H2 and/or H∞-norm model reduction of uncertain discrete-time systems

This paper addresses the problem of model reduction for uncertain discrete-time systems with convex bounded (polytope type) uncertainty. A reduced order precisely known model is obtained in such a way that the H2 and/or the H∞ guaranteed norm of the error between the original (uncertain) system and the reduced one is minimized. The optimization problems are formulated in terms of coupled (non-convex) LMIs - Linear Matrix Inequalities, being solved through iterative algorithms. Examples illustrate the results.

Algoritmos de Thinning e suas aplicações

This monograph aims to study the problem of thinning, also known by Image Skeletonization, to explore their applications in areas such as, Biometrics, Medicine, Engineering and Cartography. The algorithms of thinning can be classi ed into two major groups: iterative algorithms and non-iterative algorithms. Iterative are sub-divided into sequential algorithms and parallel algorithms. In order to develop a computer system able to extract the skeleton of an image, were studied, analyzed and implemented di erent algorithms for this problem, precisely those of Stentiford, Zhang Suen, and Holt

Isotone Recursive Methods for Overlapping Generation Models with Stochastic Nonclassical Production

Based on an order-theoretic approach, we derive sufficient conditions for the existence, characterization, and computation of Markovian equilibrium decision processes and stationary Markov equilibrium on minimal state spaces for a large class of stochastic overlapping generations models. In contrast to all previous work, we consider reduced-form stochastic production technologies that allow for a broad set of equilibrium distortions such as public policy distortions, social security, monetary equilibrium, and production nonconvexities. Our order-based methods are constructive, and we provide monotone iterative algorithms for computing extremal stationary Markov equilibrium decision processes and equilibrium invariant distributions, while avoiding many of the problems associated with the existence of indeterminacies that have been well-documented in previous work. We provide important results for existence of Markov equilibria for the case where capital income is not increasing in the aggregate stock. Finally, we conclude with examples common in macroeconomics such as models with fiat money and social security. We also show how some of our results extend to settings with unbounded state spaces.

Contribution to the quality improvement of the antenna measurement using post-processing techniques = Contribución a la mejora de la calidad de medida de antena usando técnicas de post-procesado

One important task in the design of an antenna is to carry out an analysis to find out the characteristics of the antenna that best fulfills the specifications fixed by the application. After that, a prototype is manufactured and the next stage in design process is to check if the radiation pattern differs from the designed one. Besides the radiation pattern, other radiation parameters like directivity, gain, impedance, beamwidth, efficiency, polarization, etc. must be also evaluated. For this purpose, accurate antenna measurement techniques are needed in order to know exactly the actual electromagnetic behavior of the antenna under test. Due to this fact, most of the measurements are performed in anechoic chambers, which are closed areas, normally shielded, covered by electromagnetic absorbing material, that simulate free space propagation conditions, due to the absorption of the radiation absorbing material. Moreover, these facilities can be employed independently of the weather conditions and allow measurements free from interferences. Despite all the advantages of the anechoic chambers, the results obtained both from far-field measurements and near-field measurements are inevitably affected by errors. Thus, the main objective of this Thesis is to propose algorithms to improve the quality of the results obtained in antenna measurements by using post-processing techniques and without requiring additional measurements. First, a deep revision work of the state of the art has been made in order to give a general vision of the possibilities to characterize or to reduce the effects of errors in antenna measurements. Later, new methods to reduce the unwanted effects of four of the most commons errors in antenna measurements are described and theoretical and numerically validated. The basis of all them is the same, to perform a transformation from the measurement surface to another domain where there is enough information to easily remove the contribution of the errors. The four errors analyzed are noise, reflections, truncation errors and leakage and the tools used to suppress them are mainly source reconstruction techniques, spatial and modal filtering and iterative algorithms to extrapolate functions. Therefore, the main idea of all the methods is to modify the classical near-field-to-far-field transformations by including additional steps with which errors can be greatly suppressed. Moreover, the proposed methods are not computationally complex and, because they are applied in post-processing, additional measurements are not required. The noise is the most widely studied error in this Thesis, proposing a total of three alternatives to filter out an important noise contribution before obtaining the far-field pattern. The first one is based on a modal filtering. The second alternative uses a source reconstruction technique to obtain the extreme near-field where it is possible to apply a spatial filtering. The last one is to back-propagate the measured field to a surface with the same geometry than the measurement surface but closer to the AUT and then to apply also a spatial filtering. All the alternatives are analyzed in the three most common near-field systems, including comprehensive noise statistical analyses in order to deduce the signal-to-noise ratio improvement achieved in each case. The method to suppress reflections in antenna measurements is also based on a source reconstruction technique and the main idea is to reconstruct the field over a surface larger than the antenna aperture in order to be able to identify and later suppress the virtual sources related to the reflective waves. The truncation error presents in the results obtained from planar, cylindrical and partial spherical near-field measurements is the third error analyzed in this Thesis. The method to reduce this error is based on an iterative algorithm to extrapolate the reliable region of the far-field pattern from the knowledge of the field distribution on the AUT plane. The proper termination point of this iterative algorithm as well as other critical aspects of the method are also studied. The last part of this work is dedicated to the detection and suppression of the two most common leakage sources in antenna measurements. A first method tries to estimate the leakage bias constant added by the receiver’s quadrature detector to every near-field data and then suppress its effect on the far-field pattern. The second method can be divided into two parts; the first one to find the position of the faulty component that radiates or receives unwanted radiation, making easier its identification within the measurement environment and its later substitution; and the second part of this method is able to computationally remove the leakage effect without requiring the substitution of the faulty component. Resumen Una tarea importante en el diseño de una antena es llevar a cabo un análisis para averiguar las características de la antena que mejor cumple las especificaciones fijadas por la aplicación. Después de esto, se fabrica un prototipo de la antena y el siguiente paso en el proceso de diseño es comprobar si el patrón de radiación difiere del diseñado. Además del patrón de radiación, otros parámetros de radiación como la directividad, la ganancia, impedancia, ancho de haz, eficiencia, polarización, etc. deben ser también evaluados. Para lograr este propósito, se necesitan técnicas de medida de antenas muy precisas con el fin de saber exactamente el comportamiento electromagnético real de la antena bajo prueba. Debido a esto, la mayoría de las medidas se realizan en cámaras anecoicas, que son áreas cerradas, normalmente revestidas, cubiertas con material absorbente electromagnético. Además, estas instalaciones se pueden emplear independientemente de las condiciones climatológicas y permiten realizar medidas libres de interferencias. A pesar de todas las ventajas de las cámaras anecoicas, los resultados obtenidos tanto en medidas en campo lejano como en medidas en campo próximo están inevitablemente afectados por errores. Así, el principal objetivo de esta Tesis es proponer algoritmos para mejorar la calidad de los resultados obtenidos en medida de antenas mediante el uso de técnicas de post-procesado. Primeramente, se ha realizado un profundo trabajo de revisión del estado del arte con el fin de dar una visión general de las posibilidades para caracterizar o reducir los efectos de errores en medida de antenas. Después, se han descrito y validado tanto teórica como numéricamente nuevos métodos para reducir el efecto indeseado de cuatro de los errores más comunes en medida de antenas. La base de todos ellos es la misma, realizar una transformación de la superficie de medida a otro dominio donde hay suficiente información para eliminar fácilmente la contribución de los errores. Los cuatro errores analizados son ruido, reflexiones, errores de truncamiento y leakage y las herramientas usadas para suprimirlos son principalmente técnicas de reconstrucción de fuentes, filtrado espacial y modal y algoritmos iterativos para extrapolar funciones. Por lo tanto, la principal idea de todos los métodos es modificar las transformaciones clásicas de campo cercano a campo lejano incluyendo pasos adicionales con los que los errores pueden ser enormemente suprimidos. Además, los métodos propuestos no son computacionalmente complejos y dado que se aplican en post-procesado, no se necesitan medidas adicionales. El ruido es el error más ampliamente estudiado en esta Tesis, proponiéndose un total de tres alternativas para filtrar una importante contribución de ruido antes de obtener el patrón de campo lejano. La primera está basada en un filtrado modal. La segunda alternativa usa una técnica de reconstrucción de fuentes para obtener el campo sobre el plano de la antena donde es posible aplicar un filtrado espacial. La última es propagar el campo medido a una superficie con la misma geometría que la superficie de medida pero más próxima a la antena y luego aplicar también un filtrado espacial. Todas las alternativas han sido analizadas en los sistemas de campo próximos más comunes, incluyendo detallados análisis estadísticos del ruido con el fin de deducir la mejora de la relación señal a ruido lograda en cada caso. El método para suprimir reflexiones en medida de antenas está también basado en una técnica de reconstrucción de fuentes y la principal idea es reconstruir el campo sobre una superficie mayor que la apertura de la antena con el fin de ser capaces de identificar y después suprimir fuentes virtuales relacionadas con las ondas reflejadas. El error de truncamiento que aparece en los resultados obtenidos a partir de medidas en un plano, cilindro o en la porción de una esfera es el tercer error analizado en esta Tesis. El método para reducir este error está basado en un algoritmo iterativo para extrapolar la región fiable del patrón de campo lejano a partir de información de la distribución del campo sobre el plano de la antena. Además, se ha estudiado el punto apropiado de terminación de este algoritmo iterativo así como otros aspectos críticos del método. La última parte de este trabajo está dedicado a la detección y supresión de dos de las fuentes de leakage más comunes en medida de antenas. El primer método intenta realizar una estimación de la constante de fuga del leakage añadido por el detector en cuadratura del receptor a todos los datos en campo próximo y después suprimir su efecto en el patrón de campo lejano. El segundo método se puede dividir en dos partes; la primera de ellas para encontrar la posición de elementos defectuosos que radian o reciben radiación indeseada, haciendo más fácil su identificación dentro del entorno de medida y su posterior substitución. La segunda parte del método es capaz de eliminar computacionalmente el efector del leakage sin necesidad de la substitución del elemento defectuoso.

A new system of variational inclusions with (H,eta)-monotone operators in Hilbert spaces

In this paper, we introduce and study a new system of variational inclusions involving (H, eta)-monotone operators in Hilbert space. Using the resolvent operator associated with (H, eta)monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm. (c) 2005 Elsevier Ltd. All rights reserved.

Advanced Techniques for Image Quality Assessment of Modern X-ray Computed Tomography Systems

X-ray computed tomography (CT) imaging constitutes one of the most widely used diagnostic tools in radiology today with nearly 85 million CT examinations performed in the U.S in 2011. CT imparts a relatively high amount of radiation dose to the patient compared to other x-ray imaging modalities and as a result of this fact, coupled with its popularity, CT is currently the single largest source of medical radiation exposure to the U.S. population. For this reason, there is a critical need to optimize CT examinations such that the dose is minimized while the quality of the CT images is not degraded. This optimization can be difficult to achieve due to the relationship between dose and image quality. All things being held equal, reducing the dose degrades image quality and can impact the diagnostic value of the CT examination.

A recent push from the medical and scientific community towards using lower doses has spawned new dose reduction technologies such as automatic exposure control (i.e., tube current modulation) and iterative reconstruction algorithms. In theory, these technologies could allow for scanning at reduced doses while maintaining the image quality of the exam at an acceptable level. Therefore, there is a scientific need to establish the dose reduction potential of these new technologies in an objective and rigorous manner. Establishing these dose reduction potentials requires precise and clinically relevant metrics of CT image quality, as well as practical and efficient methodologies to measure such metrics on real CT systems. The currently established methodologies for assessing CT image quality are not appropriate to assess modern CT scanners that have implemented those aforementioned dose reduction technologies.

Thus the purpose of this doctoral project was to develop, assess, and implement new phantoms, image quality metrics, analysis techniques, and modeling tools that are appropriate for image quality assessment of modern clinical CT systems. The project developed image quality assessment methods in the context of three distinct paradigms, (a) uniform phantoms, (b) textured phantoms, and (c) clinical images.

The work in this dissertation used the “task-based” definition of image quality. That is, image quality was broadly defined as the effectiveness by which an image can be used for its intended task. Under this definition, any assessment of image quality requires three components: (1) A well defined imaging task (e.g., detection of subtle lesions), (2) an “observer” to perform the task (e.g., a radiologists or a detection algorithm), and (3) a way to measure the observer’s performance in completing the task at hand (e.g., detection sensitivity/specificity).

First, this task-based image quality paradigm was implemented using a novel multi-sized phantom platform (with uniform background) developed specifically to assess modern CT systems (Mercury Phantom, v3.0, Duke University). A comprehensive evaluation was performed on a state-of-the-art CT system (SOMATOM Definition Force, Siemens Healthcare) in terms of noise, resolution, and detectability as a function of patient size, dose, tube energy (i.e., kVp), automatic exposure control, and reconstruction algorithm (i.e., Filtered Back-Projection– FPB vs Advanced Modeled Iterative Reconstruction– ADMIRE). A mathematical observer model (i.e., computer detection algorithm) was implemented and used as the basis of image quality comparisons. It was found that image quality increased with increasing dose and decreasing phantom size. The CT system exhibited nonlinear noise and resolution properties, especially at very low-doses, large phantom sizes, and for low-contrast objects. Objective image quality metrics generally increased with increasing dose and ADMIRE strength, and with decreasing phantom size. The ADMIRE algorithm could offer comparable image quality at reduced doses or improved image quality at the same dose (increase in detectability index by up to 163% depending on iterative strength). The use of automatic exposure control resulted in more consistent image quality with changing phantom size.

Based on those results, the dose reduction potential of ADMIRE was further assessed specifically for the task of detecting small (<=6 mm) low-contrast (<=20 HU) lesions. A new low-contrast detectability phantom (with uniform background) was designed and fabricated using a multi-material 3D printer. The phantom was imaged at multiple dose levels and images were reconstructed with FBP and ADMIRE. Human perception experiments were performed to measure the detection accuracy from FBP and ADMIRE images. It was found that ADMIRE had equivalent performance to FBP at 56% less dose.

Using the same image data as the previous study, a number of different mathematical observer models were implemented to assess which models would result in image quality metrics that best correlated with human detection performance. The models included naïve simple metrics of image quality such as contrast-to-noise ratio (CNR) and more sophisticated observer models such as the non-prewhitening matched filter observer model family and the channelized Hotelling observer model family. It was found that non-prewhitening matched filter observers and the channelized Hotelling observers both correlated strongly with human performance. Conversely, CNR was found to not correlate strongly with human performance, especially when comparing different reconstruction algorithms.

The uniform background phantoms used in the previous studies provided a good first-order approximation of image quality. However, due to their simplicity and due to the complexity of iterative reconstruction algorithms, it is possible that such phantoms are not fully adequate to assess the clinical impact of iterative algorithms because patient images obviously do not have smooth uniform backgrounds. To test this hypothesis, two textured phantoms (classified as gross texture and fine texture) and a uniform phantom of similar size were built and imaged on a SOMATOM Flash scanner (Siemens Healthcare). Images were reconstructed using FBP and a Sinogram Affirmed Iterative Reconstruction (SAFIRE). Using an image subtraction technique, quantum noise was measured in all images of each phantom. It was found that in FBP, the noise was independent of the background (textured vs uniform). However, for SAFIRE, noise increased by up to 44% in the textured phantoms compared to the uniform phantom. As a result, the noise reduction from SAFIRE was found to be up to 66% in the uniform phantom but as low as 29% in the textured phantoms. Based on this result, it clear that further investigation was needed into to understand the impact that background texture has on image quality when iterative reconstruction algorithms are used.

To further investigate this phenomenon with more realistic textures, two anthropomorphic textured phantoms were designed to mimic lung vasculature and fatty soft tissue texture. The phantoms (along with a corresponding uniform phantom) were fabricated with a multi-material 3D printer and imaged on the SOMATOM Flash scanner. Scans were repeated a total of 50 times in order to get ensemble statistics of the noise. A novel method of estimating the noise power spectrum (NPS) from irregularly shaped ROIs was developed. It was found that SAFIRE images had highly locally non-stationary noise patterns with pixels near edges having higher noise than pixels in more uniform regions. Compared to FBP, SAFIRE images had 60% less noise on average in uniform regions for edge pixels, noise was between 20% higher and 40% lower. The noise texture (i.e., NPS) was also highly dependent on the background texture for SAFIRE. Therefore, it was concluded that quantum noise properties in the uniform phantoms are not representative of those in patients for iterative reconstruction algorithms and texture should be considered when assessing image quality of iterative algorithms.

The move beyond just assessing noise properties in textured phantoms towards assessing detectability, a series of new phantoms were designed specifically to measure low-contrast detectability in the presence of background texture. The textures used were optimized to match the texture in the liver regions actual patient CT images using a genetic algorithm. The so called “Clustured Lumpy Background” texture synthesis framework was used to generate the modeled texture. Three textured phantoms and a corresponding uniform phantom were fabricated with a multi-material 3D printer and imaged on the SOMATOM Flash scanner. Images were reconstructed with FBP and SAFIRE and analyzed using a multi-slice channelized Hotelling observer to measure detectability and the dose reduction potential of SAFIRE based on the uniform and textured phantoms. It was found that at the same dose, the improvement in detectability from SAFIRE (compared to FBP) was higher when measured in a uniform phantom compared to textured phantoms.

The final trajectory of this project aimed at developing methods to mathematically model lesions, as a means to help assess image quality directly from patient images. The mathematical modeling framework is first presented. The models describe a lesion’s morphology in terms of size, shape, contrast, and edge profile as an analytical equation. The models can be voxelized and inserted into patient images to create so-called “hybrid” images. These hybrid images can then be used to assess detectability or estimability with the advantage that the ground truth of the lesion morphology and location is known exactly. Based on this framework, a series of liver lesions, lung nodules, and kidney stones were modeled based on images of real lesions. The lesion models were virtually inserted into patient images to create a database of hybrid images to go along with the original database of real lesion images. ROI images from each database were assessed by radiologists in a blinded fashion to determine the realism of the hybrid images. It was found that the radiologists could not readily distinguish between real and virtual lesion images (area under the ROC curve was 0.55). This study provided evidence that the proposed mathematical lesion modeling framework could produce reasonably realistic lesion images.

Based on that result, two studies were conducted which demonstrated the utility of the lesion models. The first study used the modeling framework as a measurement tool to determine how dose and reconstruction algorithm affected the quantitative analysis of liver lesions, lung nodules, and renal stones in terms of their size, shape, attenuation, edge profile, and texture features. The same database of real lesion images used in the previous study was used for this study. That database contained images of the same patient at 2 dose levels (50% and 100%) along with 3 reconstruction algorithms from a GE 750HD CT system (GE Healthcare). The algorithms in question were FBP, Adaptive Statistical Iterative Reconstruction (ASiR), and Model-Based Iterative Reconstruction (MBIR). A total of 23 quantitative features were extracted from the lesions under each condition. It was found that both dose and reconstruction algorithm had a statistically significant effect on the feature measurements. In particular, radiation dose affected five, three, and four of the 23 features (related to lesion size, conspicuity, and pixel-value distribution) for liver lesions, lung nodules, and renal stones, respectively. MBIR significantly affected 9, 11, and 15 of the 23 features (including size, attenuation, and texture features) for liver lesions, lung nodules, and renal stones, respectively. Lesion texture was not significantly affected by radiation dose.

The second study demonstrating the utility of the lesion modeling framework focused on assessing detectability of very low-contrast liver lesions in abdominal imaging. Specifically, detectability was assessed as a function of dose and reconstruction algorithm. As part of a parallel clinical trial, images from 21 patients were collected at 6 dose levels per patient on a SOMATOM Flash scanner. Subtle liver lesion models (contrast = -15 HU) were inserted into the raw projection data from the patient scans. The projections were then reconstructed with FBP and SAFIRE (strength 5). Also, lesion-less images were reconstructed. Noise, contrast, CNR, and detectability index of an observer model (non-prewhitening matched filter) were assessed. It was found that SAFIRE reduced noise by 52%, reduced contrast by 12%, increased CNR by 87%. and increased detectability index by 65% compared to FBP. Further, a 2AFC human perception experiment was performed to assess the dose reduction potential of SAFIRE, which was found to be 22% compared to the standard of care dose.

In conclusion, this dissertation provides to the scientific community a series of new methodologies, phantoms, analysis techniques, and modeling tools that can be used to rigorously assess image quality from modern CT systems. Specifically, methods to properly evaluate iterative reconstruction have been developed and are expected to aid in the safe clinical implementation of dose reduction technologies.

Regularization meets GreenAI: a new framework for image reconstruction in life sciences applications

Ill-conditioned inverse problems frequently arise in life sciences, particularly in the context of image deblurring and medical image reconstruction. These problems have been addressed through iterative variational algorithms, which regularize the reconstruction by adding prior knowledge about the problem's solution. Despite the theoretical reliability of these methods, their practical utility is constrained by the time required to converge. Recently, the advent of neural networks allowed the development of reconstruction algorithms that can compute highly accurate solutions with minimal time demands. Regrettably, it is well-known that neural networks are sensitive to unexpected noise, and the quality of their reconstructions quickly deteriorates when the input is slightly perturbed. Modern efforts to address this challenge have led to the creation of massive neural network architectures, but this approach is unsustainable from both ecological and economic standpoints. The recently introduced GreenAI paradigm argues that developing sustainable neural network models is essential for practical applications. In this thesis, we aim to bridge the gap between theory and practice by introducing a novel framework that combines the reliability of model-based iterative algorithms with the speed and accuracy of end-to-end neural networks. Additionally, we demonstrate that our framework yields results comparable to state-of-the-art methods while using relatively small, sustainable models. In the first part of this thesis, we discuss the proposed framework from a theoretical perspective. We provide an extension of classical regularization theory, applicable in scenarios where neural networks are employed to solve inverse problems, and we show there exists a trade-off between accuracy and stability. Furthermore, we demonstrate the effectiveness of our methods in common life science-related scenarios. In the second part of the thesis, we initiate an exploration extending the proposed method into the probabilistic domain. We analyze some properties of deep generative models, revealing their potential applicability in addressing ill-posed inverse problems.

Fast, scalable master equation solution algorithms. IV. Lanczos iteration with diffusion approximation preconditioned iterative inversion

In this paper we propose a second linearly scalable method for solving large master equations arising in the context of gas-phase reactive systems. The new method is based on the well-known shift-invert Lanczos iteration using the GMRES iteration preconditioned using the diffusion approximation to the master equation to provide the inverse of the master equation matrix. In this way we avoid the cubic scaling of traditional master equation solution methods while maintaining the speed of a partial spectral decomposition. The method is tested using a master equation modeling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long-lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

In this paper we propose a novel fast and linearly scalable method for solving master equations arising in the context of gas-phase reactive systems, based on an existent stiff ordinary differential equation integrator. The required solution of a linear system involving the Jacobian matrix is achieved using the GMRES iteration preconditioned using the diffusion approximation to the master equation. In this way we avoid the cubic scaling of traditional master equation solution methods and maintain the low temperature robustness of numerical integration. The method is tested using a master equation modelling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Update on the non-prewhitening model observer in computed tomography for the assessment of the adaptive statistical and model-based iterative reconstruction algorithms.

The state of the art to describe image quality in medical imaging is to assess the performance of an observer conducting a task of clinical interest. This can be done by using a model observer leading to a figure of merit such as the signal-to-noise ratio (SNR). Using the non-prewhitening (NPW) model observer, we objectively characterised the evolution of its figure of merit in various acquisition conditions. The NPW model observer usually requires the use of the modulation transfer function (MTF) as well as noise power spectra. However, although the computation of the MTF poses no problem when dealing with the traditional filtered back-projection (FBP) algorithm, this is not the case when using iterative reconstruction (IR) algorithms, such as adaptive statistical iterative reconstruction (ASIR) or model-based iterative reconstruction (MBIR). Given that the target transfer function (TTF) had already shown it could accurately express the system resolution even with non-linear algorithms, we decided to tune the NPW model observer, replacing the standard MTF by the TTF. It was estimated using a custom-made phantom containing cylindrical inserts surrounded by water. The contrast differences between the inserts and water were plotted for each acquisition condition. Then, mathematical transformations were performed leading to the TTF. As expected, the first results showed a dependency of the image contrast and noise levels on the TTF for both ASIR and MBIR. Moreover, FBP also proved to be dependent of the contrast and noise when using the lung kernel. Those results were then introduced in the NPW model observer. We observed an enhancement of SNR every time we switched from FBP to ASIR to MBIR. IR algorithms greatly improve image quality, especially in low-dose conditions. Based on our results, the use of MBIR could lead to further dose reduction in several clinical applications.

On the convergence of EM-like algorithms for image segmentation using Markov random fields.

Inference of Markov random field images segmentation models is usually performed using iterative methods which adapt the well-known expectation-maximization (EM) algorithm for independent mixture models. However, some of these adaptations are ad hoc and may turn out numerically unstable. In this paper, we review three EM-like variants for Markov random field segmentation and compare their convergence properties both at the theoretical and practical levels. We specifically advocate a numerical scheme involving asynchronous voxel updating, for which general convergence results can be established. Our experiments on brain tissue classification in magnetic resonance images provide evidence that this algorithm may achieve significantly faster convergence than its competitors while yielding at least as good segmentation results.

On the Convergence of Stochastic Iterative Dynamic Programming Algorithms

Recent developments in the area of reinforcement learning have yielded a number of new algorithms for the prediction and control of Markovian environments. These algorithms, including the TD(lambda) algorithm of Sutton (1988) and the Q-learning algorithm of Watkins (1989), can be motivated heuristically as approximations to dynamic programming (DP). In this paper we provide a rigorous proof of convergence of these DP-based learning algorithms by relating them to the powerful techniques of stochastic approximation theory via a new convergence theorem. The theorem establishes a general class of convergent algorithms to which both TD(lambda) and Q-learning belong.

Asynchronous distributed parallelization of mobile network optimization algorithms

It has been years since the introduction of the Dynamic Network Optimization (DNO) concept, yet the DNO development is still at its infant stage, largely due to a lack of breakthrough in minimizing the lengthy optimization runtime. Our previous work, a distributed parallel solution, has achieved a significant speed gain. To cater for the increased optimization complexity pressed by the uptake of smartphones and tablets, however, this paper examines the potential areas for further improvement and presents a novel asynchronous distributed parallel design that minimizes the inter-process communications. The new approach is implemented and applied to real-life projects whose results demonstrate an augmented acceleration of 7.5 times on a 16-core distributed system compared to 6.1 of our previous solution. Moreover, there is no degradation in the optimization outcome. This is a solid sprint towards the realization of DNO.

Brain-Computer Interfaces for augmented communication: Asynchronous and adaptive algorithms and evaluation with end users

This thesis aimed at addressing some of the issues that, at the state of the art, avoid the P300-based brain computer interface (BCI) systems to move from research laboratories to end users’ home. An innovative asynchronous classifier has been defined and validated. It relies on the introduction of a set of thresholds in the classifier, and such thresholds have been assessed considering the distributions of score values relating to target, non-target stimuli and epochs of voluntary no-control. With the asynchronous classifier, a P300-based BCI system can adapt its speed to the current state of the user and can automatically suspend the control when the user diverts his attention from the stimulation interface. Since EEG signals are non-stationary and show inherent variability, in order to make long-term use of BCI possible, it is important to track changes in ongoing EEG activity and to adapt BCI model parameters accordingly. To this aim, the asynchronous classifier has been subsequently improved by introducing a self-calibration algorithm for the continuous and unsupervised recalibration of the subjective control parameters. Finally an index for the online monitoring of the EEG quality has been defined and validated in order to detect potential problems and system failures. This thesis ends with the description of a translational work involving end users (people with amyotrophic lateral sclerosis-ALS). Focusing on the concepts of the user centered design approach, the phases relating to the design, the development and the validation of an innovative assistive device have been described. The proposed assistive technology (AT) has been specifically designed to meet the needs of people with ALS during the different phases of the disease (i.e. the degree of motor abilities impairment). Indeed, the AT can be accessed with several input devices either conventional (mouse, touchscreen) or alterative (switches, headtracker) up to a P300-based BCI.