A integração de diferentes modalidades de imagens médicas possibilita uma análise mais detalhada de seu conteúdo, visando-se um diagnóstico mais preciso da patologia presente. Este processo, conhecido como corregistro, busca o alinhamento das imagens através da transformação rígida (ou não rígida) das mesmas, por algoritmos matemáticos de distorção, translação, rotação e ajuste de escala. A amplitude de cada transformação é determinada por uma medida de similaridade das imagens. Quanto menor a similaridade, maior será a transformação aplicada. Neste sentido, a métrica de similaridade é uma peça chave do processo de corregistro. No presente trabalho, inicialmente são propostas novas definições para o cálculo dos erros de alinhamento nas transformações de translação, rotação e escala, com o objetivo de se avaliar o desempenho do corregistro. Em seguida, cinco experimentos são realizados. No primeiro, a Informação Mútua Generalizada é avaliada como medida de similaridade para corregistro em imagens fractais e cerebrais. Neste caso, os resultados sugerem a viabilidade do emprego desta métrica, pois em geral conduz a erros de alinhamento muito pequenos, mas sem vantagens aparentes em relação à formulação de Shannon. No segundo experimento, um estudo comparativo entre a Informação Mútua e as métricas clássicas (Coeficiente de Correlação, Média dos Quadrados, Diferença de Gradiente e Cardinalidade) é então realizado. Para as imagens binárias analisadas, as métricas com menores valores de erro de alinhamento para os corregistros de translação e rotação foram a Informação Mútua e a Diferença de Gradiente. Para o corregistro de escala, todas as métricas conduziram a erros de alinhamento próximos de zero. No terceiro experimento, o processo de alinhamento é investigado em termos do número de iterações do algoritmo de corregistro. Considerando-se ambas as variáveis erro de alinhamento e número de iterações, conclui-se que o uso da Informação Mútua Generalizada com q = 1.0 é adequado ao corregistro. No quarto experimento, a influência da dimensão fractal no corregistro de imagens fractais binárias foi estudada. Para algumas métricas, a tendência geral observada é a de uma diminuição do erro de alinhamento em resposta ao aumento da dimensão fractal. Finalmente, no quinto experimento, constatou-se a existência de correlação linear entre os erros de alinhamento de imagens em tons de cinza do córtex cerebral e de fractais do conjunto Julia. / The integration of different modalities of medical images provides a detailed analysis of its contents, aiming at a more accurate diagnosis of the pathology. This process, known as coregistration, seeks to align the images through rigid (or non-rigid) transformations, by mathematical algorithms of distortion, translation, rotation and scaling. The amplitude of each transformation is determined by a similarity measure of the images. The lower the similarity, the greater the transformation applied. In this sense, the similarity metric is the key for the coregistration process. In this work, new definitions are proposed for the calculation of alignment errors in the transformations of translation, rotation and scale, with the objective of evaluating the performance of coregistration. Then, five experiments are performed. In the first one, the Generalized Mutual Information is evaluated as a similarity measure for coregistration of brain images and fractals. In this case, the results suggest the feasibility of using this measure, since it leads to very small alignment errors, although no advantages in relation to Shannon formulation are evident. In the second experiment, a comparative study between Mutual Information and the classical metrics (Correlation Coefficient, Mean Squares, Gradient Difference and Cardinality) is performed. For the binary images analyzed, the metrics with lower alignment errors for translation and rotation are the Mutual Information and Gradient Difference. For scaling transformation, all the metrics lead to alignment errors close to zero. In the third experiment, the alignment process is investigated in terms of number of iterations of the coregistration algorithm. Considering both variables alignment error and number of iterations, it is concluded that the use of Generalized Mutual Information with q =1 is appropriate for coregistration. In the fourth experiment, it is studied the influence of fractal dimension in coregistration of binary fractal images. For some metrics, as a general trend, one observes the decay of the alignment error in response to the increase of the fractal dimension. Finally, in the fifth experiment, the results indicate the existence of a linear correlation between the alignment errors of grayscale images of the cerebral cortex and Julia set fractals.

Recent methods to infer genetic networks are based on identifying gene interactions by similarities in expression profiles. These methods are founded on the assumption that interacting genes share higher similarities in their expression profiles than non-interacting genes. In this dissertation this assumption is validated when using mutual information as a similarity measure. Three algorithms that calculate mutual information between expression data are developed: 1) a basic approach implemented with the histogram technique; 2) an extension of the basic approach that takes into consideration time delay between expression profiles; 3) an extension of the basic approach that takes into consideration that genes are regulated in a complex manner by multiple genes. In our experiments we compare the mutual information distributions for profiles of interacting and non-interacting genes. The results show that interacting genes do not share higher mutual information in their expression profiles than non-interacting genes, thus contradicting the basic assumption that similarity measures need to fulfil. This indicates that mutual information is not appropriate as similarity measure, which contradicts earlier proposals.

A characteristic of most real world problems is that collecting unlabelled examples is easier and cheaper than collecting labelled ones. As a result, learning from partially labelled data is a crucial and demanding area of machine learning, and extending techniques from fully to partially supervised scenarios is a challenging problem. Our work focuses on two types of partially labelled data that can occur in binary problems: semi-supervised data, where the labelled set contains both positive and negative examples, and positive-unlabelled data, a more restricted version of partial supervision where the labelled set consists of only positive examples. In both settings, it is very important to explore a large number of features in order to derive useful and interpretable information about our classification task, and select a subset of features that contains most of the useful information. In this thesis, we address three fundamental and tightly coupled questions concerning feature selection in partially labelled data; all three relate to the highly controversial issue of when does additional unlabelled data improve performance in partially labelled learning environments and when does not. The first question is what are the properties of statistical hypothesis testing in such data? Second, given the widespread criticism of significance testing, what can we do in terms of effect size estimation, that is, quantification of how strong the dependency between feature X and the partially observed label Y? Finally, in the context of feature selection, how well can features be ranked by estimated measures, when the population values are unknown? The answers to these questions provide a comprehensive picture of feature selection in partially labelled data. Interesting applications include for estimation of mutual information quantities, structure learning in Bayesian networks, and investigation of how human-provided prior knowledge can overcome the restrictions of partial labelling. One direct contribution of our work is to enable valid statistical hypothesis testing and estimation in positive-unlabelled data. Focusing on a generalised likelihood ratio test and on estimating mutual information, we provide five key contributions. (1) We prove that assuming all unlabelled examples are negative cases is sufficient for independence testing, but not for power analysis activities. (2) We suggest a new methodology that compensates this and enables power analysis, allowing sample size determination for observing an effect with a desired power by incorporating user’s prior knowledge over the prevalence of positive examples. (3) We show a new capability, supervision determination, which can determine a-priori the number of labelled examples the user must collect before being able to observe a desired statistical effect. (4) We derive an estimator of the mutual information in positive-unlabelled data, and its asymptotic distribution. (5) Finally, we show how to rank features with and without prior knowledge. Also we derive extensions of these results to semi-supervised data. In another extension, we investigate how we can use our results for Markov blanket discovery in partially labelled data. While there are many different algorithms for deriving the Markov blanket of fully supervised nodes, the partially labelled problem is far more challenging, and there is a lack of principled approaches in the literature. Our work constitutes a generalization of the conditional tests of independence for partially labelled binary target variables, which can handle the two main partially labelled scenarios: positive-unlabelled and semi-supervised. The result is a significantly deeper understanding of how to control false negative errors in Markov Blanket discovery procedures and how unlabelled data can help. Finally, we present how our results can be used for information theoretic feature selection in partially labelled data. Our work extends naturally feature selection criteria suggested for fully-supervised data, to partially labelled scenarios. These criteria can capture both the relevancy and redundancy of the features and can be used for semi-supervised and positive-unlabelled data.

Multiple-input-multiple-output (MIMO) systems of current LTE releases are capable of adaptation in the azimuth only. More recently, the trend is to enhance the system performance by exploiting the channel's degrees of freedom in the elevation through the dynamic adaptation of the vertical antenna beam pattern. This necessitates the derivation and characterization of three-dimensional (3D) channels. Over the years, channel models have evolved to address the challenges of wireless communication technologies. In parallel to theoretical studies on channel modeling, many standardized channel models like COST-based models, 3GPP SCM, WINNER, ITU have emerged that act as references for industries and telecommunication companies to assess system-level and link-level performances of advanced signal processing techniques over real-like channels. Given the existing channels are only two dimensional (2D) in nature; a large effort in channel modeling is needed to study the impact of the channel component in the elevation direction. The first part of this work sheds light on the current 3GPP activity around 3D channel modeling and beamforming, an aspect that to our knowledge has not been extensively covered by a research publication. The standardized MIMO channel model is presented, that incorporates both the propagation effects of the environment and the radio effects of the antennas. In order to facilitate future studies on the use of 3D beamforming, the main features of the proposed 3D channel model are discussed. A brief overview of the future 3GPP 3D channel model being outlined for the next generation of wireless networks is also provided. In the subsequent part of this work, we present an information-theoretic channel model for MIMO systems that supports the elevation dimension. The model is based on the principle of maximum entropy, which enables us to determine the distribution of the channel matrix consistent with the prior information on the angles of departure and angles of arrival of the propagation paths. Based on this model, an analytical expression for the cumulative density function (CDF) of the mutual information (MI) for systems with a single receive and finite number of transmit antennas in the general signal-to-interference-plus-noise-ratio (SINR) regime is provided. The result is extended to systems with multiple receive antennas in the low SINR regime. A Gaussian approximation to the asymptotic behavior of the MI distribution is derived for the large number of transmit antennas and paths regime. Simulation results study the performance gains realizable through meticulous selection of the transmit antenna down tilt angles, confirming the potential of elevation beamforming to enhance system performance. The results validate the proposed analytical expressions and elucidate the dependence of system performance on azimuth and elevation angular spreads and antenna patterns. We believe that the derived expressions will help evaluate the performance of 3D 5G massive MIMO systems in the future.

This work analyzes and discuss a issue of implementation feature selection method called Dynamic mutual information (DMIFS). Original description of the DMIFS contains several irregularities, therefore DMIFS can not be implemented exactly as original method. Results of implemented DMIFS is compared with results of original DMIFS. This results shows that implemented DMIFS is similar to the DMIFS. Next part of the work describes design of two new methods based on the DMIFS. The first method called DmRMR merges mRMR and DMIFS. Better performance but worse stability of DmRMR was proved by several tests. The second method called WDMIFS is weighted version of the DMIFS based on AdaBoost algorithm. The WDMIFS has worse performance than DMIFS. Finnaly, manual for implementing DMIFS to RapidMiner and Weka is provided.

Soil moisture influences the water and energy cycles of terrestrial environments, and thus plays an important climatic role. However, the behavior of soil moisture at large scales, including its impact on atmospheric processes such as precipitation, is not well characterized. Satellite remote sensing allows for indirect observation of large-scale soil moisture, but validation of these data is complicated by the difference in scales between remote sensing footprints and direct ground-based measurements. To address this problem, a method, based on information theory (specifically, mutual information), was developed to determine the useful information content of satellite soil moisture records using precipitation observations. This method was applied to three soil moisture datasets derived from Advanced Microwave Scanning Radiometer for EOS (AMSR-E) measurements over the contiguous U.S., allowing for spatial identification of the algorithm with the least inferred error. Ancillary measures of biomass and topography revealed a strong dependence between algorithm performance and confounding surface properties. Next, statistical causal identification methods (i.e. Granger causality) were used to examine the link between AMSR-E soil moisture and the occurrence of next day precipitation, accounting for long term variability and autocorrelation in precipitation. The probability of precipitation occurrence was modeled using a probit regression framework, and soil moisture was added to the model in order to test for statistical significance and sign. A contrasting pattern of positive feedback in the western U.S. and negative feedback in the east was found, implying a possible amplification of drought and flood conditions in the west and damping in the east. Finally, observations and simulations were used to demonstrate the pitfalls of determining causality between soil moisture and precipitation. It is shown that ignoring long term variability and precipitation autocorrelation can result in artificial positive correlation between soil moisture and precipitation, unless explicitly accounted for in the analysis. In total, this dissertation evaluates large-scale soil moisture measurements, outlines important factors that can cloud the determination of land surface-atmosphere hydrologic feedback, and examines the causal linkage between soil moisture and precipitation at large scales.

This thesis intends to familiarise the reader with quantum error correction, and also show some relations to the well known concept of information - and the lesser known quantum information. Quantum information describes how information can be carried by quantum states, and how interaction with other systems give rise to a full set of quantum phenomena, many of which have no correspondence in classical information theory. These phenomena include decoherence, as a consequence of entanglement. Decoherence can also be understood as "information leakage", i.e., knowledge of an event is transferred to the reservoir - an effect that in general destroys superpositions of pure states. It is possible to protect quantum states (e.g., qubits) from interaction with the environment - but not by amplification or duplication, due to the "no-cloning" theorem. Instead, this is done using coding, non-demolition measurements, and recovery operations. In a typical scenario, however, not all types of destructive events are likely to occur, but only those allowed by the information carrier, the type of interaction with the environment, and how the environment "picks up" information of the error events. These characteristics can be incorporated into a code, i.e., a channel-adapted quantum error-correcting code. Often, it is assumed that the environment's ability to distinguish between error events is small, and I will denote such environments "memory-less".  This assumption is not always valid, since the ability to distinguish error events is related to the \emph{temperature} of the environment, and in the particular case of information coded onto photons, <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?k_%7B%5Ctext%7BB%7D%7DT_%7B%5Ctext%7BR%7D%7D%5Cll%5Chbar%5Comega" /> typically holds, and one must then assume that the environment has a "memory". In this thesis, I describe a short quantum error-correcting code (QECC), adapted for photons interacting with a cold environment, i.e., this code protects from an environment that continuously records which error occurred in the coded quantum state. Also, it is of interest to compare the performance of different QECCs - But which yardstick should one use? We compare two such figures of merit, namely the quantum mutual information and the quantum fidelity, and show that they can not, in general, be simultaneously maximised in an error correcting procedure. To show this, we have used a five-qubit perfect code, but assumed a channel that only cause bit-flip errors. It appears that quantum mutual information is the better suited yardstick of the two, however more tedious to calculate than quantum fidelity - which is more commonly used. / Denna avhandling är en introduktion till kvantfelrättning, där jag undersöker släktskapet med teorin om klassisk information - men också det mindre välkända området kvantinformation. Kvantinformation beskriver hur information kan bäras av kvanttillstånd, och hur växelverkan med andra system ger upphov till åtskilliga typer av fel och effekter, varav många saknar motsvarighet i den klassiska informationsteorin. Bland dessa effekter återfinns dekoherens - en konsekvens av s.k. sammanflätning. Dekoherens kan också förstås som "informationsläckage", det vill säga att kunskap om en händelse överförs till omgivningen - en effekt som i allmänhet förstör superpositioner i rena kvanttillstånd.  Det är möjligt att med hjälp av kvantfelrättning skydda kvanttillstånd (t.ex. qubitar) från omgivningens påverkan, dock kan sådana tillstånd aldrig förstärkas eller dupliceras, p.g.a icke-kloningsteoremet. Tillstånden skyddas genom att införa redundans, varpå tillstånden interagerar med omgivningen. Felen identifieras m.h.a. icke-förstörande mätningar och återställs med unitära grindar och ancilla-tillstånd.Men i realiteten kommer inte alla tänkbara fel att inträffa, utan dessa begränsas av vilken informationsbärare som används, vilken interaktion som uppstår med omgivningen, samt hur omgivningen "fångar upp" information om felhändelserna. Med kunskap om sådan karakteristik kan man bygga koder, s.k. kanalanpassade kvantfelrättande koder. Vanligtvis antas att omgivningens förmåga att särskilja felhändelser är liten, och man kan då tala om en minneslös omgivning. Antagandet gäller inte alltid, då denna förmåga bestäms av reservoirens temperatur, och i det speciella fall då fotoner används som informationsbärare gäller typiskt <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?k_%7B%5Ctext%7BB%7D%7DT_%7B%5Ctext%7BR%7D%7D%5Cll%5Chbar%5Comega" />, och vi måste anta att reservoiren faktiskt har ett "minne". I avhandlingen beskrivs en kort, kvantfelrättande kod som är anpassad för fotoner i växelverkan med en "kall" omgivning, d.v.s. denna kod skyddar mot en omgivning som kontinuerligt registrerar vilket fel som uppstått i det kodade tillståndet.  Det är också av stort intresse att kunna jämföra prestanda hos kvantfelrättande koder, utifrån någon slags "måttstock" - men vilken? Jag jämför två sådana mått, nämligen ömsesidig kvantinformation, samt kvantfidelitet, och visar att dessa i allmänhet inte kan maximeras samtidigt i en felrättningsprocedur. För att visa detta har en 5-qubitarskod använts i en tänkt kanal där bara bitflip-fel uppstår, och utrymme därför finns att detektera fel. Ömsesidig kvantinformation framstår som det bättre måttet, dock är detta mått betydligt mer arbetskrävande att beräkna, än kvantfidelitet - som är det mest förekommande måttet. / <p>QC 20121206</p>

No description available.

No description available.

Multimodal image registration is essential when combining functional and structural imaging modalities. Among the most common combinations, numerous methods have been developed for co-registration of CT and PET, typically validated on human size scanners. However, only a few registration studies have been performed for the combination of small animal miniPET and microCT imaging. The Jonasson Center for Medical Imaging at KTH possesses an integrated miniPET/ microCT for pre-clinical research purposes. The motivation for this work is the need for the development of fusion method(s) for combining the data of these two modalities. In this work, a novel pipeline registration method, employing image processing and Mutual Information (MI) is proposed and implemented. The method starts with a pre-alignment step before acquisition of the miniPET/microCT volumes, followed by scaling, binarization and processing of the two volumes and finally, a registration procedure by Maximization of Mutual Information (MIM) as a voxel-based similarity metric. A established intrinsic landmarks based method is also implemented for comparison. For the validation of the methods, volumes acquired by in-house designed 3D printed Polyethylene (PE) phantoms, filled with multiple concentrations of FDG were used. The misalignment between corresponding points volumes after registration, is analyzed and compared in terms of absolute spatial distance. The proposed method based on 3D processed volumes outperformed the Landmarks based registration method, showing average misalignments of 0.5 mm. The registered volumes were also successfully visualized together using Alpha blending. By so, an automatic fusion method for miniPET/microCT has thus been implemented, presented and evaluated, raising prospects for multimodal imaging research at the Jonasson Center for Medical Imaging. / Kombinationen av funktionell och strukturell avbildning är vanlig inom medicinsk bildgivning, och koregistrering av bildvolymerna utgör en essentiell del i den multimodala framställningen. PET/CT-avbildning hör till de vanligast förekommande multimodala avbildningskombinationerna, och till följd av detta har ett antal koregistreringsmetoder utvecklats för just detta. Vad gäller pre-klinisk avbildning är dock validerade koregisteringsmetoder inte lika vanliga, och framförallt inom forskningsbaserad avbildning (där egendesignade scanners förekommer) är behovet av effektiva metoder tydligt. Inom Jonassons centrum för medicinsk avbildning på KTH har ett multimodalt miniPET/ microCT-system utvecklats, och det är just behovet av koregistering som utgjort basen för följande examensarbete. I följande arbete har en koregistreringsmetod baserad på fördefinierad bildbehandling och analys av gemensam information (mutual information, MI) implementerats och testats. Metoden bygger på ett initialt upplinjeringssteg innan microCT/ miniPET bildtagning. Efter detta genomförs en rad bildbehandlingssteg (skalning, binärisering) innan en slutgiltig koregistrering genomförs med hjälp av s.k. maximering av gemensam information (Maximization of Mutual Information, MIM). En etablerad landmärkesbaserad metod implementerades även som jämförelse. Metoderna testades sedan genom multimodal avbildning av egendesignade 3D-printade fantomer, fyllda med varierande aktivitet av FDG. Den föreslagna MI-metoden överträffade den etablerade landmärkesmetoden, med ett genomsnittligt koregistreringsfel på 0.5 mm. Visualisering av de koregistrerade volymerna genomfördes även genom så kallad alpha blending. Genom detta har en koregistreringsmetod för miniPET/microCT:n på Jonassons center för medicinsk avbildning implementerats och testats, vilket möjliggör för framtida studier av multimodal avbilning på KTH.