Η διπλωματική έχει σαν στόχο να μελετήσει και να αξιολογήσει τεχνικές συμπίεσης που εφαρμόζονται στην περίπτωση ατόμων με πρόβλημα βαρηκοΐας. Η διαδικασία της συμπίεσης αποσκοπεί στο να αλλάξει τα επίπεδα ισχύος των ακουστικών σημάτων έτσι, ώστε να ανταποκρίνονται καλύτερα στις ακουστικές δυνατότητες του ασθενούς. Οι συμπιεστές υλοποιούνται με δυναμικές διαδικασίες επεξεργασίας σήματος ώστε να αντιδρούν άμεσα στις αλλαγές των χαρακτηριστικών του προς επεξεργασία ήχου. Οι επικρατέστερες τεχνικές θα υλοποιηθούν σε ειδική πλατφόρμα επεξεργασίας και θα αξιολογηθούν ως προς την απόδοσή τους. Θα γίνει επίσης σύγκριση με νέες τεχνικές οι οποίες θα προταθούν για πρώτη φορά στην παρούσα διπλωματική. / .

Cette thèse est le fruit d'un partenariat entre la BL TVFE de NXP Semiconductors et l'ESIEE dans le cadre d'une thèse CIFRE. Le but est d'apporter une solution qui permette la réception de plusieurs canaux pour le câble. Ce sujet est lié à la problématique de numérisation large bande. Dans la première partie, nous faisons un état-de-l'art sur les convertisseurs analogiques-numériques (CAN), sur les architectures parallèles (entrelacement temporel et bancs de filtres hybrides (BFH)), et sur les méthodes d'échantillonnage (passe-bande et complexe). Puis, nous étudions une architecture composée d'un banc de filtres analogiques et un banc de CANs. Nous cherchons à réduire surtout le taux d'échantillonnage. Nous comparons notre solution à un CAN large bande performant, avec notre fonction de coût. L'un des avantages de cette architecture est que tous les composants sont faisables, même les CANs, et qu'il est possible d'éteindre des sous-bandes pour diminuer la consommation. Cette solution est intéressante pour le moment mais n'est pas compétitive en termes de consommation et de surface. Nous proposons une alternative dans la partie 3, avec les BFH. Nous étudions cette architecture, en gardant à l'esprit la faisabilité de la solution. Nous avons choisi un BFH à deux voies, avec un filtre analogique passe-bas et un passe-haut. Puis, nous proposons un algorithme d'optimisation des filtres de synthèse pour atteindre nos objectifs de distorsion et de réjection de repliement. Une identification des filtres analogiques est aussi présentée. Finalement, une réalisation physique prouve le concept et valide les limitations théoriques de cette architecture / This thesis is a partnership between the BL TVFE of NXP Semiconductors and ESIEE. Its goal is to provide a solution to multi-channel reception for cable network. This is linked to the problematic of broadband digitization. In the first part, the state-of-the art of ADCs, parallel architectures (TI and HFB) and sampling methods (bandpass sampling and complex sampling) is recalled. Then we study an architecture called RFFB with a bank of analog filters and a bank of ADCs. We try to reduce the constraints on ADCs, especially the sampling rate with the different sampling. We propose an interesting solution to broadband digitization and compare this solution to a challenging wideband ADC, using the cost function we introduce. This architecture has the major advantage that all the components are feasible, even the ADCs, and it is possible to switch-off subbands to save power. It could be a good solution at the present time but it is not competitive in terms of power consumption and surface. An alternative is proposed in Part 3, where we study Hybrid Filter Banks. It is interesting to study this architecture with realization feasibility in mind. This is why we select a 2-channel HFB with a lowpass filter and a highpass filter as analog filters. Then we propose an efficient optimization algorithm to find the best synthesis filters and reach our targets of distortion and aliasing rejection. An identification of analog filters is also suggested to cope with the issue of sensitivity to analog errors. Finally, a physical realization proves the concept of aliasing rejection and confirms the theoretical issues of this architecture

Afin de réaliser des traitements locaux sur des données de diverses natures (volumes, images ou signaux) contenant des éléments informatifs dans certaines bandes de fréquence, nous nous intéressons dans cette thèse à l’étude de bancs de filtres (BdF). Plus précisément, nous étudions l’existence et la synthèse de BdF de réponses impulsionnelles finies (RIF) inverses d’un BdF d’analyse RIF redondant complexe fixé. Nous proposons en particulier des méthodes testant l’inversibilité de la matrice d’analyse et la construction d’un inverse explicite à l’aide de la formulation polyphase. À partir de ce dernier, nous proposons une paramétrisation réduite de l’ensemble des BdF de synthèse permettant d’optimiser leurs réponses selon différents critères. Cette étude est étendue au cas multidimensionnel notamment par l’utilisation de la notion de résultant. Ces outils permettant de représenter efficacement certaines informations structurées dans des données, il devient possible de les préserver tout en rejetant d’éventuelles perturbations. Le premier cadre considéré est celui du bruit gaussien. Nous avons utilisé le principe de Stein pour proposer deux méthodes de débruitage : FB-SURELET-E et FBSURELET-C. Elles sont comparées à des méthodes récentes de débruitage conduisant à de bons résultats en particulier pour des images texturées. Un autre type d’application est ensuite considéré : la séparation des structures orientées. Afin de traiter ce problème, nous avons développé une méthode de filtrage anisotrope. Les algorithmes réalisés sont finalement testés sur des données issues de différents domaines applicatifs (sismique, microscopie, vibrations) / Our main purpose in this PhD thesis is to perform local frequential (or directional) processing in different kind of data (volumes, images or signals). To this end, filter banks (FBs) are studied. More precisely, we first investigate the existence and the construction of synthesis FBs inverse to a given FIR complex analysis FB. Through the study of the polyphase analysis matrix, we are able to propose methods to test the invertibility and to build one inverse FB. Using this inverse, we provide a parametrization of the set of synthesis FB, with which we optimize filter responses with different criteria. The same study is performed in the multidimensional case. Since FBs provide an efficient representation of structured information in data, it is then possible to preserve them while rejecting unwanted perturbations. By associating Stein’s principle and those FB, we proposed two methods to denoise signals and images corrupted by Gaussian noise. These methods, named FB-SURELET-E and FB-SURELET-C, are compared to recent denoising methods and are found to offer good results, especially for textured images. Another type of application is then investigated : separation of oriented structures. To this end, we have developed an anisotropic filtering method. The different proposed methods are finally applied on images and signals from various fields : seismic images and cubes, transmission electron microscopy (TEM) images of catalysts and vibration signals from car engines

Research Doctorate - Doctor of Philosophy (PhD) / This thesis presents results on optimal coding and decoding of discrete-time stochastic signals, in the sense of minimizing a distortion metric subject to a constraint on the bit-rate and on the signal transfer function from source to reconstruction. The first (preliminary) contribution of this thesis is the introduction of new distortion metric that extends the mean squared error (MSE) criterion. We give this extension the name Weighted-Correlation MSE (WCMSE), and use it as the distortion metric throughout the thesis. The WCMSE is a weighted sum of two components of the MSE: the variance of the error component uncorrelated to the source, on the one hand, and the remainder of the MSE, on the other. The WCMSE can take account of signal transfer function constraints by assigning a larger weight to deviations from a target signal transfer function than to source-uncorrelated distortion. Within this framework, the second contribution is the solution of a family of feedback quantizer design problems for wide sense stationary sources using an additive noise model for quantization errors. These associated problems consist of finding the frequency response of the filters deployed around a scalar quantizer that minimize the WCMSE for a fixed quantizer signal-to-(granular)-noise ratio (SNR). This general structure, which incorporates pre-, post-, and feedback filters, includes as special cases well known source coding schemes such as pulse coded modulation (PCM), Differential Pulse-Coded Modulation (DPCM), Sigma Delta converters, and noise-shaping coders. The optimal frequency response of each of the filters in this architecture is found for each possible subset of the remaining filters being given and fixed. These results are then applied to oversampled feedback quantization. In particular, it is shown that, within the linear model used, and for a fixed quantizer SNR, the MSE decays exponentially with oversampling ratio, provided optimal filters are used at each oversampling ratio. If a subtractively dithered quantizer is utilized, then the noise model is exact, and the SNR constraint can be directly related to the bit-rate if entropy coding is used, regardless of the number of quantization levels. On the other hand, in the case of fixed-rate quantization, the SNR is related to the number of quantization levels, and hence to the bit-rate, when overload errors are negligible. It is shown that, for sources with unbounded support, the latter condition is violated for sufficiently large oversampling ratios. By deriving an upper bound on the contribution of overload errors to the total WCMSE, a lower bound for the decay rate of the WCMSE as a function of the oversampling ratio is found for fixed-rate quantization of sources with finite or infinite support. The third main contribution of the thesis is the introduction of the rate-distortion function (RDF) when WCMSE is the distortion metric, denoted by WCMSE-RDF. We provide a complete characterization for Gaussian sources. The resulting WCMSE-RDF yields, as special cases, Shannon's RDF, as well as the recently introduced RDF for source-uncorrelated distortions (RDF-SUD). For cases where only source-uncorrelated distortion is allowed, the RDF-SUD is extended to include the possibility of linear-time invariant feedback between reconstructed signal and coder input. It is also shown that feedback quantization schemes can achieve a bit-rate only 0.254 bits/sample above this RDF by using the same filters that minimize the reconstruction MSE for a quantizer-SNR constraint. The fourth main contribution of this thesis is to provide a set of conditions under which knowledge of a realization of the RDF can be used directly to solve encoder-decoder design optimization problems. This result has direct implications in the design of subband coders with feedback, as well as in the design of encoder-decoder pairs for applications such as networked control. As the fifth main contribution of this thesis, the RDF-SUD is utilized to show that, for Gaussian sta-tionary sources with memory and MSE distortion criterion, an upper bound on the information-theoretic causal RDF can be obtained by means of an iterative numerical procedure, at all rates. This bound is tighter than 0:5 bits/sample. Moreover, if there exists a realization of the causal RDF in which the re-construction error is jointly stationary with the source, then the bound obtained coincides with the causal RDF. The iterative procedure proposed here to obtain Ritc(D) also yields a characterization of the filters in a scalar feedback quantizer having an operational rate that exceeds the bound by less than 0:254 bits/sample. This constitutes an upper bound on the optimal performance theoretically attainable by any causal source coder for stationary Gaussian sources under the MSE distortion criterion.

The low-voltage power distribution network is considered today as a serious candidate to provide residential customers with a high-speed access to communication services such as Internet. Outdoor Power-Line Communications (PLC) systems represent an alternative to the other classical 'last-mile solutions' such as ADSL, cable modems, or wireless access systems. We developed an accurate powerline channel simulation tool based on the Multiconductor Transmission Line theory. This tool is able to predict the end-to-end channel responses on the basis of the multiconductor cable structure and the network topology. Then the issue of optimal resource allocation in a multiuser environment was addressed in the light of the Multiuser Information Theory. Simultaneously active users are in competition for the limited resources that are the power (constrained by electro-magnetic compatibility restrictions) and the bandwidth (in the range of 1 to 10 MHz for outdoor PLC). The concept of multiuser balanced capacity was introduced to characterize the optimal resource allocation providing the maximum data rates with fairness constraints among the subscribers. The optimal PLC system was shown to require the shaping of the signal spectrum in the transmitters, and successive decoding in the receiver. A generic multiple access scheme based on Filter Banks (FB) was proposed, which offers the required spectral shaping with limited degrees of freedom. Classical multiple-access techniques (TDMA, CDMA, OFDMA) can be obtained by selecting the appropriate FB. The Minimum-Mean-Square-Error Decision-Feedback Joint Detector was shown to approach the performance of the optimal successive decoding receiver. Finally, the robustness of the proposed system against channel estimation and timing synchronization errors was addressed. The problem of multiuser timing synchronization was introduced, and practical multiuser timing error detectors were proposed.

In Chapters 1 and 2, we introduce the definition of interpolating refinable function vectors in dimension one and high dimensions, characterize such interpolating refinable function vectors in terms of their masks, and derive their sum rule structure explicitly. We study biorthogonal refinable function vectors from interpolating refinable function vectors. We also study the symmetry property of an interpolating refinable function vector and characterize a symmetric interpolating refinable function vector in any dimension with respect to certain symmetry group in terms of its mask. Examples of interpolating refinable function vectors with some desirable properties, such as orthogonality, symmetry, compact support, and so on, are constructed according to our characterization results. In Chapters 3 and 4, we turn to the study of general matrix extension problems with symmetry for the construction of orthogonal and biorthogonal multiwavelets. We give characterization theorems and develop step-by-step algorithms for matrix extension with symmetry. To illustrate our results, we apply our algorithms to several examples of interpolating refinable function vectors with orthogonality or biorthogonality obtained in Chapter 1. In Chapter 5, we discuss some possible future research topics on the subjects of matrix extension with symmetry in high dimensions and frequency-based non-stationary tight wavelet frames with directionality. We demonstrate that one can construct a frequency-based tight wavelet frame with symmetry and show that directional analysis can be easily achieved under the framework of tight wavelet frames. Potential applications and research directions of such tight wavelet frames with directionality are discussed. / Applied Mathematics

The aim of speech scrambling algorithms is to transform clear speech into an unintelligible signal so that it is difficult to decrypt it in the absence of the key. Most of the existing speech scrambling algorithms tend to retain considerable residual intelligibility in the scrambled speech and are easy to break. Typically, a speech scrambling algorithm involves permutation of speech segments in time, frequency or time-frequency domain or permutation of transform coefficients of each speech block. The time-frequency algorithms have given very low residual intelligibility and have attracted much attention. We first study the uniform filter bank based time-frequency scrambling algorithm with respect to the block length and number of channels. We use objective distance measures to estimate the departure of the scrambled speech from the clear speech. Simulations indicate that the distance measures increase as we increase the block length and the number of chan­nels. This algorithm derives its security only from the time-frequency segment permutation and it has been estimated that the effective number of permutations which give a low residual intelligibility is much less than the total number of possible permutations. In order to increase the effective number of permutations, we propose a time-frequency scrambling algorithm based on wavelet packets. By using different wavelet packet filter banks at the analysis and synthesis end, we add an extra level of security since the eavesdropper has to choose the correct analysis filter bank, correctly rearrange the time-frequency segments, and choose the correct synthesis bank to get back the original speech signal. Simulations performed with this algorithm give distance measures comparable to those obtained for the uniform filter bank based algorithm. Finally, we introduce the 2-channel perfect reconstruction circular convolution filter bank and give a simple method for its design. The filters designed using this method satisfy the paraunitary properties on a discrete equispaced set of points in the frequency domain.

No description available.

Research Doctorate - Doctor of Philosophy (PhD) / This thesis presents results on optimal coding and decoding of discrete-time stochastic signals, in the sense of minimizing a distortion metric subject to a constraint on the bit-rate and on the signal transfer function from source to reconstruction. The first (preliminary) contribution of this thesis is the introduction of new distortion metric that extends the mean squared error (MSE) criterion. We give this extension the name Weighted-Correlation MSE (WCMSE), and use it as the distortion metric throughout the thesis. The WCMSE is a weighted sum of two components of the MSE: the variance of the error component uncorrelated to the source, on the one hand, and the remainder of the MSE, on the other. The WCMSE can take account of signal transfer function constraints by assigning a larger weight to deviations from a target signal transfer function than to source-uncorrelated distortion. Within this framework, the second contribution is the solution of a family of feedback quantizer design problems for wide sense stationary sources using an additive noise model for quantization errors. These associated problems consist of finding the frequency response of the filters deployed around a scalar quantizer that minimize the WCMSE for a fixed quantizer signal-to-(granular)-noise ratio (SNR). This general structure, which incorporates pre-, post-, and feedback filters, includes as special cases well known source coding schemes such as pulse coded modulation (PCM), Differential Pulse-Coded Modulation (DPCM), Sigma Delta converters, and noise-shaping coders. The optimal frequency response of each of the filters in this architecture is found for each possible subset of the remaining filters being given and fixed. These results are then applied to oversampled feedback quantization. In particular, it is shown that, within the linear model used, and for a fixed quantizer SNR, the MSE decays exponentially with oversampling ratio, provided optimal filters are used at each oversampling ratio. If a subtractively dithered quantizer is utilized, then the noise model is exact, and the SNR constraint can be directly related to the bit-rate if entropy coding is used, regardless of the number of quantization levels. On the other hand, in the case of fixed-rate quantization, the SNR is related to the number of quantization levels, and hence to the bit-rate, when overload errors are negligible. It is shown that, for sources with unbounded support, the latter condition is violated for sufficiently large oversampling ratios. By deriving an upper bound on the contribution of overload errors to the total WCMSE, a lower bound for the decay rate of the WCMSE as a function of the oversampling ratio is found for fixed-rate quantization of sources with finite or infinite support. The third main contribution of the thesis is the introduction of the rate-distortion function (RDF) when WCMSE is the distortion metric, denoted by WCMSE-RDF. We provide a complete characterization for Gaussian sources. The resulting WCMSE-RDF yields, as special cases, Shannon's RDF, as well as the recently introduced RDF for source-uncorrelated distortions (RDF-SUD). For cases where only source-uncorrelated distortion is allowed, the RDF-SUD is extended to include the possibility of linear-time invariant feedback between reconstructed signal and coder input. It is also shown that feedback quantization schemes can achieve a bit-rate only 0.254 bits/sample above this RDF by using the same filters that minimize the reconstruction MSE for a quantizer-SNR constraint. The fourth main contribution of this thesis is to provide a set of conditions under which knowledge of a realization of the RDF can be used directly to solve encoder-decoder design optimization problems. This result has direct implications in the design of subband coders with feedback, as well as in the design of encoder-decoder pairs for applications such as networked control. As the fifth main contribution of this thesis, the RDF-SUD is utilized to show that, for Gaussian sta-tionary sources with memory and MSE distortion criterion, an upper bound on the information-theoretic causal RDF can be obtained by means of an iterative numerical procedure, at all rates. This bound is tighter than 0:5 bits/sample. Moreover, if there exists a realization of the causal RDF in which the re-construction error is jointly stationary with the source, then the bound obtained coincides with the causal RDF. The iterative procedure proposed here to obtain Ritc(D) also yields a characterization of the filters in a scalar feedback quantizer having an operational rate that exceeds the bound by less than 0:254 bits/sample. This constitutes an upper bound on the optimal performance theoretically attainable by any causal source coder for stationary Gaussian sources under the MSE distortion criterion.

[pt] Neste trabalho é feito um estudo sobre compressão de imagens para canal ruidoso.Inicialmente, esquemas de complexidade moderada sem a utilização do princípio da separação de Shannon são investigados e simulados. Com isso, mostra-se que esquemas eficientes de codificação conjunta fonte/canal existem e podem eventualmente apresentar melhor performance do que esquemas separados de codificação e canal e fonte. São também investigados, algoritmos de codificação de imagens visando a transmissão num capital ruidoso. Nesse contexto, é proposto um esquema utilizando transformadas com superposição com boa performance, como mostram as simulações realizadas. O esquema posteriormente estendido para imagens multi- espectrais mostrando-se igualmente eficiente. / [en] In the present dissertation we investigate image compression techniques for transmission over binary symmetric channels poluted with noise. Frist we simulate some known techniques for joint source/channel coding that dispenses with the use of error correcting codes. These techiniques may exhibit better performance when complexity and delay constraits are at stake. We further propose an image compression algorithm for noisy channels based on lapped/block transforms and block source/channel coding. We simulate the proposed scheme for various channel situations. The algorithm is further extented to handle compression and transmission of multiepectral remote sensing satellite imagery. Results for natural and multiespectral images are presented showing the good performance attained by the proposed schemes.