado de repouso. Resultados simulados mostram que a LSCA é apropriada para identificar fontes esparsas locais. Em dados de FMRI no estado de repouso, a LSCA é capaz de identificar as mesmas fontes que são identificadas pela ICA, permitindo uma análise mais detalhada das relações entre regiões dentro de e entre componentes e sugerindo que muitos componentes identificados pela ICA em FMRI durante o estado de repouso representam um conjunto de componentes esparsos locais. Utilizando a LSCA, grande parte das fontes identificadas pela ICA podem ser decompostas em um conjunto de fontes esparsas locais que não são necessariamente independentes entre si. Além disso, as fontes identificadas pela LSCA aproximam muito melhor o sinal temporal observado nas regiões representadas por seus componentes do que as fontes identificadas pela ICA. Finalmente, uma análise mais elaborada utilizando a LSCA permite estimar também relações dinâmicas entre os componentes previamente identificados. Assim, a LSCA permite identificar relações clássicas bem como relações causais entre componentes do estado de repouso. As principais implicações desse resultado são que diferentes premissas permitem decomposições aproximadamente equivalentes, entretanto, critérios menos restritivos tais como esparsidade e localização permitem construir modelos mais compactos e biologicamente mais plausíveis. / This thesis presents Local Sparse Component Analysis (LSCA), a new method for analyzing resting state functional magnetic resonance imaging (fMRI) datasets. LSCA, a extension of Sparse Component Analysis (SCA), takes into account data spatial information to reconstruct temporal sources representing connected regions of significant activity. This study contains simulation data and real data. The simulated data were prepared to evaluate the LSCA in different scenarios. In the first scenario, the LSCA is compared with Principal Component Analysis (PCA) for detecting local sources under Gaussian white noise. Then, LSCA is compared with the expectation maximization algorithm (EM) for detecting the dynamics of local sources. Real data were collected for comparative and illustrative purposes. FMRI images from eleven healthy volunteers were acquired using a 3T MRI scanner during a resting state protocol. Images were preprocessed and analyzed using LSCA and Independent Components Analysis (ICA). LSCA components were compared with commonly reported ICA components. In addition, LSCA was applied for characterizing the dynamics of resting state networks. Simulated results have shown that LSCA is suitable for identifying local sparse sources.For real resting state FMRI data, LSCA is able to identify the same sources that are identified using ICA, allowing detailed functional connectivity analysis of the identified regions within and between components. This suggests that ICA resting state networks can be further decomposed into local sparse components that are not necessarily independent from each other. Moreover, LSCA sources better represent local FMRI signal oscillations than ISCA sources. Finally, brain connectivity analysis shows that LSCA can identify both instantaneous and causal relationships between resting state components. The main implication of this study is that independence and sparsity are equivalent assumptions in resting state FMRI. However, less restrictive criteria such as sparsity and source localization allow building much more compact and biologically plausible brain connectivity models.

Esta tese apresenta um novo método para analisar dados de ressonância magnética funcional (FMRI) durante o estado de repouso denominado Análise de Componentes Esparsos Locais (LSCA). A LSCA é uma especialização da Análise de Componentes Esparsos (SCA) que leva em consideração a informação espacial dos dados para reconstruir a informação temporal de fontes bem localizadas, ou seja, fontes que representam a atividade de regiões corticais conectadas. Este estudo contém dados de simulação e dados reais. Os dados simulados foram preparados para avaliar a LSCA em diferentes cenários. Em um primeiro cenário, a LSCA é comparada com a Análise de Componentes Principais (PCA) em relação a capacidade de detectar fontes locais sob ruído branco e gaussiano. Em seguida, a LSCA é comparada com o algoritmo de Maximização da Expectativa (EM) no quesito detecção de fontes dinâmicas locais. Os dados reais foram coletados para fins comparativos e ilustrativos. Imagens de FMRI de onze voluntários sadios foram adquiridas utilizando um equipamento de ressonância magnética de 3T durante um protocolo de estado de repouso. As imagens foram pré-processadas e analisadas por dois métodos: a LSCA e a Análise de Componentes Independentes (ICA). Os componentes identificados pela LSCA foram comparados com componentes comumente reportados na literatura utilizando a ICA. Além da comparação direta com a ICA, a LSCA foi aplicada com o propósito único de caracterizar a dinâmica das redes de estado de repouso. Resultados simulados mostram que a LSCA é apropriada para identificar fontes esparsas locais. Em dados de FMRI no estado de repouso, a LSCA é capaz de identificar as mesmas fontes que são identificadas pela ICA, permitindo uma análise mais detalhada das relações entre regiões dentro de e entre componentes e sugerindo que muitos componentes identificados pela ICA em FMRI durante o estado de repouso representam um conjunto de componentes esparsos locais. Utilizando a LSCA, grande parte das fontes identificadas pela ICA podem ser decompostas em um conjunto de fontes esparsas locais que não são necessariamente independentes entre si. Além disso, as fontes identificadas pela LSCA aproximam muito melhor o sinal temporal observado nas regiões representadas por seus componentes do que as fontes identificadas pela ICA. Finalmente, uma análise mais elaborada utilizando a LSCA permite estimar também relações dinâmicas entre os componentes previamente identificados. Assim, a LSCA permite identificar relações clássicas bem como relações causais entre componentes do estado de repouso. As principais implicações desse resultado são que diferentes premissas permitem decomposições aproximadamente equivalentes, entretanto, critérios menos restritivos tais como esparsidade e localização permitem construir modelos mais compactos e biologicamente mais plausíveis. / This thesis presents Local Sparse Component Analysis (LSCA), a new method for analyzing resting state functional magnetic resonance imaging (fMRI) datasets. LSCA, a extension of Sparse Component Analysis (SCA), takes into account data spatial information to reconstruct temporal sources representing connected regions of significant activity. This study contains simulation data and real data. The simulated data were prepared to evaluate the LSCA in different scenarios. In the first scenario, the LSCA is compared with Principal Component Analysis (PCA) for detecting local sources under Gaussian white noise. Then, LSCA is compared with the expectation maximization algorithm (EM) for detecting the dynamics of local sources. Real data were collected for comparative and illustrative purposes. FMRI images from eleven healthy volunteers were acquired using a 3T MRI scanner during a resting state protocol. Images were preprocessed and analyzed using LSCA and Independent Components Analysis (ICA). LSCA components were compared with commonly reported ICA components. In addition, LSCA was applied for characterizing the dynamics of resting state networks. Simulated results have shown that LSCA is suitable for identifying local sparse sources.For real resting state FMRI data, LSCA is able to identify the same sources that are identified using ICA, allowing detailed functional connectivity analysis of the identified regions within and between components. This suggests that ICA resting state networks can be further decomposed into local sparse components that are not necessarily independent from each other. Moreover, LSCA sources better represent local FMRI signal oscillations than ISCA sources. Finally, brain connectivity analysis shows that LSCA can identify both instantaneous and causal relationships between resting state components. The main implication of this study is that independence and sparsity are equivalent assumptions in resting state FMRI. However, less restrictive criteria such as sparsity and source localization allow building much more compact and biologically plausible brain connectivity models.

In this dissertation, some new algorithms are developed for hyperspectral imaging analysis enhancement. Tensor data format is applied in hyperspectral dataset sparse and low-rank decomposition, which could enhance the classification and detection performance. And multi-view learning technique is applied in hyperspectral imaging clustering. Furthermore, kernel version of multi-view learning technique has been proposed, which could improve clustering performance. Most of low-rank and sparse decomposition algorithms are based on matrix data format for HSI analysis. As HSI contains high spectral dimensions, tensor based extended low-rank and sparse decomposition (TELRSD) is proposed in this dissertation for better performance of HSI classification with low-rank tensor part, and HSI detection with sparse tensor part. With this tensor based method, HSI is processed in 3D data format, and information between spectral bands and pixels maintain integrated during decomposition process. This proposed algorithm is compared with other state-of-art methods. And the experiment results show that TELRSD has the best performance among all those comparison algorithms. HSI clustering is an unsupervised task, which aims to group pixels into different groups without labeled information. Low-rank sparse subspace clustering (LRSSC) is the most popular algorithms for this clustering task. The spatial-spectral based multi-view low-rank sparse subspace clustering (SSMLC) algorithms is proposed in this dissertation, which extended LRSSC with multi-view learning technique. In this algorithm, spectral and spatial views are created to generate multi-view dataset of HSI, where spectral partition, morphological component analysis (MCA) and principle component analysis (PCA) are applied to create others views. Furthermore, kernel version of SSMLC (k-SSMLC) also has been investigated. The performance of SSMLC and k-SSMLC are compared with sparse subspace clustering (SSC), low-rank sparse subspace clustering (LRSSC), and spectral-spatial sparse subspace clustering (S4C). It has shown that SSMLC could improve the performance of LRSSC, and k-SSMLC has the best performance. The spectral clustering has been proved that it equivalent to non-negative matrix factorization (NMF) problem. In this case, NMF could be applied to the clustering problem. In order to include local and nonlinear features in data source, orthogonal NMF (ONMF), graph-regularized NMF (GNMF) and kernel NMF (k-NMF) has been proposed for better clustering performance. The non-linear orthogonal graph NMF combine both kernel, orthogonal and graph constraints in NMF (k-OGNMF), which push up the clustering performance further. In the HSI domain, kernel multi-view based orthogonal graph NMF (k-MOGNMF) is applied for subspace clustering, where k-OGNMF is extended with multi-view algorithm, and it has better performance and computation efficiency.