If communicating via a teleconference phone the desired transmitted signal (speech) needs to be crystal clear so that all participants experience a good communication ability. However, there are many environmental conditions that contaminates the signal with background noise, i.e sounds not of interest for communication purposes, which impedes the ability to communicate due to interfering sounds. Noise can be removed from the signal if it is known and so this work has evaluated different ways of estimating the characteristics of the background noise. Focus was put on using speech detection to define the noise, i.e. the non-speech part of the signal, but other methods not solely reliant on speech detection but rather on characteristics of the noisy speech signal were included. The implemented techniques were compared and evaluated to the current solution utilized by the teleconference phone in two ways, firstly for their speech detection ability and secondly for their ability to correctly estimate the noise characteristics. The evaluation process was based on simulations of the methods' performance in various noise conditions, ranging from harsh to mild environments. It was shown that the proposed method showed improvement over the existing solution, as implemented in this study, in terms of speech detection ability and for the noise estimate it showed improvement in certain conditions. It was also concluded that using the proposed method would enable two sources of noise estimation compared to the current single estimation source and it was suggested to investigate how utilizing two noise estimators could affect the performance.

Bone age assessment is a method of assigning a level of biological maturity to a child. It is usually performed either by comparing an x-ray of a child's left hand and wrist with an atlas of known bones, or by analysing specific features of bones such as ratios of width to height, or the degree of overlap with other bones. Both methods of assessment are labour intensive and prone to both inter- and intra-observer variability. This is motivation for developing a computerised method of bone age assessment. The majority of research and development on computerised bone age assessment has focussed on analysing the bones of the hand. The wrist bones, especially the carpal bones, have received far less attention and have only been analysed in young children in which there is clear separation of the bones. An argument is presented that the evidence for excluding the carpal bones from computerised bone age assessment is weak and that research is required to identify the role of carpal bones in the computerised assessment of bone age for children over eight years of age. Computerised analysis of the carpal bones in older children is a difficult computer vision problem plagued by radiographic noise, poor image contrast, and especially poor definition of bone contours. Traditional image processing methods such as region growing fail and even the very successful Canny linear edge detector can only find the simplest of bone edges in these images. The field of partial differential equation-based image processing provides some possible solutions to this problem, such as the use of active contour models to impose constraints upon the contour continuity. However, many of these methods require regularisation to achieve unique and stable solutions. An important part of this regularisation is image denoising. Image denoising was approached through development of a noise model for the Kodak computed radiography system, estimation of noise parameters using a robust estimator of noise per pixel intensity bin, and incorporation of the noise model into a denoising method based on oriented Laplacians. The results for this approach only showed a marginal improvement when using the signal-dependent noise model, although this likely reflects how the noise characteristics were incorporated into the anisotropic diffusion method, rather than the principle of this approach. Even without the signal-dependent noise term the oriented Laplacians denoising of the hand-wrist radiographs was very effective at removing noise and preserving edges.

No / Spectrum sensing is used in cognitive radio systems to detect the availability of spectrum holes for secondary usage. The simplest and most famous spectrum sensing techniques are based either on energy detection or eigenspace analysis from Random Matrix Theory (RMT) such as using the Marchenko-Pastur law. These schemes suffer from uncertainty in estimating the noise variance which reduces their performance. In this paper we propose a new method to evaluate the noise variance that can eliminate the limitations of the aforementioned schemes. This method estimates the noise variance from a measurement set of noisy signals or noise-only signals. Extensive simulations show that the proposed method performs well in estimating the noise variance. Its performance greatly improves with increasing numbers of measurements and also with increasing numbers of samples taken per measurement.

Heart is a vital organ that pumps blood to whole body. Synchronous contraction of the heart muscles assures that the required blood flow is supplied to organs. But sometimes the synchrony between those muscles is distorted, which results in reduced cardiac output that might lead to severe diseases, and even death. The most common of heart diseases are myocardial infarction and arrhythmias. The contraction of heart muscles is controlled by the electrical activity of the heart, therefore determination of that electrical activity could give us the information regarding the severeness and type of the disease. In order to diagnose heart diseases, classical 12 lead electrocardiogram (ECG) is the standard clinical tool. Although many cardiac diseases could be diagnosed with the 12 lead ECG, measurements from sparse electrode locations limit the interpretations. The main objective of this thesis is to determine the cardiac electrical activity from dense body surface measurements. This problem is called the inverse problem of electrocardiography. The high resolution maps of epicardial potentials could supply the physician the information that could not be obtained with any other method. But the calculation of those epicardial potentials are not easy / the problem is severely ill-posed due to the discretization and attenuation within the thorax. To overcome this ill-posedness, the solution should be constrained using prior information on the epicardial potential distributions. In this thesis, spatial and spatio-temporal Bayesian maximum a posteriori estimation (MAP), Tikhonov regularization and Kalman filter and Kalman smoother approaches are used to overcome the ill-posedness that is associated with the inverse problem of ECG. As part of the Kalman filter approach, the state transition matrix (STM) that determines the evolution of epicardial potentials over time is also estimated, both from the true epicardial potentials and previous estimates of the epicardial potentials. An activation time based approach was developed to overcome the computational complexity of the STM estimation problem. Another objective of this thesis is to study the effects of geometric errors to the solutions, and modify the inverse solution algorithms to minimize these effects. Geometric errors are simulated by changing the size and the location of the heart in the mathematical torso model. These errors are modeled as additive Gaussian noise in the inverse problem formulation. Residual-based and expectation maximization methods are implemented to estimate the measurement and process noise variances, as well as the geometric noise.

La vision de nuit des pilotes d’hélicoptère est artificiellement assistée par un dispositif de vision bas niveau de lumière constitué d’un intensificateur de lumière (IL) couplé à une caméra numérique d’une part, et d’une caméra infrarouge (IR) d’autre part. L’objectif de cette thèse est d’améliorer ce dispositif en ciblant les défauts afin de les corriger.Une première partie consiste à réduire le bruit dont souffrent les images IL. Cela nécessite d’évaluer la nature du bruit qui corrompt ces images. Pour cela, une méthode d’estimation automatique du bruit est mise en place. L’estimation repose sur la détection non paramétrique de zones homogènes de l’image. Les statistiques du bruit peuvent être alors être estimées à partir de ces régions homogènes à l’aide d’une méthode d’estimation robuste de la fonction de niveau de bruit par minimisation l1.Grâce à l’estimation du bruit, les images IL peuvent alors débruitées. Nous avons pour cela développé dans la seconde partie un algorithme de débruitage d’images qui associe les moyennes non locales aux méthodes variationnelles en effectuant une régularisation adaptative pondérée parune attache aux données non locale. Une adaptation au débruitage de séquences d’images permet ensuite de tenir compte de la redondance d’information apportée par le flux vidéo, en garantissant stabilité temporelle et préservation des structures fines.Enfin, dans la troisième partie les informations issues des capteurs optique et infrarouge sont recalées dans un même référentiel. Nous proposons pour cela un critère de recalage multimodal basé sur l’alignement des contours des images. Combiné à une résolution par montée de gradient et à un schéma temporel, l’approche proposée permet de recaler de façon robuste les deuxmodalités, en vue d’une ultérieure fusion. / Night vision for helicopter pilots is artificially enhanced by a night vision system. It consists in a light intensifier (LI) coupled with a numerical camera, and an infrared camera. The goal of this thesis is to improve this device by analyzing the defaults in order to correct them.The first part consists in reducing the noise level on the LI images. This requires to evaluate the nature of the noise corrupting these images, so an automatic noise estimation method has been developed. The estimation is based on a non parametric detection of homogeneous areas.Then the noise statistics are estimated using these homogeneous regions by performing a robust l`1 estimation of the noise level function.The LI images can then be denoised using the noise estimation. We have developed in the second part a denoising algorithm that combines the non local means with variational methods by applying an adaptive regularization weighted by a non local data fidelity term. Then this algorithm is adapted to video denoising using the redundancy provided by the sequences, hence guaranteeing temporel stability and preservation of the fine structures.Finally, in the third part data from the optical and infrared sensors are registered. We propose an edge based multimodal registration metric. Combined with a gradient ascent resolution and a temporel scheme, the proposed method allows robust registration of the two modalities for later fusion.

La fonte rapide des glaces de l'Arctique dans le contexte actuel du réchauffement climatique est un sujet scientifique majeur de ces 30 dernières années. L'Arctique joue un rôle fondamental dans l'équilibre du climat et requiert une attention particulière. Les régions arctiques sont alors surveillées par des observations satellitaires et des mesures in-situ. L'impact climatique de la fonte totale de la glace arctique est encore spéculatif. Des recherches sont donc nécessaires pour le suivi à long terme de l'Océan Arctique, en particulier la dynamique spatio-temporelle de la couverture de glace et ses conséquences sur les écosystèmes. Notre travail s'inscrit dans ce contexte, et est porté sur le paysage sonore des régions polaires avant leur possible industrialisation qui accompagnera la fonte de la glace. Ainsi, nous avons d'abord examiné les conséquences de la disparition du couvert de glace sur les paysages sonores de ces régions. Nous avons alors étudié les variations saisonnières du bruit de fond et ses pilotes environnementaux. De ce fait, nous avons développé un algorithme d'estimation du bruit ambiant afin de pouvoir constituer des séries temporelles à partir des données acoustiques longue durée. Deuxièmement, nous avons étudié les transitoires générés par le comportement mécanique de la banquise en Arctique. Cette étude vise d'une part à comprendre le mécanisme de production de ces transitoires sous la glace, et d'autre part à évaluer leur potentiel comme moyen d'observation de la dynamique de la glace de mer. / The Arctic sea ice melting, in the global warming context, has become a major scientific topic during the last 30 years. The Arctic Ocean plays a fundamental role in the global climate balance and requires a particular attention. The Arctic Regions are then monitored by satellite observations and in-situ measurements. The climatic impact of the total melting of the Arctic sea ice is not yet understood and researches are still needed for long term monitoring of Arctic Ocean, particularly the dynamics of the ice cover and its consequences on the ecosystems. Our work focused on the natural soundscapes of these Polar Regions prior to their possible industrialization. So, we first examined the impact of climate warming alone on polar soundscapes by studying the seasonal variability of ambient noise and its environmental drivers. We then developed an ambient noise estimation algorithm for automatic extraction of this noise component from long term measurements. In second, we examined the acoustic transients generated by the mechanical behavior of the ice cover at its maximum extent. This aims to better understanding of the physical processes involved in under-ice noise production and their potential use for sea ice monitoring.

Title: Numerical Methods in Discrete Inverse Problems Author: Marie Kubínová Department: Department of Numerical Mathematics Supervisor: RNDr. Iveta Hnětynková, Ph.D., Department of Numerical Mathe- matics Abstract: Inverse problems represent a broad class of problems of reconstruct- ing unknown quantities from measured data. A common characteristic of these problems is high sensitivity of the solution to perturbations in the data. The aim of numerical methods is to approximate the solution in a computationally efficient way while suppressing the influence of inaccuracies in the data, referred to as noise, that are always present. Properties of noise and its behavior in reg- ularization methods play crucial role in the design and analysis of the methods. The thesis focuses on several aspects of solution of discrete inverse problems, in particular: on propagation of noise in iterative methods and its representation in the corresponding residuals, including the study of influence of finite-precision computation, on estimating the noise level, and on solving problems with data polluted with noise coming from various sources. Keywords: discrete inverse problems, iterative solvers, noise estimation, mixed noise, finite-precision arithmetic - iii -

Zur Verminderung des Rauschens sehr hochauflösender Satellitenbilder existieren eine Vielzahl von Glättungsalgorithmen. Die Wirkung verschiedener Tiefpaß- und kantenerhaltender Filter auf das Verhalten eines objektorientierten Segmentierungsverfahrens wird anhand zweier synthetischer Grauwertbilder und einer IKONOS-Aufnahme untersucht. Als Rauschmaß hat sich ein modifiziertes, ursprünglich von Baltsavias et al. [2001] vorgeschlagenes Verfahren bewährt, in dem je Grauwert nur die Standardabweichungen der gleichförmigsten Gebiete berücksichtigt werden. In Vergleich mit synthetisch verrauschten Bildern zeigt sich jedoch, daß auf diese Weise das Rauschen im Bild systematisch um fast den Faktor zwei unterschätzt wird. Einfache Filter wie Mittelwertfilter und davon abgeleitete Verfahren verschlechtern die Präzision der Objekterkennung dramatisch, kantenerhaltende Filter können bei stärker verrauschten Daten vorteilhaft sein.Als bester Filter, der bei Ansprüchen an präzise Segmentgrenzen im Pixelbereich sinnvoll einzusetzen ist und dabei mit nur einem Parameter gesteuert werden kann, erweist sich der modifizierte EPOS-Filter, ursprünglich vorgestellt von Haag und Sties [1994, 1996]. Die generellen Bildparameter, wie Standardabweichung oder Histogramm werden durch diesen kantenerhaltenden Filter nur unwesentlich beeinflußt.