[pt] Este trabalho estuda o problema de compressão de imagens de sensoriamento remoto segundo a ótica da codificação conjunta fonte-canal. É analisado o desempenho de métodos baseados em quantização vetorial segundo o algoritmo LBG, principalmente o COVQ (Channel Optimized Vector Quantizer) bem como a quantização vetorial estruturada em árvore. Dentro desse contexto, são propostos 2 novos métodos para a resolução do problema: (1)Uma quantização vetorial estruturada em árvores que leva em conta a transmissão através de canais ruidosos, solução denominada COTSVQ (Channel-Design Tree Strutured Vecotr Quantizer), bem como (2) uma classe de métodos que se utiliza de códigos corretores de erro sobre a estrutura progressiva do TSVQ, de forma a proteger os dados de forma ativa durante a transmissão. Os dois métodos propostos podem ser combinados no mesmo compressor, de forma a originar uma classe ampla de compressores adaptados à transmissão por canais com ruído. São apresentados resultados que comparam os desempenhos dos métodos propostos com aqueles já existentes para uma análise de desempenho, na situação de transmissão via satélite de imagens captadas e comprimidas para uma taxa de 1,5bpp. Os resultados mostram que os métodos propostos são muito menos complexos que os já existentes, porém conseguindo atingir uma qualidade de imagem equivalente, ou, em alguns casos, superior. / [en] This work studies the problem of remote sensorng image compression by joint source-channel coding. The vector quantizer methods evaluated are those designed with the LBG algorithm, the COVQ (channel-optimized vector quantizer) algorithm as well as tree-structured vector quantizer. The noisy channel is modelled as a BSC. In this context, two news methods are proposed: (1) A tree- structures vector quantizer that considers the transmission through noisy channels (denominated CD-TSVQ), and (2) a new class of compressors that uses forward error- correcting codes over the TSVQ structure, as a way to actively protect data during the transmission. The twoproposed methods can be combined on the same compressor architecture, resulting in a vast class of compressors well-adapted to the transmission through noisy channels. Results allowing the comparision of the proposed methods with existing ones are presented. Performance evaluated in a scenery where images are compressed to be transmited at a rate of 1.5bpp. Results yield to the conclusion that the porposed methods are much less complex than the existing methods, yet achieve equivalent or, in some situations, improved performance.

Šis darbas yra skirtas šiuolaikinės atomo trikdžių teorijos matematinio aparato, paremto efektinių operatorių formalizmu, plėtojimui. Darbe nuosekliai ir sistemingai, pradedant nuo pačių bendriausių principų, nagrinėjami Foko erdvės apribojimo į redukavimo grupių neredukuotinus poerdvius metodai bei pateikiama neredukuotinų tenzorinių operatorių, charakterizuojančių fizikines ir efektines sąveikas, klasifikacija bendrais ir tam tikrais atskirais atvejais. Gautos išraiškos ir iš jų išplaukiančios išvados yra grindžiamos matematine kalba. Dauguma esminių rezultatų yra suformuluoti teoremų pavidalu. Disertaciją sudaro 101 puslapis, 5 skyriai, 4 priedai, 40 lentelių ir 9 paveikslėliai. Pagrindiniai rezultatai, pateikti disertacijoje, yra publikuoti fizikos ir matematikos mokslų žurnaluose. / The principal goals of the thesis are subjected to general methods and forms of effective operators by the nowadays demands of theoretical application of many-body perturbation theory to atomic physics. The present theoretical research follows up step by step by systematic observation of various possibilities to restrict the Fock space operators to their irreducible subspaces and the classification of irreducible tensor operators which represent the physical as well as the effective interactions. To ground the results of the thesis, the symbolic preparation of obtained expressions is strictly proved mathematically. Most of the main results are listed in theorems. The doctoral dissertation contains 101 pages, 5 sections, 4 appendices, 40 tables and 9 figures. The main results described in the present dissertation have been published in journals of physical and mathematical sciences.

The principal goals of the thesis are subjected to general methods and forms of effective operators by the nowadays demands of theoretical application of many-body perturbation theory to atomic physics. The present theoretical research follows up step by step by systematic observation of various possibilities to restrict the Fock space operators to their irreducible subspaces and the classification of irreducible tensor operators which represent the physical as well as the effective interactions. To ground the results of the thesis, the symbolic preparation of obtained expressions is strictly proved mathematically. Most of the main results are listed in theorems. The doctoral dissertation contains 101 pages, 5 sections, 4 appendices, 40 tables and 9 figures. The main results described in the present dissertation have been published in journals of physical and mathematical sciences. / Šis darbas yra skirtas šiuolaikinės atomo trikdžių teorijos matematinio aparato, paremto efektinių operatorių formalizmu, plėtojimui. Darbe nuosekliai ir sistemingai, pradedant nuo pačių bendriausių principų, nagrinėjami Foko erdvės apribojimo į redukavimo grupių neredukuotinus poerdvius metodai bei pateikiama neredukuotinų tenzorinių operatorių, charakterizuojančių fizikines ir efektines sąveikas, klasifikacija bendrais ir tam tikrais atskirais atvejais. Gautos išraiškos ir iš jų išplaukiančios išvados yra grindžiamos matematine kalba. Dauguma esminių rezultatų yra suformuluoti teoremų pavidalu. Disertaciją sudaro 101 puslapis, 5 skyriai, 4 priedai, 40 lentelių ir 9 paveikslėliai. Pagrindiniai rezultatai, pateikti disertacijoje, yra publikuoti fizikos ir matematikos mokslų žurnaluose.

[pt] Este trabalho examina o impacto da quantização vetorial das LSFs sobre a qualidade de voz em codecs a baixas taxas operando em redes IP e em diversos ambientes ruidosos. São considerados diferentes esquemas de quantização vetorial (QV) multiestágio com busca em árvore envolvendo QV sem memória e QV preditiva chaveada com 2 e 4 classes. A distribuição de perda de quadros em redes IP foi modelada de acordo com o Modelo de Gilbert e a avaliação de desempenho foi realizada tanto em termos das distorções espectrais como da qualidade de voz resultante de codecs a baixas taxas. Ainda neste trabalho, foi avaliada a qualidade da voz codificada após a utilização de uma técnica de supressão de ruído baseada em transformadas wavelets (Wavelet Denoising). / [en] This work investigates the impact of LSF vector quantisation over the voice quality in low rate codecs operating in IP networks. Tree-structured multistage vector quantisation (VQ) schemes involving memoryless VQ and switched-predictive VQ with 2 and 4 classes are considered. The packet loss frame distribution in IP networks was modelled according to the Gilbert Model and the performance was carried out both in terms of spectral distortions and the speech quality at the out put of low rate codecs. In this work, we also evaluated the quality of the coded speech after employing Wavelet Denoising.

No description available.

Ce travail, à la frontière de l’analyse et des probabilités, s’intéresse à l’étude de systèmes différentiels a priori mal posés. Nous cherchons, grâce à des techniques issues de la théorie des chemins rugueux et de l’étude trajectorielle des processus stochastiques, à donner un sens à de tels systèmes puis à les résoudre, tout en montrant que les notions proposées ici étendent bien les notions classiques de solutions. Cette thèse se décompose en trois chapitres. Le premier traite des systèmes différentiels ordinaires perturbés additivement par des processus irréguliers éventuellement stochastiques ainsi que des effets de régularisation de tels processus. Le deuxième chapitre concerne l’équation de transport linéaire perturbée multiplicativement par des chemins rugueux ; enfin, le dernier chapitre s’intéresse à une équation de la chaleur non linéaire perturbée par un bruit blanc espace-temps, l’équation de quantisation stochastique phi4 en dimension 3. / In this work we investigate a priori ill-posed differential systems from an analytic and probabilistic point of view. Thanks to technics inspired by the rough path theory and pathwise study of stochastic processes, we want to define those ill-posed systems and then study them. The first chapter of this thesis is related to ordinary differential equations perturbed by some irregular (stochastic) processes and the effects induced by the regularization of such processes. The second chapter deals with the linear transport equation multiplicatively perturbed by a rough path. Finally, in the last chapter we investigate the stochastic quantization equation Phi4 in three dimensions.

[pt] Nesta tese é proposto um novo método de agrupamento de dados sísmicos para a visualização em mapas sísmicos. Os dados sísmicos (sinal + ruído) têm distribuições assimétricas. A classificação dos dados sísmicos é, atualmente, realizada através de métodos que induzem as referências dos grupos propostos às suas médias. No entanto, a média é sensível aos ruídos e aos outliers e as classificações com este estimador estão sujeitas a distorções nos resultados. Embora outros trabalhos sugiram o uso da mediana nos casos em que as distribuições são assimétricas - devido ao fato deste estimador ser robusto aos ruídos e aos outliers - em nenhum foi encontrado um método que induza as referências dos grupos propostos às medianas no tratamento dos dados sísmicos. O método proposto incluí um algoritmo que induz as referências dos grupos propostos às suas medianas. O tratamento iterativo dos dados sísmicos através da aplicação de uma função não linear adequada ao gradiente descendente gera resultados cujos erros médios quadráticos são inferiores aos dos resultados dos métodos que induzem à média. Um parâmetro existente no algoritmo, a constante de não linearidade, determina a maneira como os dados são induzidos, a partir da média, na direção da mediana. A convergência aos resultados requer poucas iterações no método proposto. O método proposto é uma ferramenta para o dimensionamento de reservatórios de petróleo e serve para a determinação de diferenças entre as propriedades de estruturas geológicas similares. / [en] This thesis suggests the use of a new method of seismic data clustering that can aid in the visualization of seismic maps. Seismic data are primarily made of signal and noise and, due to its dual composition, have asymmetric distributions. Seismic data are traditionally classified by methods that lead the proposed groups` references to their mean values. The mean value is, however, sensitive to noise and outliers and the classification methods that make use of this estimator are, consequently, subjected to generating distorted results. Although other works have suggested the use of the median in cases where the distributions are asymmetric - due to the fact that the estimator is robust with respect to noise and outliers - none have proposed a method that would lead the groups` references to the median while treating seismic data. The method proposed in this work includes, therefore, an algorithm that leads the groups` references to their medians. The iterative treatment of seismic data through the use of a non-linear function that is adequate for the gradient descent generates results with meansquare errors inferior to those of results generated by the use of the mean value. The algorithm`s non- linearity constant determines how the seismic data are led from the mean value towards the median. The proposed method requires little iteration for the results to converge. The proposed method can, therefore, be used as a tool in the sizing of petroleum reservoirs and can also be used to determine the differences between similar geological structures.

The aim of the dissertation was to design a realistic, low-complexity non-binary (NB) low density parity check (LDPC) coded space-time-frequency (STF) coded multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system with an iterative joint decoder and detector structure at the receiver. The goal of the first part of the dissertation was to compare the performance of different design procedures for NB-LDPC codes on an additive white Gaussian noise (AWGN) channel, taking into account the constraint on the code length. The effect of quantisation on the performance of the code was also analysed. Different methods for choosing the NB elements in the parity check matrix were compared. For the STF coding, a class of universal STF codes was used. These codes use linear pre-coding and a layering approach based on Diophantine numbers to achieve full diversity and a transmission rate (in symbols per channel use per frequency) equal to the number of transmitter antennas. The study of the system considers a comparative performance analysis of di erent ST, SF and STF codes. The simulations of the system were performed on a triply selective block fading channel. Thus, there was selectivity in the fading over time, space and frequency. The effect of quantisation at the receiver on the achievable diversity of linearly pre-coded systems (such as the STF codes used) was mathematically derived and verified with simulations. A sphere decoder (SD) was used as a MIMO detector. The standard method used to create a soft-input soft output (SISO) SD uses a hard-to-soft process and the max-log-map approximation. A new approach was developed which combines a Hopfield network with the SD. This SD-Hopfield detector was connected with the fast Fourier transform belief propagation (FFT-BP) algorithm in an iterative structure. This iterative system was able to achieve the same bit error rate (BER) performance as the original SISO-SD at a reduced complexity. The use of the iterative Hopfield-SD and FFT-BP decoder system also allows performance to be traded off for complexity by varying the number of decoding iterations. The complete system employs a NB-LDPC code concatenated with an STF code at the transmitter with a SISO-SD and FFT-BP decoder connected in an iterative structure at the receiver. The system was analysed in varying channel conditions taking into account the effect of correlation and quantisation. The performance of different SF and STF codes were compared and analysed in the system. An analysis comparing different numbers of FFT-BP and outer iterations was also done. AFRIKAANS : Die doel van die verhandeling was om ’n realistiese, lae-kompleksiteit nie-binˆere (NB) LDPC gekodeerde ruimte-tyd-frekwensie-gekodeerde MIMO-OFDM-sisteem met iteratiewe gesamentlike dekodeerder- en detektorstrukture by die ontvanger te ontwerp. Die eerstem deel van die verhandeling was om die werkverrigting van verskillende ontwerpprosedures vir NB-LDPC kodes op ’n gesommeerde wit Gausruiskanaal te vergelyk met inagneming van die beperking op die lengte van die kode. Verskillende metodes om die nie-bineêre elemente in die pariteitstoetsmatriks te kies, is gebruik. Vir die ruimte-tyd-frekwensiekodering is ’n klas universele ruimte-tyd-frekwensiekodes gebruik. Hierdie kodes gebruik lineêre pre-kodering en ’n laagbenadering gebaseer op Diofantiese syfers om volle diversiteit te bereik en ’n oordragtempo (in simbole per kanaalgebruik per frekwensie) gelyk aan die aantal senderantennes. Die studie van die sisteem oorweeg ’n vergelykende werkverrigtinganalisie van verskillende ruimte-tyd-, ruimte-freksensie- en ruimte-tyd-frekwensiekodes. Die simulasies van die sisteem is gedoen op ’n drievoudig selektiewe blokwegsterwingskanaal. Daar was dus selektiwiteit in die wegsterwing oor tyd, ruimte en frekwensie. Die effek van kwantisering by die ontvanger op die bereikbare diversiteit van lineêr pre-gekodeerde sisteme (soos die ruimte-tyd-frekwensiekodes wat gebruik is) is matematies afgelei en bevestig deur simulasies. ’n Sfeerdekodeerder (SD) is gebruik as ’n MIMO-detektor. Die standaardmetode wat gebuik is om ’n sagte-inset-sagte-uitset (SISO) SD te skep, gebruik ’n harde-na-sagte proses en die maksimum logaritmiese afbeelding-benadering. ’n Nuwe benadering wat ’n Hopfield-netwerk met die SD kombineer, is ontwikkel. Hierdie SD-Hopfield-detektor is verbind met die FFT-BP-algoritme in iteratiewe strukture. Hierdie iteratiewe sisteem was in staat om dieselfde bisfouttempo te bereik as die oorspronklike SISO-SD, met laer kompleksiteit. Die gebruik van die iteratiewe Hopfield-SD en FFT-BP-dekodeerdersisteem maak ook daarvoor voorsiening dat werkverrigting opgeweeg kan word teen kompleksiteit deur die aantal dekodering-iterasies te varieer. Die volledige sisteem maak gebruik van ’n QC-NB-LDPC-kode wat met ’n ruimte-tyd-frekwensiekode by die sender aaneengeskakel is met ’n SISO-SD en FFT-BP-dekodeerder wat in ’n iteratiewe struktuur by die ontvanger gekoppel is. Die sisteem is onder ’n verskeidenheid kanaalkondisies ge-analiseer met inagneming van die effek van korrelasie en kwantisering. Die werkverrigting van verskillende ruimte-frekwensie- en ruimte-tyd-frekwensiekodes is vergelyk en in die sisteem ge-analiseer. ’n Analise om ’n wisselende aantal FFT-BP en buite-iterasies te vergelyk, is ook gedoen. Copyright / Dissertation (MEng)--University of Pretoria, 2010. / Electrical, Electronic and Computer Engineering / unrestricted

Thesis deals with multimedia signal comparison of compression options focused on video and advanced codecs. Specifically it describes the encoding and decoding of video recordings according to the MPEG standard. The theoretical part of the thesis describes characteristic properties of the video signal and justification for the need to use recording and transmission compression. There are also described methods for elimination of encoded video signal redundancy and irrelevance. Further on are discussed ways of measuring the video signal quality. A separate chapter is focused on the characteristics of currently used and promising codecs. In the practical part of the thesis were created functions in Matlab environment. These functions were implemented into graphic user interface that simulates the activity of functional blocks of the encoder and decoder. Based on user-specified input parameters it performs encoding and decoding of any given picture, composed of images in RGB format, and displays the outputs of individual functional blocks. There are implemented algorithms for the initial processing of the input sequence including sub-sampling, as well as DCT, quantization, motion compensation and their inverse operations. Separate chapters are dedicated to the realisation of codec description in the Matlab environment and to the individual processing steps output. Further on are mentioned compress algorithm comparisons and the impact of parameter change onto the final signal. The findings are summarized in conclusion.

[pt] Esta dissertação propõe algoritmos para codificações de voz a taxas médias em torno de 1,2 Kb/s. Um esquema de quantização vetorial preditiva chaveada com desempenho superior aos esquemas previamente descritos na literatura é proposto e avaliado em canal com ou sem ruído. Detectores eficientes de período fundamental e de sons oclusivos e fricativos são examinados e adaptados ao codificador proposto. Técnicas de exitação a baixas taxas de bits são investigadas a fim de reproduzir uma boa qualidade de voz decodificada. O modelo de exitação mista em multi-bandas com três sub-bandas é adotado para codificar os quadros sonoros. Para os quadros surdos são empregadas técnicas de modelagem e síntese de sinais fricativos e oclusivos, capazes de oferecer qualidade de voz satisfatória, reduzindo a taxa de bits destes quadros para apenas 0,4 Kb/s. Técnicas de pós-filtragem para reduzir o ruído de codificação e melhorar a qualidade de voz reconstruída são também examinadas e comparadas em uma mesma plataforma. Para reduzir o nível de ruído ambiente são ainda analisados métodos de supressão de ruído. Finalmente, o codificador proposto é comparado ao padrão norte-americano Mixed Excitation Linear Prediction (MELP), por meios de teste de comparação do tipo A/B. Os testes realizados indicam que o sistema proposto, operando a 1,2 Kb/s, apresenta qualidade de voz ligeiramente superior ao MELP, operando a 2,4 Kb/s. Para situações de transcodificação, o codificador proposto também apresenta desempenho superior ao MELP. / [en] This dissertation presents algorithms to encode at an avarage bit rate of 1.2 Kb/s. A novel switched-predictive vector quantiser technique that outperforms previously reported schemes is proposed and assessed under noise-free and noisy channels. Efficient detectors for the pitch period and fricative and stop sounds are examined and adapted to the proposed coder. Low bit rate excitation methods are investigated in order to reproduce rather high quality speech. A mixed multiband excitation approach with three sub-bands is employed to encode voiced frames. For unvoiced frames, fricatives and stops modelling and synthesis techniques are used. This approach has shown to provide high quality synthesised speech, whilts it reduces the bit rate to only 0.4 Kb/s for unvoiced frames. To reduce coding noise and improve decoded speech, post- filtering techniques are analysed and compared on the same plataform. To reduce background noise, noise suppression methods are also examined. Finally, the propose coder is evaluated against the North American Mixed Prediction (MELP) coder, through A/B comparison tests. Assessment results have shown that the proposed system, operating at 1.2 Kb/s, slightly outperformed the MELP coder, operating at 2.4 Kb/s. For tandem connection situations, the proposed algorithm has presented a superior performance than the MELP coder. / [es] Esta disertación propone algoritmos para codificaciones de voz a tasas medias en torno de 1,2 Kb/s. Se propone un esquema de cuantización vectorial predictiva, con desempeño superior a los esquemas previamente descritos en la literatura. Este esquema se evalúa en canal con o sin ruido. Se examinan detectores eficientes de período fundamental y de sueños oclusivos y fricativos se adaptan al codificador propuesto. Técnicas de exitación a bajas tasas de bits son investigadas a fin de reproducir una boa calidad de voz decodificada. Se adopta el modelo de exitación mixta en multi-bandas con tres sub-bandas para codificar los cuadros sonoros. Para los cuadros surdos se emplean técnicas de modelación y síntesis de señales fricativos y oclusivos, capaces de ofrecer calidad de voz satisfactoria, reduciendo la tasa de bits de estos cuadros para apenas 0,4 Kb/s. También se examinan y se comparan las técnicas de pós-filtragen para reducir el ruido de codificación y mejorar la calidad de voz reconstruída. Para reducir el nível de ruído ambiente se analizan métodos de supresión de ruido. Finalmente, el codificador propuesto se compara al padrón norteamericano Mixed Excitation Lineal Prediction (MELP), por medio de pruebas de comparación del tipo LA/B. Las pruebas realizadas indican que el sistema propuesto, operando a 1,2 Kb/s, presenta calidad de voz ligeramente superior al MELP, operando a 2,4 Kb/s. Para situaciones de transcodificación, el codificador propuesto también presenta desempeño superior al MELP.