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<p>X-ray computed tomography (CT) is a non-destructive medical imaging technique for assessing the cross-sectional images of an object in terms of attenuation. As it is designed based on the physical processes involved in the x-ray and matter interactions, faithfully modeling the physics in the reconstruction procedure can yield accurate attenuation distribution of the scanned object. Otherwise, unrealistic physical assumptions can result in unwanted artifacts in reconstructed images. For example, the current reconstruction algorithms assume the photons emitted by the x-ray source are mono-energetic. This oversimplified physical model neglects the poly-energetic properties of the x-ray source and the nonlinear attenuations of the scanned materials, and results in the well-known beam-hardening artifacts (BHAs). The purpose of this work was to incorporate the poly-energetic nature of the x-ray spectrum and then to eliminate BHAs. By accomplishing this, I can improve the image quality, enable the quantitative reconstruction ability of the single-spectrum CT scanner, and potentially reduce unnecessary radiation dose to patients.</p><p>In this thesis, in order to obtain accurate spectrum for poly-energetic reconstruction, I first presented a novel spectral estimation technique, with which spectra across a large range of angular trajectories of the imaging field of view can be estimated with a single phantom and a single axial acquisition. The experimental results with a 16 cm diameter cylindrical phantom (composition: ultra-high-molecular-weight polyethylene [UHMWPE]) on a clinical scanner showed that the averaged absolute mean energy differences and the normalized root mean square differences with respect to the actual spectra across kVp settings (i.e., 80, 100, 120, 140) and angular trajectories were less than 0.61 keV and 3.41%, respectively</p><p>With the previous estimation of the x-ray spectra, three poly-energetic reconstruction algorithms are proposed for different clinical applications. The first algorithm (i.e., poly-energetic iterative FBP [piFBP]) can be applied to routine clinical CT exams, as the spectra of the x-ray source and the nonlinear attenuations of diverse body tissues and metal implant materials are incorporated to eliminate BHAs and to reduce metal artifacts. The simulation results showed that the variation range of the relative errors of various tissues across different phantom sizes (i.e., 16, 24, 32, and 40 cm in diameter) and kVp settings (80, 100, 120, 140) were reduced from [-7.5%, 17.5%] for conventional FBP to [-0.1%, 0.1%] for piFBP, while the noise was maintained at the same low level (about [0.3%, 1.7%]).</p><p>When iodinated contrast agents are involved and patient motions are not readily correctable (e.g., in myocardial perfusion exam), a second algorithm (i.e., poly-energetic simultaneous algebraic reconstruction technique [pSART]) can be applied to eliminate BHAs and to quantitatively determine the iodine concentrations of blood-iodine mixtures with our new technique. The phantom experiment on a clinical CT scanner indicated that the maximum absolute relative error across material inserts was reduced from 4.1% for conventional simultaneous algebraic reconstruction technique [SART] to 0.4% for pSART.</p><p>Extending the work beyond minimizing BHAs, if patient motions are correctable or negligible, a third algorithm (i.e., poly-energetic dynamic perfusion algorithm [pDP]) is developed to retrieve iodine maps of any iodine-tissue mixtures in any perfusion exams, such as breast, lung, or brain perfusion exams. The quantitative results of the simulations with a dynamic anthropomorphic thorax phantom indicated that the maximum error of iodine concentrations can be reduced from 1.1 mg/cc for conventional FBP to less than 0.1 mg/cc for pDP.</p><p>Two invention disclosure forms based on the work presented in this thesis have been submitted to Office of Licensing & Ventures of Duke University.</p> / Dissertation

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Este trabalho apresenta um estudo para a qualificação do sensor de detonação como elemento de realimentação para o sistema de controle eletrônico de motores de combustão interna. A metodologia proposta consiste no uso do sensor de detonação, previamente instalado pelo fabricante do motor com a finalidade de eliminar o indesejável efeito da combustão espontânea, para amostrar as vibrações mecânicas produzidas pelo motor em funcionamento. Tal vibração, resultado de massas em movimento e da oscilação natural do sistema excitado pela combustão, produz uma figura espectral na faixa de freqüências do som audível. O método proposto contempla ainda as variações espectrais das vibrações de um mesmo motor operando com diferentes misturas combustíveis. / This dissertation analyses the suitability of using the knock sensor as a feedback element for the electronic control of internal combustion engines. The proposed approach consists of using the knock sensor, originally installed by the engine maker in order to eliminate the spontaneous combustion effect, to sample the mechanical vibration produced by the engine. This vibration, which results from the moving parts and the natural oscillation of the system in combustion, produces an output in the range of audible sound. This research contemplates using the spectral variation of that sound to estimate information about an engine operating with different fuel blends.

Este trabalho apresenta um novo algoritmo para a estimação de frequências e amortecimentos de vibrações, baseado em aproximantes de Padé, a partir da análise de sinais temporais oriundos de estruturas de grande porte. O algoritmo se baseia nas propriedades de convergência dos aproximantes de Padé, que garantem a existência de pólos que representam corretamente as componentes senoidais do sinal, e numa peculiar distribuição de pólos e zeros espúrios que decorrem da sobre-determinação do aproximante. O comportamento estatístico do algoritmo é estudado através de experimentos numéricos e sua aplicação em um caso real é feita. / This work introduces a novel estimation technique for vibration frequency and damping estimation, based on Padé approximants, and using time series taken from large structures. The algorithm is based on convergence properties of Padé approximants that assures the existence of real poles representing the sinusoidal components of the signal, and a remarkable distribution of stray poles and zeros, resulting from the approximant overdetermination. Its statistical behavior is analyzed through numerical experiments and an application for a real structure is provided as example.

Este trabalho apresenta um novo algoritmo para a estimação de frequências e amortecimentos de vibrações, baseado em aproximantes de Padé, a partir da análise de sinais temporais oriundos de estruturas de grande porte. O algoritmo se baseia nas propriedades de convergência dos aproximantes de Padé, que garantem a existência de pólos que representam corretamente as componentes senoidais do sinal, e numa peculiar distribuição de pólos e zeros espúrios que decorrem da sobre-determinação do aproximante. O comportamento estatístico do algoritmo é estudado através de experimentos numéricos e sua aplicação em um caso real é feita. / This work introduces a novel estimation technique for vibration frequency and damping estimation, based on Padé approximants, and using time series taken from large structures. The algorithm is based on convergence properties of Padé approximants that assures the existence of real poles representing the sinusoidal components of the signal, and a remarkable distribution of stray poles and zeros, resulting from the approximant overdetermination. Its statistical behavior is analyzed through numerical experiments and an application for a real structure is provided as example.

Este trabalho apresenta um estudo para a qualificação do sensor de detonação como elemento de realimentação para o sistema de controle eletrônico de motores de combustão interna. A metodologia proposta consiste no uso do sensor de detonação, previamente instalado pelo fabricante do motor com a finalidade de eliminar o indesejável efeito da combustão espontânea, para amostrar as vibrações mecânicas produzidas pelo motor em funcionamento. Tal vibração, resultado de massas em movimento e da oscilação natural do sistema excitado pela combustão, produz uma figura espectral na faixa de freqüências do som audível. O método proposto contempla ainda as variações espectrais das vibrações de um mesmo motor operando com diferentes misturas combustíveis. / This dissertation analyses the suitability of using the knock sensor as a feedback element for the electronic control of internal combustion engines. The proposed approach consists of using the knock sensor, originally installed by the engine maker in order to eliminate the spontaneous combustion effect, to sample the mechanical vibration produced by the engine. This vibration, which results from the moving parts and the natural oscillation of the system in combustion, produces an output in the range of audible sound. This research contemplates using the spectral variation of that sound to estimate information about an engine operating with different fuel blends.

This thesis is concerned with convex optimization problems over matrix polynomials that are constrained to be positive semidefinite on the unit circle. Problems of this form appear in signal processing and can often be solved as semidefinite programs (SDPs). Interior-point solvers for these SDPs scale poorly, and this thesis aims to design first-order methods that are more efficient. We propose methods based on a generalized proximal operator defined in terms of a Bregman divergence. Empirical results on three applications in signal processing demonstrate that the proposed methods scale much better than interior-point solvers. As an example, for sparse estimation of spectral density matrices, Douglas--Rachford splitting with the generalized proximal operator is about 1000 times faster and scales to much larger problems. The ability to solve larger problems allows us to perform functional connectivity analysis of the brain by constructing a sparse estimate of the inverse spectral density matrix.

The aim of this study is to examine the capability, performance, and relevance of a signal processing toolkit in Java, a programming language for Web-based applications. Due to the simplicity, ease and application use of the toolkit and with the advanced Internet technologies such as Remote Method Invocation (RMI), a spectral estimation applet has been created in the Java environment. This toolkit also provides an interactive and visual approach in understanding the various theoretical concepts of spectral estimation and shows the need to create more application applets to better understand the various concepts of signal and image processing. This study also focuses on creating a Java toolkit for embedded systems, such as Personal Digital Assistants (PDAs), embedded Java board, and supporting integer precision, and utilizing COordinate Rotation DIgital Computer (CORDIC) algorithm, both aimed to provide good performance in resource-limited environments. The results show a feasibility and necessity of developing a standardized Application Programming Interface (API) for the fixed-point signal processing library.

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