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Advances in Modelling, Animation and RenderingVince, J.A., Earnshaw, Rae A. January 2002 (has links)
No / This volume contains the papers presented at Computer Graphics International 2002, in July, at the University of Bradford, UK. These papers represent original research in computer graphics from around the world.
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AZIP, audio compression system: Research on audio compression, comparison of psychoacoustic principles and genetic algorithmsChen, Howard 01 January 2005 (has links)
The purpose of this project is to investigate the differences between psychoacoustic principles and genetic algorithms (GA0). These will be discussed separately. The review will also compare the compression ratio and the quality of the decompressed files decoded by these two methods.
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Περίληψη βίντεο με μη επιβλεπόμενες τεχνικές ομαδοποίησηςΜπεσύρης, Δημήτριος 11 October 2013 (has links)
Η ραγδαία ανάπτυξη που παρουσιάστηκε τα τελευταία χρόνια σε διάφορους τομείς της πληροφορικής με την αύξηση της ισχύος επεξεργασίας και της δυνατότητας αποθήκευσης ενός τεράστιου όγκου δεδομένων έδωσε νέα ώθηση στον τομέα διαχείρισης, αναζήτησης, σύνοψης και εξαγωγής της πληροφορίας από ένα βίντεο. Για την διαχείριση αυτής της πληροφορίας αναπτύχθηκαν τεχνικές περίληψης βίντεο. Η περίληψη ενός βίντεο υπό μορφή μιας στατικής ακολουθίας χαρακτηριστικών καρέ, μειώνει τον απαραίτητο όγκο της πληροφορίας που απαιτείται σε συστήματα αναζήτησης, ενώ διαμορφώνει την βάση για την αντιμετώπιση του σημασιολογικού περιεχομένου του σε εφαρμογές ανάκτησης.
Το ερευνητικό αντικείμενο της παρούσας διδακτορικής διατριβής αναφέρεται σε τεχνικές αυτόματης περίληψης βίντεο με χρήση της θεωρίας γράφων, για την ανάπτυξη μη επιβλεπόμενων αλγόριθμων ομαδοποίησης. Κάθε καρέ της ακολουθίας του βίντεο δεν αντιμετωπίζεται ως ένα διακριτό στοιχείο, αλλά λαμβάνεται υπόψη ο βαθμός συσχέτισης μεταξύ τους. Με αυτόν τον τρόπο το πρόβλημα της ομαδοποίησης ανάγεται από μια τυπική διαδικασία αναγνώρισης ομάδων σε ένα σύστημα ανάλυσης της δομής που περιέχεται στο σύνολο των δεδομένων. Ακόμη παρουσιάζεται μια νέα τεχνική βελτίωσης του βαθμού ομοιότητας των καρέ, η οποία βασίζεται στο θεωρητικό φορμαλισμό τεχνικών ημί-επιβλεπόμενης εκμάθησης, με χρήση όμως αλγόριθμων δυναμικής συμπίεσης, για την αναπαράσταση του οπτικού περιεχομένου τους. Τα αναλυτικά πειραματικά αποτελέσματα που παρατίθενται, αποδεικνύουν την βελτίωση της απόδοσης των προτεινόμενων μεθόδων σε σχέση με γνωστές τεχνικές περίληψης. Τέλος, προτείνονται κάποιες μελλοντικές κατευθύνσεις έρευνας στο αντικείμενο που πραγματεύεται η παρούσα διατριβή, με άμεσες επεκτάσεις στο πεδίο ανάκτησης εικόνας και βίντεο. / The rapid development witnessed in the recent years enabling the storage and processing of a huge amount of data, in various fields of computer technology and image/video understanding, has given new impetus to the field of video manipulation, browsing, indexing, and retrieval. Video summarization, as a static sequence of key frames, reduces the amount of information required for video searching, while provides the basis for understanding the semantic content in video retrieval applications.
The research subject of this doctoral thesis is the incorporation of graph theory and unsupervised clustering algorithms in Automatic Video Summarization applications of large video sequences. In this context, every frame from a video sequence is not processed as a discrete element, but the relations between the frames are considered. Thus, the clustering problem is transformed from a typical computation procedure, to the problem of data structure analysis. Detailed experimental results demonstrate the performance improvement provided by the proposed methods in comparison with well-known video summarization techniques from the literature. Finally, future research directions are proposed, directly applicable to the fields of image and video retrieval.
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Canevas de programmation pour gérer l'hétérogénéité et la consommation d'énergie des mobiles dans un environnement ubiquitaire / Managing heterogeneity and energy via high-level programming frameworkGuan, Hongyu 01 June 2012 (has links)
L'hétérogénéité et l'énergie sont deux considérations fondamentales pour les environnements informatiques ubiquitaires. Dans cette thèse, nous présentons notre approche pour gérer l'hétérogénéité et pour économiser l'énergie via des canevas de programmation intégrés. Pour gérer l'hétérogénéité, nous proposons une méthodologie et un support de programmation qui vise à faire communiquer les différentes entités de l’environnement ubiquitaire en utilisant le protocole SIP considéré alors comme un bus logique universel de communication. Nous avons intégré ce bus SIP dans le langage de description d’architecture DiaSpec développé par notre équipe Phoenix. Concernant la consommation d’énergie, nous proposons une méthodologie qui utilise les techniques d’offloading et de compression de données pour minimiser la consommation d'énergie des applications mobiles. Nous avons ainsi construit une stratégie d’aide à la conception au travers d’un outil qui permet de déterminer le meilleur mode d’exécution pour une tâche donnée que nous proposons d’intégrer dans le langage de description DiaSpec. / The topics of heterogeneity and energy are two fundamental considerations for pervasive computing environments. Inthis thesis, we describe our approach to manage heterogeneity and to handle energy concerns via a high-level programming framework.To manage heterogeneity, we describe a methodology and a programming support that use the SIP protocol as a universal communication bus in pervasive computing environments. Ourwork enables homogeneous communications between heterogeneous distributed entities. In doing so, we integrate the SIP communication bus into our programming framework. We rely on adeclarative language named DiaSpec to describe the architecture of pervasive applications. This description is passed to a generator for producing a Java programming framework dedicated to the application area. We leverage the generated framework with SIP adaptations to raise the abstraction level of SIP operations.We then present a classification of a wide variety of entities interms of features, capabilities and network connectors. Based on this classification, a methodology and a programming supportare described for connecting entities on the SIP communication bus. This work has been validated by applications using theSIP communication bus to coordinate widely varying entities,including serial-based sensors (RS232, 1-Wire), ZigBee devices,X10 devices, PDA, native SIP entities, and software components.Regarding the energy concerns, we describe a methodology that uses two strategies, namely computation offloading and data compression, to minimize energy cost of mobile applications.In doing so, we present an execution and transfer model for atask of a mobile application and define its five different stubs forthree program execution and data transfer modes. Based on this model and our two strategies, we construct a strategy scheme to determine the most efficient stub in terms of energy consumption.We then design the OffDeci tool, using this strategy scheme, toprovide energy feedback for the developer and to analyze thebalance between local and remote computing with consideration of data compression. Our experimental study demonstrates thefeasibility of the strategy scheme of our approach. Finally, weextend DiaSpec with declarations dedicated to manage energy concerns during the application design phase. We sketched the integration of this energy-handling declaration and OffDeci intoour high-level programming framework. This integration permitsto determine the best stub of a declared DiaSpec component interms of its energy cost.
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[en] TREATMENT AND WAVELET-BASED COMPRESSION OF SENSOR DATA / [pt] TRATAMENTO E COMPRESSÃO BASEADA EM WAVELETS PARA DADOS ADQUIRIDOS POR SENSORESMARCELO GONELLA FERNANDEZ 31 March 2008 (has links)
[pt] Esta dissertação apresenta uma estratégia para desenvolver
mecanismos de compressão de dados adquiridos por sensores,
seguindo como inspiração o processo utilizado no formato
JPG2000. A estratégia adota a abordagem das séries
históricas dos dados sob o ponto de vista do processamento
de sinais. Dada à natureza instável dos sensores é natural
que ruídos sejam adicionados ao sinal original. Estes
ruídos são detectados e tratados enquanto o sinal é
suavizado e limpo, facilitando a análise, ao passo que em
que componentes pouco relevantes são removidos
ou aproximados, permitindo que o sinal seja comprimido com
pouca perda de informação. / [en] This dissertation introduces a strategy to develop a
compression method for sensor data inspired on the JPG2000
techniques. The strategy adopted processes data streams
much in the same way as signal processing. Due to the
unstable nature of sensor data, noise is added to the
original signal. This noise is detected and treated while
the signal is cleaned and smoothed, making it easier to
analyze the data stream. Less relevant signal components
are removed or approximated allowing the signal to be
compressed with few information loss.
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Transformada Wavelet e técnicas de inteligência computacional aplicadas à identificação, compressão e armazenamento de sinais no contexto de qualidade da energia elétrica / Wavelet transform and soft computing techniques applied to identification, compression and storage of signals in the power quality contextAndrade, Luciano Carli Moreira de 06 July 2017 (has links)
A presença de distúrbios na energia elétrica fornecida aos consumidores pode causar a diminuição no tempo de vida útil dos equipamentos, mal funcionamento ou até mesmo sua perda. Desse modo, ferramentas capazes de realizar a detecção, localização, classificação, compressão e o armazenamento de sinais de forma automática e organizada são essenciais para garantir um processo de monitoramento adequado ao sistema elétrico de potência como um todo. Dentre as ferramentas comumente aplicadas às tarefas supramencionadas, pode-se destacar a Transformada Wavelet (TW) e as Redes Neurais Artificiais (RNAs). Contudo, ainda não foi estabelecida uma metodologia para obtenção e validação da TW e seu nível de decomposição, bem como da arquitetura e da topologia de RNAs mais apropriadas às tarefas supracitadas. O principal fato que levou a esta constatação deve-se à análise da literatura correlata, onde é possível notar o uso de distintas TW e RNAs. Neste contexto, a primeira contribuição desta pesquisa foi o projeto e desenvolvimento de um método eficiente de segmentação de sinais com distúrbios associados à Qualidade da Energia Elétrica (QEE). O método desenvolvido se beneficia das propriedades da TW de identificação temporal de descontinuidades em sinais. A segunda contribuição é o desenvolvimento de um algoritmo automático que, por meio do método de segmentação desenvolvido e de classificação por RNAs, indique as melhores ferramentas (Wavelets e RNAs) para as tarefas de segmentação, extração de características e classificação de distúrbios de QEE. Esse algoritmo foi desenvolvido com base nos recursos dos Algoritmos Evolutivos (AEs) e adotou RNAs do tipo Perceptron Multicamadas, pois, esta arquitetura pode ser considerada consagrada no que se refere à classificação de padrões. Por fim, a terceira contribuição é relativa ao desenvolvimento de um procedimentos baseados em AEs, a fim de se aprimorar métodos de compressão de dados que preservem as informações relevantes nos sinais de QEE. Assim, é importante mencionar que os resultados dessa pesquisa poderão determinar mecanismos automáticos a serem utilizados no processo de registro, tratamento e armazenamento de informações que serão importantes para se manter um banco de dados (histórico) atualizado nas concessionárias de energia, a partir do qual, índices e um melhor mapeamento e entendimento de todos os distúrbios relacionados à QEE poderão ser melhor entendidos e solucionados. / The presence of disturbances in the electrical power supplied to consumers can decrease the lifetime of the equipment, cause malfunction or even their breakdown. Thus, tools able to perform detection, localization, classification, compression and storage of signals automatically and organized manner are essential to ensure adequate monitoring process to electric power systems as a whole. Among the tools commonly applied to the tasks mentioned above, one can highlight the Wavelet Transform (WT) and Artificial Neural Networks (ANN). However, the WT has not been established yet and nor its level of decomposition, as well as the most appropriate ANN architecture and topology to the tasks already mentioned. The main fact that has led to this finding is due to the review of related literature, where it is possible to note the use of distinct WT and ANN. Therefore, the first contribution of this research was the design and development of an efficient method of segmentation of signals associate to Power Quality (PQ) disturbances. The developed method take advantage of WT properties of temporal identification of signal discontinuities. The second contribution is the development of an automatic algorithm that, through the segmentation method developed and classification by ANN, indicates the best tools (Wavelets and ANN) for the tasks of segmentation, extraction of characteristics and classification of QEE disturbances. This algorithm was developed based on the resources of the Evolutionary Algorithms and it adopts Multi-layered Perceptron type ANN, once this architecture can be considered consecrated with regard to the pattenrs classification. Finally, the third contribution is related to the development of EA based procedures in order to improve data compression methods that preserve the relevant information in the PQ signals. Thus, it is important to mention that the results of this research may determine automatic mechanisms to be used in the process of recording, processing and storing information that will be important in order to maintain an up-to-date (historical) database in the utilities, from which , indexes and a better mapping and understanding of all PQ related disturbances can be better understood and solved.
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Transformada Wavelet e técnicas de inteligência computacional aplicadas à identificação, compressão e armazenamento de sinais no contexto de qualidade da energia elétrica / Wavelet transform and soft computing techniques applied to identification, compression and storage of signals in the power quality contextLuciano Carli Moreira de Andrade 06 July 2017 (has links)
A presença de distúrbios na energia elétrica fornecida aos consumidores pode causar a diminuição no tempo de vida útil dos equipamentos, mal funcionamento ou até mesmo sua perda. Desse modo, ferramentas capazes de realizar a detecção, localização, classificação, compressão e o armazenamento de sinais de forma automática e organizada são essenciais para garantir um processo de monitoramento adequado ao sistema elétrico de potência como um todo. Dentre as ferramentas comumente aplicadas às tarefas supramencionadas, pode-se destacar a Transformada Wavelet (TW) e as Redes Neurais Artificiais (RNAs). Contudo, ainda não foi estabelecida uma metodologia para obtenção e validação da TW e seu nível de decomposição, bem como da arquitetura e da topologia de RNAs mais apropriadas às tarefas supracitadas. O principal fato que levou a esta constatação deve-se à análise da literatura correlata, onde é possível notar o uso de distintas TW e RNAs. Neste contexto, a primeira contribuição desta pesquisa foi o projeto e desenvolvimento de um método eficiente de segmentação de sinais com distúrbios associados à Qualidade da Energia Elétrica (QEE). O método desenvolvido se beneficia das propriedades da TW de identificação temporal de descontinuidades em sinais. A segunda contribuição é o desenvolvimento de um algoritmo automático que, por meio do método de segmentação desenvolvido e de classificação por RNAs, indique as melhores ferramentas (Wavelets e RNAs) para as tarefas de segmentação, extração de características e classificação de distúrbios de QEE. Esse algoritmo foi desenvolvido com base nos recursos dos Algoritmos Evolutivos (AEs) e adotou RNAs do tipo Perceptron Multicamadas, pois, esta arquitetura pode ser considerada consagrada no que se refere à classificação de padrões. Por fim, a terceira contribuição é relativa ao desenvolvimento de um procedimentos baseados em AEs, a fim de se aprimorar métodos de compressão de dados que preservem as informações relevantes nos sinais de QEE. Assim, é importante mencionar que os resultados dessa pesquisa poderão determinar mecanismos automáticos a serem utilizados no processo de registro, tratamento e armazenamento de informações que serão importantes para se manter um banco de dados (histórico) atualizado nas concessionárias de energia, a partir do qual, índices e um melhor mapeamento e entendimento de todos os distúrbios relacionados à QEE poderão ser melhor entendidos e solucionados. / The presence of disturbances in the electrical power supplied to consumers can decrease the lifetime of the equipment, cause malfunction or even their breakdown. Thus, tools able to perform detection, localization, classification, compression and storage of signals automatically and organized manner are essential to ensure adequate monitoring process to electric power systems as a whole. Among the tools commonly applied to the tasks mentioned above, one can highlight the Wavelet Transform (WT) and Artificial Neural Networks (ANN). However, the WT has not been established yet and nor its level of decomposition, as well as the most appropriate ANN architecture and topology to the tasks already mentioned. The main fact that has led to this finding is due to the review of related literature, where it is possible to note the use of distinct WT and ANN. Therefore, the first contribution of this research was the design and development of an efficient method of segmentation of signals associate to Power Quality (PQ) disturbances. The developed method take advantage of WT properties of temporal identification of signal discontinuities. The second contribution is the development of an automatic algorithm that, through the segmentation method developed and classification by ANN, indicates the best tools (Wavelets and ANN) for the tasks of segmentation, extraction of characteristics and classification of QEE disturbances. This algorithm was developed based on the resources of the Evolutionary Algorithms and it adopts Multi-layered Perceptron type ANN, once this architecture can be considered consecrated with regard to the pattenrs classification. Finally, the third contribution is related to the development of EA based procedures in order to improve data compression methods that preserve the relevant information in the PQ signals. Thus, it is important to mention that the results of this research may determine automatic mechanisms to be used in the process of recording, processing and storing information that will be important in order to maintain an up-to-date (historical) database in the utilities, from which , indexes and a better mapping and understanding of all PQ related disturbances can be better understood and solved.
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Optimisation des techniques de compression d'images fixes et de vidéo en vue de la caractérisation des matériaux : applications à la mécanique / Optimization of compression techniques for still images and video for characterization of materials : mechanical applicationsEseholi, Tarek Saad Omar 17 December 2018 (has links)
Cette thèse porte sur l’optimisation des techniques de compression d'images fixes et de vidéos en vue de la caractérisation des matériaux pour des applications dans le domaine de la mécanique, et s’inscrit dans le cadre du projet de recherche MEgABIt (MEchAnic Big Images Technology) soutenu par l’Université Polytechnique Hauts-de-France. L’objectif scientifique du projet MEgABIt est d’investiguer dans l’aptitude à compresser de gros volumes de flux de données issues d’instrumentation mécanique de déformations à grands volumes tant spatiaux que fréquentiels. Nous proposons de concevoir des algorithmes originaux de traitement dans l’espace compressé afin de rendre possible au niveau calculatoire l’évaluation des paramètres mécaniques, tout en préservant le maximum d’informations fournis par les systèmes d’acquisitions (imagerie à grande vitesse, tomographie 3D). La compression pertinente de la mesure de déformation des matériaux en haute définition et en grande dynamique doit permettre le calcul optimal de paramètres morpho-mécaniques sans entraîner la perte des caractéristiques essentielles du contenu des images de surface mécaniques, ce qui pourrait conduire à une analyse ou une classification erronée. Dans cette thèse, nous utilisons le standard HEVC (High Efficiency Video Coding) à la pointe des technologies de compression actuelles avant l'analyse, la classification ou le traitement permettant l'évaluation des paramètres mécaniques. Nous avons tout d’abord quantifié l’impact de la compression des séquences vidéos issues d’une caméra ultra-rapide. Les résultats expérimentaux obtenus ont montré que des taux de compression allant jusque 100 :1 pouvaient être appliqués sans dégradation significative de la réponse mécanique de surface du matériau mesurée par l’outil d’analyse VIC-2D. Finalement, nous avons développé une méthode de classification originale dans le domaine compressé d’une base d’images de topographie de surface. Le descripteur d'image topographique est obtenu à partir des modes de prédiction calculés par la prédiction intra-image appliquée lors de la compression sans pertes HEVC des images. La machine à vecteurs de support (SVM) a également été introduite pour renforcer les performances du système proposé. Les résultats expérimentaux montrent que le classificateur dans le domaine compressé est robuste pour la classification de nos six catégories de topographies mécaniques différentes basées sur des méthodologies d'analyse simples ou multi-échelles, pour des taux de compression sans perte obtenus allant jusque 6: 1 en fonction de la complexité de l'image. Nous avons également évalué les effets des types de filtrage de surface (filtres passe-haut, passe-bas et passe-bande) et de l'échelle d'analyse sur l'efficacité du classifieur proposé. La grande échelle des composantes haute fréquence du profil de surface est la mieux appropriée pour classer notre base d’images topographiques avec une précision atteignant 96%. / This PhD. thesis focuses on the optimization of fixed image and video compression techniques for the characterization of materials in mechanical science applications, and it constitutes a part of MEgABIt (MEchAnic Big Images Technology) research project supported by the Polytechnic University Hauts-de-France (UPHF). The scientific objective of the MEgABIt project is to investigate the ability to compress large volumes of data flows from mechanical instrumentation of deformations with large volumes both in the spatial and frequency domain. We propose to design original processing algorithms for data processing in the compressed domain in order to make possible at the computational level the evaluation of the mechanical parameters, while preserving the maximum of information provided by the acquisitions systems (high-speed imaging, tomography 3D). In order to be relevant image compression should allow the optimal computation of morpho-mechanical parameters without causing the loss of the essential characteristics of the contents of the mechanical surface images, which could lead to wrong analysis or classification. In this thesis, we use the state-of-the-art HEVC standard prior to image analysis, classification or storage processing in order to make the evaluation of the mechanical parameters possible at the computational level. We first quantify the impact of compression of video sequences from a high-speed camera. The experimental results obtained show that compression ratios up to 100: 1 could be applied without significant degradation of the mechanical surface response of the material measured by the VIC-2D analysis tool. Then, we develop an original classification method in the compressed domain of a surface topography database. The topographical image descriptor is obtained from the prediction modes calculated by intra-image prediction applied during the lossless HEVC compression of the images. The Support vector machine (SVM) is also introduced for strengthening the performance of the proposed system. Experimental results show that the compressed-domain topographies classifier is robust for classifying the six different mechanical topographies either based on single or multi-scale analyzing methodologies. The achieved lossless compression ratios up to 6:1 depend on image complexity. We evaluate the effects of surface filtering types (high-pass, low-pass, and band-pass filter) and the scale of analysis on the efficiency of the proposed compressed-domain classifier. We verify that the high analysis scale of high-frequency components of the surface profile is more appropriate for classifying our surface topographies with accuracy of 96 %.
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Managing and Exploring Large Data Sets Generated by Liquid Separation - Mass SpectrometryBäckström, Daniel January 2007 (has links)
<p>A trend in natural science and especially in analytical chemistry is the increasing need for analysis of a large number of complex samples with low analyte concentrations. Biological samples (urine, blood, plasma, cerebral spinal fluid, tissue etc.) are often suitable for analysis with liquid separation mass spectrometry (LS-MS), resulting in two-way data tables (time vs. m/z). Such biological 'fingerprints' taken for all samples in a study correspond to a large amount of data. Detailed characterization requires a high sampling rate in combination with high mass resolution and wide mass range, which presents a challenge in data handling and exploration. This thesis describes methods for managing and exploring large data sets made up of such detailed 'fingerprints' (represented as data matrices). </p><p>The methods were implemented as scripts and functions in Matlab, a wide-spread environment for matrix manipulations. A single-file structure to hold the imported data facilitated both easy access and fast manipulation. Routines for baseline removal and noise reduction were intended to reduce the amount of data without loosing relevant information. A tool for visualizing and exploring single runs was also included. When comparing two or more 'fingerprints' they usually have to be aligned due to unintended shifts in analyte positions in time and m/z. A PCA-like multivariate method proved to be less sensitive to such shifts, and an ANOVA implementation made it easier to find systematic differences within the data sets.</p><p>The above strategies and methods were applied to complex samples such as plasma, protein digests, and urine. The field of application included urine profiling (paracetamole intake; beverage effects), peptide mapping (different digestion protocols) and search for potential biomarkers (appendicitis diagnosis) . The influence of the experimental factors was visualized by PCA score plots as well as clustering diagrams (dendrograms).</p>
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Constrained measurement systems of low-dimensional signalsYap, Han Lun 20 December 2012 (has links)
The object of this thesis is the study of constrained measurement systems of signals having low-dimensional structure using analytic tools from Compressed Sensing (CS). Realistic measurement systems usually have architectural constraints that make them differ from their idealized, well-studied counterparts. Nonetheless, these measurement systems can exploit structure in the signals that they measure. Signals considered in this research have low-dimensional structure and can be broken down into two types: static or dynamic. Static signals are either sparse in a specified basis or lying on a low-dimensional manifold (called manifold-modeled signals). Dynamic signals, exemplified as states of a dynamical system, either lie on a low-dimensional manifold or have converged onto a low-dimensional attractor.
In CS, the Restricted Isometry Property (RIP) of a measurement system ensures that distances between all signals of a certain sparsity are preserved.
This stable embedding ensures that sparse signals can be distinguished one from another by their measurements and therefore be robustly recovered. Moreover, signal-processing and data-inference algorithms can be performed directly on the measurements instead of requiring a prior signal recovery step. Taking inspiration from the RIP, this research analyzes conditions on realistic, constrained measurement systems (of the signals described above) such that they are stable embeddings of the signals that they measure.
Specifically, this thesis focuses on four different types of measurement systems. First, we study the concentration of measure and the RIP of random block diagonal matrices that represent measurement systems constrained to make local measurements. Second, we study the stable embedding of manifold-modeled signals by existing CS matrices. The third part of this thesis deals with measurement systems of dynamical systems that produce time series observations. While Takens' embedding result ensures that this time series output can be an embedding of the dynamical systems' states, our research establishes that a stronger stable embedding result is possible under certain conditions. The final part of this thesis is the application of CS ideas to the study of the short-term memory of neural networks. In particular, we show that the nodes of a recurrent neural network can be a stable embedding of sparse input sequences.
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