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Dans cette thèse, nous développons des modèles et des méthodes statistiques pour le traitement d’images de microscopie confocale de la peau dans le but de détecter une maladie de la peau appelée lentigo. Une première contribution consiste à proposer un modèle statistique paramétrique pour représenter la texture dans le domaine des ondelettes. Plus précisément, il s’agit d’une distribution gaussienne généralisée dont on montre que le paramètre d’échelle est caractéristique des tissus sousjacents. La modélisation des données dans le domaine de l’image est un autre sujet traité dans cette thèse. A cette fin, une distribution gamma généralisée est proposée. Notre deuxième contribution consiste alors à développer un estimateur efficace des paramètres de cette loi à l’aide d’une descente de gradient naturel. Finalement, un modèle d’observation de bruit multiplicatif est établi pour expliquer la distribution gamma généralisée des données. Des méthodes d’inférence bayésienne paramétrique sont ensuite développées avec ce modèle pour permettre la classification d’images saines et présentant un lentigo. Les algorithmes développés sont appliqués à des images réelles obtenues d’une étude clinique dermatologique. / In this work, we develop statistical models and processing methods for confocal microscopy images. The first contribution consists of a parametric statistical model to represent textures in the wavelet domain. Precisely, a generalized Gaussian distribution is proposed, whose scale parameter is shown to be discriminant of the underlying tissues. The thesis deals also with modeling data in the image domain using the generalized gamma distribution. The second contribution develops an efficient parameter estimator for this distribution based on a natural gradient approach. The third contribution establishes a multiplicative noise observation model to explain the distribution of the data. Parametric Bayesian inference methods are subsequently developed based on this model to classify healthy and lentigo images. All algorithms developed in this thesis have been applied to real images from a dermatologic clinical study.

The extent of Arctic sea ice has decreased over the years and the importance of sea ice monitoring is expected to increase. Remote sensing change detection compares images acquired over the same geographic area at different times in order to identify changes that might have occurred in the area of interest. Change detection methods have been developed for cryospheric topics. The Kittler-Illingworth thresholding algorithm has proven to be an effective change detection tool, but has not been used for sea ice. Here it is applied to Arctic sea ice data. The objective is to investigate the unsupervised detection of changes in Arctic sea ice using multi-temporal SAR images. The well-known Kittler-Illingworth algorithm is tested using two density function models, i.e., the generalized Gaussian and the log-normal model. The difference image is obtained using the modified ratio operator. The histogram of the change image, which approximates its probability distribution, is considered to be a combination of two classes, i.e., the changed and unchanged classes. Histogram fitting techniques are used to estimate the unknown density functions and the prior probabilities. The optimum threshold is selected using a criterion function directly related to classification error. In this thesis three datasets were used covering parts of the Beaufort Sea from the years 1992, 2002, 2007 and 2009. The SAR and ASAR C-band data came from satellites ERS and ENVISAT respectively. All three were interpreted visually. For all three datasets, the generalized Gaussian detected a lot of change, whereas the log-normal detected less. Only one small subset of a dataset was validated against reference data. The log-normal distribution then obtained 0% false alarm rate through all trials. The generalized Gaussian obtained false alarm rates around 4% for most of the trials. The generalized Gaussian achieved detection accuracies around 95%, whereas the log-normal achieved detection accuracies around 70%. The overall accuracies for the generalized Gaussian were about 95% in most trials. The log-normal achieved overall accuracies at around 85%. The KHAT for the generalized Gaussian was in the range of 0.66-0.93. The KHAT for log-normal was in the range of 0.68-0.77. Using one additional speckle filter iteration increased the accuracy for the log-normal distribution. Generally, the detection of positive change has been accomplished with higher level of accuracy compared with negative change detection. A visual inspection shows that the generalized Gaussian distribution probably over-estimates the change. The log-normal distribution consistently detects less change than the generalized Gaussian. Lack of validation data made validation of the results difficult. The performed validation might not be reliable since the available validation data was only SAR imagery and differentiating change and no-change is difficult in the area. Further due to the lack of reference data it could not be decided, with certainty, which distribution performed the best. / Ytan av arktisk havsis har minskat genom åren och vikten av havsisövervakning förväntas öka. Förändrigsdetection jämför bilder från samma geografiska område från olika tidpunkter föra att identifiera förändringar som kan ha skett i intresseområdet. Förändringsdekteringsmetoder har utvecklats för kryosfäriska ämnen. Tröskelvärdesbestämning med Kittler-Illingworth algoritmen har visats sig vara ett effektivt verktyg för förändringsdetektion, men har inte änvänts på havsis. Här appliceras algoritmen på arktisk havsis. Målet är att undersökra oövervakad förändringsdetektion i arktisk havsis med multitemporella SAR bilder. Den välkända Kittler-Illingworth algoritmen testas med två täthetsfunktioner, nämligen generaliserad normaldistribution och log-normal distributionen. Differensbilden erhålls genom den modifierad ratio-operator. Histogrammet från förändringsbilden skattar dess täthetsfunktion, vilken anses vara en kombination av två klasser, förändring- och ickeförändringsklasser. Histogrampassningstekniker används för att uppskatta de okända täthetsfunktionerna och a priori sannolikheterna. Det optimala tröskelvärdet väljs genom en kriterionfunktion som är direkt relaterad till klassifikationsfel. I detta examensarbete användes tre dataset som täcker delar av Beaufort-havet från åren 1992, 2002, 2007 och 2009. SAR C-band data kom från satelliten ERS och ASAR C-band data kom från satelliten ENVISAT. Alla tre tolkades visuellt och för alla tre detekterade generaliserad normaldistribution mycket mer förändring än lognormal distributionen. Bara en mindre del av ett dataset validerades mot referensdata. Lognormal distributionen erhöll då 0% falska alarm i alla försök. Generalised normaldistributionen erhöll runt 4% falska alarm i de flesta försöken. Generaliserad normaldistributionen nådde detekteringsnoggrannhet runt 95% medan lognormal distributionen nådde runt 70%. Generell noggrannheten för generaliserad normaldistributionen var runt 95% i flesta försöken. För lognormal distributionen nåddes en generell noggrannhet runt 85%. KHAT koefficienten för generaliserad normaldistributionen var i intervallet 0.66-0.93. För lognormal distributionen var den i intervallet 0.68-0.77. Med en extra speckle-filtrering ökades nogranneheten för lognormal distributionen. Generellt sett, detekterades positiv förändring med högre nivå av noggrannhet än negativ förändring. Visuell inspektion visar att generaliserad normaldistribution troligen överskattar förändringen. Lognormal distributionen detekterar konsistent mindre förändring än generaliserad normaldistributionen. Bristen på referensdata gjorde valideringen av resultaten svårt. Den utförda valideringen är kanske inte så trovärdig, eftersom den tillgänliga referensdatan var bara SAR bilder och att särskilja förändring och ickeförändring är svårt i området. Vidare, på grund av bristen på referensdata, kunde det inte bestämmas med säkerhet vilken distribution som var bäst.

Ultra Wideband (UWB) communication has recently drawn considerable attention from academia and industry. This is mainly owing to the ultra high speeds and cognitive features it could offer. The employability of UWB in numerous areas including but not limited to Wireless Personal Area Networks, WPAN's, Body Area Networks, BAN's, radar and medical imaging etc. has opened several avenues of research and development. However, still there is a disagreement on the standardization of UWB. Two contesting radios for UWB are Multiband Orthogonal Frequency Division Multiplexing (MB-OFDM) and DS-UWB (Direct Sequence Ultra Wideband). As nearly all of the reported research on UWB hasbeen about a very narrow/specific area of the communication system, this thesis looks at the end-to-end performance of an MB-OFDM approach. The overall aim of this project has been to first focus on three different aspects i.e. interference, antenna and propagation aspects of an MB-OFDM system individually and then present a holistic or an end-to-end system analysis finally. In the first phase of the project the author investigated the performance of MB-OFDM system under the effect of his proposed generic or technology non-specific interference. Avoiding the conventional Gaussian approximation, the author has employed an advanced stochastic method. A total of two approaches have been presented in this phase of the project. The first approach is an indirect one which involves the Moment Generating Functions (MGF's) of the Signal-to-Interference-plus-Noise-Ratio (SINR) and the Probability Density Function (pdf) of the SINR to calculate the Average Probabilities of Error of an MB-OFDM system under the influence of proposed generic interference. This approach assumed a specific two-dimensional Poisson spatial/geometric placement of interferers around the victim MB-OFDM receiver. The second approach is a direct approach and extends the first approach by employing a wider class of generic interference. In the second phase of the work the author designed, simulated, prototyped and tested novel compact monopole planar antennas for UWB application. In this phase of the research, compact antennas for the UWB application are presented. These designs employ low-loss Rogers duroid substrates and are fed by Copla-nar Waveguides. The antennas have a proposed feed-line to the main radiating element transition region. This transition region is formed by a special step-generating function-set called the "Inverse Parabolic Step Sequence" or IPSS. These IPSS-based antennas are simulated, prototyped and then tested in the ane-choic chamber. An empirical approach, aimed to further miniaturize IPSS-based antennas, was also derived in this phase of the project. The empirical approach has been applied to derive the design of a further miniaturized antenna. More-over, an electrical miniaturization limit has been concluded for the IPSS-based antennas. The third phase of the project has investigated the effect of the indoor furnishing on the distribution of the elevation Angle-of-Arrival (AOA) of the rays at the receiver. Previously, constant distributions for the AOA of the rays in the elevation direction had been reported. This phase of the research has proposed that the AOA distribution is not fixed. It is established by the author that the indoor elevation AOA distributions depend on the discrete levels of furnishing. A joint time-angle-furnishing channel model is presented in this research phase. In addition, this phase of the thesis proposes two vectorial or any direction AOA distributions for the UWB indoor environments. Finally, the last phase of this thesis is presented. As stated earlier, the overall aim of the project has been to look at three individual aspects of an MB-OFDM system, initially, and then look at the holistic system, finally. Therefore, this final phase of the research presents an end-to-end MB-OFDM system analysis. The interference analysis of the first phase of the project is revisited to re-calculate the probability of bit error with realistic/measured path loss exponents which have been reported in the existing literature. In this method, Gaussian Quadrature Rule based approximations are computed for the average probability of bit error. Last but not the least, an end-to-end or comprehensive system equation/impulse response is presented. The proposed system equation covers more aspects of an indoor UWB system than reported in the existing literature.