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We explore the applicability of local polynomial approximation of signals for noise suppression. In the context of data regression, Savitzky and Golay showed that least-squares approximation of data with a polynomial of fixed order, together with a constant window length, is identical to convolution with a finite impulse response filter, whose characteristics depend entirely on two parameters, namely, the order and window length. Schafer’s recent article in IEEE Signal Processing Magazine provides a detailed account of one-dimensional Savitzky-Golay (SG) filters. Drawing motivation from this idea, we present an elaborate study of two-dimensional SG filters and employ them for image denoising by optimizing the filter response to minimize the mean-squared error (MSE) between the original image and the filtered output. The key contribution of this thesis is a method for optimal selection of order and window length of SG filters for denoising images. First, we apply the denoising technique for images contaminated by additive Gaussian noise. Owing to the absence of ground truth in practice, direct minimization of the MSE is infeasible. However, the classical work of C. Stein provides a statistical method to overcome the hurdle. Based on Stein’s lemma, an estimate of the MSE, namely Stein’s unbiased risk estimator (SURE), is derived, and the two critical parameters of the filter are optimized to minimize the cost. The performance of the technique improves when a regularization term, which penalizes fast variations in the estimate, is added to the optimization cost. In the next three chapters, we focus on non-Gaussian noise models. In Chapter 3, image degradation in the presence of a compound noise model, where images are corrupted by mixed Poisson-Gaussian noise, is addressed. Inspired by Hudson’s identity, an estimate of MSE, namely Poisson unbiased risk estimator (PURE), which is analogous to SURE, is developed. Combining both lemmas, Poisson-Gaussian unbiased risk estimator (PGURE) minimization is performed to obtain the optimal filter parameters. We also show that SG filtering provides better lowpass approximation for a multiresolution denoising framework. In Chapter 4, we employ SG filters for reducing multiplicative noise in images. The standard SG filter frequency response can be controlled along horizontal or vertical directions. This limits its ability to capture oriented features and texture that lie at other angles. Here, we introduce the idea of steering the SG filter kernel and perform mean-squared error minimization based on the new concept of multiplicative noise unbiased risk estimation (MURE). Finally, we propose a method to robustify SG filters, robustness to deviation from Gaussian noise statistics. SG filters work on the principle of least-squares error minimization, and are hence compatible with maximum-likelihood (ML) estimation in the context of Gaussian statistics. However, for heavily-tailed noise such as the Laplacian, where ML estimation requires mean-absolute error minimization in lieu of MSE minimization, standard SG filter performance deteriorates. `1 minimization is a challenge since there is no closed-form solution. We solve the problem by inducing the `1-norm criterion using the iteratively reweighted least-squares (IRLS) method. At every iteration, we solve an l`2 problem, which is equivalent to optimizing a weighted SG filter, but, as iterations progress, the solution converges to that corresponding to `1 minimization. The results thus obtained are superior to those obtained using the standard SG filter.

Approved for public release, distribution is unlimited / Despite the increase in the demand for high speed Internet services, the last-mile solutions currently available neither are inexpensive enough to attract the majority of the population, nor are they available in low density populated areas. This thesis examines Fixed Broadband Wireless (FBW) as an alternative technology to the current last-mile solutions. The analysis shows that LMDS and MMDS are the most promising emerging FBW technologies and that they are able, by utilizing microwave radio as their fundamental transport medium and using high modulation schemes, to provide digital two-way voice, data, video and Internet services. The thesis shows that both technologies are constrained by free space loss and line-of-sight impairments with rain absorption being the most significant cause of attenuation in the LMDS case, while vegetation and multipath fading play a significant role mostly in the MMDS case. Additionally, it is shown that there is a positive association between the data rate achieved and the level of influence due to Additive White Gaussian Noise (AWGN). Based on the analysis and using the coverage areas, the total capacity, the achieved data rates, the weather and line-of-sight limitations as well as the cost as the most important criteria, it is concluded that LMDS is a preferable solution for enterprise end-users in densely populated urban areas outside the reach of fiber networks, while MMDS targets residential end-users in rural or suburban areas that are not able to receive service through high-speed wireline connections. / Lieutenant Junior Grade, Hellenic Navy

Approved for public release; distribution in unlimited. / In this thesis, a performance analysis and improvement of a phase sampling interferometer antenna system based on the Robust Symmetrical Number System (RSNS) in the presence of noise is investigated. Previous works have shown that the RSNS-based DF technique can provide high bearing resolution with a minimum number of antenna elements. However, the previous experimental data showed significant deviation from the theoretical results expected due to imperfections, errors, and noise. Therefore, an additive Gaussian noise model of RSNS-based DF was established and simulated. Simulation results show that the presence of noise distorts the signal amplitudes used in the RSNS processor and causes degradation of the angle-ofarrival estimates. A performance analysis was undertaken by first introducing the quadrature modulation configuration into RSNS-based DF system, which provided a digital antenna approach for more flexibility in the signal processing. With a digital approach, variable resolution signal preprocessing can be employed, using a virtual channel concept. The virtual channel concept changes moduli values without changing the actual physical antenna element spacing. This attractive property allows the RSNS algorithm to be implemented into existing antenna arrays and only requires modifying the antenna signal processor. Computer simulation results showed that the proposed method can successfully improve the system performance and also mitigate the effects of noise. / Captain, Taiwan Army

Tese de doutoramento. Engenharia Electrotécnica e de Computadores. Universidade do Porto. Faculdade de Engenharia. 2011

<p>Behaviour occurs in time, and precise timing in the range of seconds and fractions of seconds is for most living organisms necessary for successful interaction with the environment. Our ability to time discrete actions and to predict events on the basis of prior events indicates the existence of an internal timing mechanism. The nature of this mechanism provides essential constraints on models of the functional organisation of the brain. </p><p>The present work indicates that there are discontinuities in the function of time close to 1 s and 1.4 s, both in the amount of drift in a series of produced intervals (Study I) and in the detectability of drift in a series of sounds (Study II). The similarities across different tasks further suggest that action and perceptual judgements are governed by the same (kind of) mechanism. Study III showed that series of produced intervals could be characterised by different amounts of positive fractal dependency related to the aforementioned discontinuities. </p><p>In conjunction with other findings in the literature, these results suggest that timing of intervals up to a few seconds is strongly dependent on previous intervals and on the duration to be timed. This argues against a clock-counter mechanism, as proposed by scalar timing theory, according to which successive intervals are random and the size of the timing error conforms to Weber's law. </p><p>A functional model is proposed, expressed in an autoregressive framework, which consists of a single-interval timer with error corrective feedback. The duration-specificity of the proposed model is derived from the order of error correction, as determined by a semi-flexible temporal integration span. </p>

Behaviour occurs in time, and precise timing in the range of seconds and fractions of seconds is for most living organisms necessary for successful interaction with the environment. Our ability to time discrete actions and to predict events on the basis of prior events indicates the existence of an internal timing mechanism. The nature of this mechanism provides essential constraints on models of the functional organisation of the brain. The present work indicates that there are discontinuities in the function of time close to 1 s and 1.4 s, both in the amount of drift in a series of produced intervals (Study I) and in the detectability of drift in a series of sounds (Study II). The similarities across different tasks further suggest that action and perceptual judgements are governed by the same (kind of) mechanism. Study III showed that series of produced intervals could be characterised by different amounts of positive fractal dependency related to the aforementioned discontinuities. In conjunction with other findings in the literature, these results suggest that timing of intervals up to a few seconds is strongly dependent on previous intervals and on the duration to be timed. This argues against a clock-counter mechanism, as proposed by scalar timing theory, according to which successive intervals are random and the size of the timing error conforms to Weber's law. A functional model is proposed, expressed in an autoregressive framework, which consists of a single-interval timer with error corrective feedback. The duration-specificity of the proposed model is derived from the order of error correction, as determined by a semi-flexible temporal integration span.

Estimation of the self-similarity exponent has attracted growing interest in recent decades and became a research subject in various fields and disciplines. Real-world data exhibiting self-similar behavior and/or parametrized by self-similarity exponent (in particular Hurst exponent) have been collected in different fields ranging from finance and human sciencies to hydrologic and traffic networks. Such rich classes of possible applications obligates researchers to investigate qualitatively new methods for estimation of the self-similarity exponent as well as identification of long-range dependencies (or long memory). In this thesis I present the Bayesian estimation of the Hurst exponent. In contrast to previous methods, the Bayesian approach allows the possibility to calculate the point estimator and confidence intervals at the same time, bringing significant advantages in data-analysis as discussed in this thesis. Moreover, it is also applicable to short data and unevenly sampled data, thus broadening the range of systems where the estimation of the Hurst exponent is possible. Taking into account that one of the substantial classes of great interest in modeling is the class of Gaussian self-similar processes, this thesis considers the realizations of the processes of fractional Brownian motion and fractional Gaussian noise. Additionally, applications to real-world data, such as the data of water level of the Nile River and fixational eye movements are also discussed. / Die Abschätzung des Selbstähnlichkeitsexponenten hat in den letzten Jahr-zehnten an Aufmerksamkeit gewonnen und ist in vielen wissenschaftlichen Gebieten und Disziplinen zu einem intensiven Forschungsthema geworden. Reelle Daten, die selbsähnliches Verhalten zeigen und/oder durch den Selbstähnlichkeitsexponenten (insbesondere durch den Hurst-Exponenten) parametrisiert werden, wurden in verschiedenen Gebieten gesammelt, die von Finanzwissenschaften über Humanwissenschaften bis zu Netzwerken in der Hydrologie und dem Verkehr reichen. Diese reiche Anzahl an möglichen Anwendungen verlangt von Forschern, neue Methoden zu entwickeln, um den Selbstähnlichkeitsexponenten abzuschätzen, sowie großskalige Abhängigkeiten zu erkennen. In dieser Arbeit stelle ich die Bayessche Schätzung des Hurst-Exponenten vor. Im Unterschied zu früheren Methoden, erlaubt die Bayessche Herangehensweise die Berechnung von Punktschätzungen zusammen mit Konfidenzintervallen, was von bedeutendem Vorteil in der Datenanalyse ist, wie in der Arbeit diskutiert wird. Zudem ist diese Methode anwendbar auf kurze und unregelmäßig verteilte Datensätze, wodurch die Auswahl der möglichen Anwendung, wo der Hurst-Exponent geschätzt werden soll, stark erweitert wird. Unter Berücksichtigung der Tatsache, dass der Gauß'sche selbstähnliche Prozess von bedeutender Interesse in der Modellierung ist, werden in dieser Arbeit Realisierungen der Prozesse der fraktionalen Brown'schen Bewegung und des fraktionalen Gauß'schen Rauschens untersucht. Zusätzlich werden Anwendungen auf reelle Daten, wie Wasserstände des Nil und fixierte Augenbewegungen, diskutiert.

Physical systems far from thermo dynamic equilibrium present excitability and irreversibility. The excitability is responsible for the great sensitivity of these systems to external stimuli while the irreversibility is associated with energy dissipation. The thermal fluctuations, inevitable in any real system, arise due to the interaction between many particles of the system. For such systems one of the best approaches is given by the non-equilibrium Statistical Mechanics, since it is virtually impossible an individualized approach of the motion equations. Many works in the current literature use a Gaussian stochastic modeling (without correlations) to represent the fluctuations. However, there is a growing number of studies reporting the occurrence of correlated fluctuations, mainly related to biological systems. In this thesis we investigate the influence of non-Gaussian stochastic distribution on the properties for two representative excitable models. In the first model we study the influence of distribution on the neural dynamics through the stochastic resonance (SR) mechanism. In the second model we approach the ratchet effect (RE) on directed transport of particles. In both systems we use a non-Gaussian power-law distributed noise obtained through a random multiplicative process (RMP). This process allows a fine tuning of the asymptotic power-law decay exponent. The optimization conditions are reported. In particular, we show that the optimization conditions for resonance and directed transport in Brownian ratchets are reached for a finit decay exponent of the stochastic distribution that represents a Strong non-Gaussian character. As non-Gaussian fluctuations occur with great frequency in natural systems, we believe that the non-Gaussian character can optimize the efficiency on the stochastic transport mechanisms in micro and nanoscale. / Fundação de Amparo a Pesquisa do Estado de Alagoas / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Sistemas físicos fora do equilíbrio termo dinâmico apresentam excitabilidade e irreversibilidade. A excitabilidade é responsável pela grande sensibilidade desses sistemas a estímulos externos enquanto a irreversibilidade está asso ciada à dissipação de energia. As flutuações térmicas, inevitáveis em qualquer sistema real, surgem devido à interação entre as inúmeras partículas do meio. Para tais sistemas uma das melhores abordagens é dada pela Mecânica Estatística de não-equilíbrio, uma vez que é praticamente impossível uma abordagem individualizada das equações de movimento. Muitos trabalhos na literatura atual utilizam uma modelagem estocástica gaussiana (sem correlação) para representar as flutuações. No entanto, há um número crescente de trabalhos que relatam a ocorrência de flutuações correlacionadas, principalmente em sistemas biológicos. Nesta tese nós investigamos a influência da distribuição estocástica não-gaussiana sobre as propriedades de dois modelos excitáveis representativos. No primeiro, estudamos a influência da distribuição sobre a dinâmica neural através do mecanismo de ressonância estocástica (RE). No segundo, abordamos o mecanismo do efeito catraca (EC) sobre o transporte direcionado de partículas. Nos dois sistemas utilizamos um ruído colorido não-gaussiano com distribuição tipo lei de potência obtido através de um processo multiplicativo aleatório (PMA). Esse processo permite o ajuste no do expoente de decaimento assintótico da lei de potência. As condições de otimização são relatadas. Em particular, obtivemos que as condições de otimização para a ressonância e para o transporte direcionado em catracas brownianas são atingidas para um valor finito do expoente da distribuição estocástica que representa um caráter fortemente não-gaussiano. Como flutuações não-gaussianas o correm com muita frequência nos sistemas naturais, acreditamos que o caráter não-gaussiano pode otimizar a eficiência dos mecanismos estocásticos de transporte em micro e nanoescala.

A Broadcast Channel is a communication path between a single source and two or more receivers or users. The source intends to communicate independent information to the users. A particular case of interest is the Gaussian Broadcast Channel (GBC) where the noise at each user is additive white Gaussian noise (AWGN). The capacity region of GBC is well known and the input to the channel is distributed as Gaussian. The capacity region of another special case of GBC namely Fading Broadcast Channel (FBC)was given in [Li and Goldsmith, 2001]and was shown that superposition of Gaussian codes is optimal for the FBC (treated as a vector degraded Broadcast Channel). The capacity region obtained when the input to the channel is distributed uniformly over a finite alphabet(Constellation)is termed as Constellation Constrained(CC) capacity region [Biglieri 2005]. In this thesis the CC capacity region for two-user GBC and the FBC are obtained. In case of GBC the idea of superposition coding with input from finite alphabet and CC capacity was explored in [Hupert and Bossert, 2007]but with some limitations. When the participating individual signal sets are nearly equal i.e., given total average power constraint P the rate reward α (also the power sharing parameter) is approximately equal to 0.5, we show via simulation that with rotation of one of the signal sets by an appropriate angle the CC capacity region is maximally enlarged. We analytically derive the expression for optimal angle of rotation. In case of FBC a heuristic power allocation procedure called finite-constellation power allocation procedure is provided through which it is shown (via simulation)that the ergodic CC capacity region thus obtained completely subsumes the ergodic CC capacity region obtained by allocating power using the procedure given in[Li and Goldsmith, 2001].It is shown through simulations that rotating one of the signal sets by an optimal angle (obtained by trial and error method)for a given α maximally enlarges the ergodic CC capacity region when finite-constellation power allocation is used. An expression for determining the optimal angle of rotation for the given fading state, is obtained. And the effect of rotation is maximum around the region corresponding to α =0.5. For both GBC and FBC superposition coding is done at the transmitter and successive decoding is carried out at the receivers.