The separation of independent sources from mixed observed data is a fundamental problem in many practical situations. A typical example is speech recordings made in an acoustic environment in the presence of background noise or other speakers. Problems of signal separation are explored by a group of methods called Blind Source Separation. Blind Source Separation (BSS) consists on estimating a set of N unknown sources from P observations resulting from the mixture of these sources and unknown background. Some existing solutions for instantaneous mixtures are reviewed and in Matlab implemented , i.e Independent Componnent Analysis (ICA) and Time-Frequency Analysis (TF). The acoustic signals recorded in real environment are not instantaneous, but convolutive mixtures. In this case, an ICA algorithm for separation of convolutive mixtures in frequency domain is introduced and in Matlab implemented. This diploma thesis examines the useability and comparisn of proposed separation algorithms.

Perfusion magnetic resonance imaging is modern diagnostic method used mainly in oncology. In this method, contrast agent is injected to the subject and then is continuously monitored the progress of its concentration in the affected area in time. Correct determination of the arterial input function (AIF) is very important for perfusion analysis. One possibility is to model AIF by multichannel blind deconvolution but the estimated AIF is necessary to be scaled. This master´s thesis is focused on description of scaling methods and their influence on perfussion parameters in dependence on used model of AIF in different tissues.

This thesis deals with the possibilities of determining perfusion parameters of vascular system, using contrast-enhanced ultrasound imaging, which is non-invasive method. Properties of ultrasonography and use of contrast agents are briefly summarized. The methods selected for perfusions analysis were Bolus-tracking¬¬, Burst-replenishment and both of them combined – Bolus&Burst. Parametric models based on these methods were created for modelling an approximation of set perfusion parameters with the use of blind deconvolution.

This master thesis deals with the contrast agents and their application in the ultrasound perfusion analysis. It is focused on Bolus & Burst method which, as a combination of two approaches that have been used so far, allows an absolute quantification of perfusion parameters in the region of interest. Contrast agent concentration time sequence is modeled as a convolution of the parametrically defined arterial input function and the tissue residual funkction. Thesis discusses different mathematical models of these functions as well as the methods of the parameters estimation. The methods functionality is validated on simulated and also preclinical data.

Cette thèse traite un problème inverse en astronomie. L’objectif est de reconstruire un objet 2D+λ, ayant une distribution spatiale et spectrale, à partir d’un ensemble de données multispectrales de basse résolution fournies par l’imageur MIRI (Mid-InfraRed Instrument), qui est à bord du prochain télescope spatial James Webb Space Telescope (JWST). Les données multispectrales observées souffrent d’un flou spatial qui dépend de la longueur d’onde. Cet effet est dû à la convolution par la réponse optique (PSF). De plus, les données multi-spectrales souffrent également d’une sévère dégradation spectrale en raison du filtrage spectral et de l’intégration par le détecteur sur de larges bandes. La reconstruction de l’objet original est un problème mal posé en raison du manque important d’informations spectrales dans l’ensemble de données multispectrales. La difficulté se pose alors dans le choix d’une représentation de l’objet permettant la reconstruction de l’information spectrale. Un modèle classique utilisé jusqu’à présent considère une PSF invariante spectralement par bande, ce qui néglige la variation spectrale de la PSF. Cependant, ce modèle simpliste convient que dans le cas d’instrument à une bande spectrale très étroite, ce qui n’est pas le cas pour l’imageur de MIRI. Notre approche consiste à développer une méthode pour l’inversion qui se résume en quatre étapes : (1) concevoir un modèle de l’instrument reproduisant les données multispectrales observées, (2) proposer un modèle adapté pour représenter l’objet à reconstruire, (3) exploiter conjointement l’ensemble des données multispectrales, et enfin (4) développer une méthode de reconstruction basée sur la régularisation en introduisant des priori à la solution. Les résultats de reconstruction d’objets spatio-spectral à partir de neuf images multispectrales simulées de l’imageur de MIRI montrent une augmentation significative des résolutions spatiale et spectrale de l’objet par rapport à des méthodes conventionnelles. L’objet reconstruit montre l’effet de débruitage et de déconvolution des données multispectrales. Nous avons obtenu une erreur relative n’excédant pas 5% à 30 dB et un temps d’exécution de 1 seconde pour l’algorithme de norm-l₂ et 20 secondes avec 50 itérations pour l’algorithme norm-l₂/l₁. C’est 10 fois plus rapide que la solution itérative calculée par l’algorithme de gradient conjugué. / This thesis deals with an inverse problem in astronomy. The objective is to reconstruct a spatio-spectral object, having spatial and spectral distributions, from a set of low-resolution multispectral data taken by the imager MIRI (Mid-InfraRed Instrument), which is on board the next space telescope James Webb Space Telescope (JWST). The observed multispectral data suffers from a spatial blur that varies according to the wavelength due to the spatial convolution with a shift-variant optical response (PSF). In addition the multispectral data also suffers from severe spectral degradations because of the spectral filtering and the integration by the detector over broad bands. The reconstruction of the original object is an ill-posed problem because of the severe lack of spectral information in the multispectral dataset. The difficulty then arises in choosing a representation of the object that allows the reconstruction of this spectral information. A common model used so far considers a spectral shift-invariant PSF per band, which neglects the spectral variation of the PSF. This simplistic model is only suitable for instruments with a narrow spectral band, which is not the case for the imager of MIRI. Our approach consists of developing an inverse problem framework that is summarized in four steps: (1) designing an instrument model that reproduces the observed multispectral data, (2) proposing an adapted model to represent the sought object, (3) exploiting all multispectral dataset jointly, and finally (4) developing a reconstruction method based on regularization methods by enforcing prior information to the solution. The overall reconstruction results obtained on simulated data of the JWST/MIRI imager show a significant increase of spatial and spectral resolutions of the reconstructed object compared to conventional methods. The reconstructed object shows a clear denoising and deconvolution of the multispectral data. We obtained a relative error below 5% at 30 dB, and an execution time of 1 second for the l₂-norm algorithm and 20 seconds (with 50 iterations) for the l₂/l₁-norm algorithm. This is 10 times faster than the iterative solution computed by conjugate gradients.

L'objectif de cette thèse est de simuler l'histoire temporelle de la réponse d'un bâtiment de grande hauteur sous sollicitation sismique et de proposer des méthodologies simplifiées qui reproduisent correctement une telle réponse. Initialement, un modèle tridimensionnel par éléments finis est produit afin de valider sa fiabilité pour simuler le comportement réel du bâtiment pendant les mouvements du sol, enregistrés à l'aide d'accéléromètres. Il est proposé d'améliorer la précision du modèle numérique en imposant de multiples excitations, compte-tenu des effets de basculement et de la variabilité spatiale sur la sollicitation d'entrée. L'utilisation de fonctions de Green empiriques est proposée pour simuler la réponse sismique directement à partir d'enregistrements d'événements passés, sans avoir besoin de dessins de construction ni d'étalonnage des paramètres mécaniques. Une méthode de sommation stochastique, déjà utilisée pour prédire les mouvements du sol, est adoptée pour générer des signaux synthétiques à des hauteurs différentes du bâtiment, par extension du chemin de propagation des ondes du sol à la structure. Une représentation simplifiée du bâtiment comme une poutre homogène Timoshenko est proposée pour simuler la réponse sismique directement à partir des enregistrements des vibrations ambiantes. Des paramètres mécaniques équivalents sont identifiés à l'aide de l'interférométrie par déconvolution en termes de dispersion des ondes, de fréquences naturelles et de rapport de vitesse des ondes de cisaillement et de compression dans le milieu / The aim of this thesis is to simulate the time history response of a high rise building under seismic excitation and provide simplified methodologies that properly reproduce such response. Firstly, a detailed three-dimensional finite element model is produced to validate its reliability to simulate the real behavior of the building during ground motions, recorded using accelerometers. It is proposed to improve the accuracy of the numerical model by imposing multiple excitations, considering rocking effect and spatial variability on the input motion. The use of empirical Green's functions is proposed to simulate the seismic response directly from past event records, without the need of construction drawings and mechanical parameters calibration. A stochastic summation scheme, already used to predict ground motions, is adopted to generate synthetic signals at different heights of the building, extending the wave propagation path from the ground to the structure. A simplified representation of the building as a homogeneous Timoshenko beam is proposed to simulate the seismic response directly from ambient vibration records. Equivalent mechanical parameters are identified using deconvolution interferometry in terms of wave dispersion, natural frequencies and shear to compressional wave

This dissertation describes the improvement of signal analysis in ultrasonic microscopy for nondestructive testing. Specimens with many thin layers, like modern electronic components, pose a particular challenge for identifying and localizing defects. In this thesis, new evaluation algorithms have been developed which enable analysis of highly complex layer-stacks. This is achieved by a specific evaluation of multiple reflections, a newly developed iterative reconstruction and deconvolution algorithm, and the use of classification algorithms with a highly optimized simulation algorithm. Deep delaminations inside a 19-layer component can now not only be detected, but also localized. The new analysis methods also enable precise determination of elastic material parameters, sound velocities, thicknesses, and densities of multiple layers. The highly improved precision of determined reflections parameters with deconvolution also provides better and more conclusive results with common analysis methods.:Kurzfassung......................................................................................................................II Abstract.............................................................................................................................V List ob abbreviations........................................................................................................X 1 Introduction.......................................................................................................................1 1.1 Motivation.....................................................................................................................2 1.2 System theoretical description.....................................................................................3 1.3 Structure of the thesis..................................................................................................6 2 Sound field.........................................................................................................................8 2.1 Sound field measurement............................................................................................8 2.2 Sound field modeling..................................................................................................11 2.2.1 Reflection and transmission coefficients.........................................................11 2.2.2 Sound field modeling with plane waves..........................................................13 2.2.3 Generalized sound field position.....................................................................19 2.3 Receiving transducer signal.......................................................................................20 2.3.1 Calculation of the transducer signal from the sound field...............................20 2.3.2 Received signal amplitude..............................................................................21 2.3.3 Measurement of reference signals..................................................................24 3 Ultrasonic Simulation......................................................................................................27 3.1 State of the art............................................................................................................27 3.2 Simulation approach..................................................................................................28 3.2.1 Sound field measurement based simulation...................................................28 3.2.2 Reference signal based simulation.................................................................30 3.3 Determination of the impulse response.....................................................................31 3.3.1 1D ray-trace algorithm....................................................................................31 3.3.2 2D ray-trace algorithm....................................................................................33 3.3.3 Complexity reduction – optimizations.............................................................35 4 Deconvolution – Determination of reflection parameters............................................38 4.1 State of the art............................................................................................................39 4.1.1 Decomposition techniques..............................................................................39 4.1.2 Deconvolution.................................................................................................41 4.2 Analytic signal investigations for deconvolution.........................................................42 4.3 Single reference pulse deconvolution........................................................................44 4.4 Multi-pulse deconvolution..........................................................................................47 4.4.1 Homogeneous multi-pulse deconvolution.......................................................48 4.4.2 Multi-pulse deconvolution with simulated GSP profile....................................49 5 Reconstruction.................................................................................................................50 5.1 State of the art............................................................................................................50 5.2 Reconstruction approach...........................................................................................51 5.3 Direct material parameter estimation.........................................................................52 5.3.1 Sound velocities and layer thickness..............................................................52 5.3.2 Density, elastic modules and acoustic attenuation.........................................54 5.4 Iterative material parameter determination of a single layer......................................56 5.5 Reconstruction of complex specimens......................................................................60 5.5.1 Material characterization of multiple layers ....................................................60 5.5.2 Iterative simulation parameter optimization with correlation...........................62 5.5.3 Pattern recognition reconstruction of specimens with known base structure. 66 6 Applications and results.................................................................................................71 6.1 Analysis of stacked components................................................................................71 6.2 Time-of-flight and material analysis...........................................................................74 7 Conclusions and perspectives.......................................................................................78 References.......................................................................................................................82 Figures.............................................................................................................................86 Tables...............................................................................................................................88 Appendix..........................................................................................................................89 Acknowledgments.........................................................................................................100 Danksagung...................................................................................................................101 / Die vorgelegte Dissertation befasst sich mit der Verbesserung der Signalauswertung für die Ultraschallmikroskopie in der zerstörungsfreien Prüfung. Insbesondere bei Proben mit vielen dünnen Schichten, wie bei modernen Halbleiterbauelementen, ist das Auffinden und die Bestimmung der Lage von Fehlstellen eine große Herausforderung. In dieser Arbeit wurden neue Auswertealgorithmen entwickelt, die eine Analyse hochkomplexer Schichtabfolgen ermöglichen. Erreicht wird dies durch die gezielte Auswertung von Mehrfachreflexionen, einen neu entwickelten iterativen Rekonstruktions- und Entfaltungsalgorithmus und die Nutzung von Klassifikationsalgorithmen im Zusammenspiel mit einem hoch optimierten neu entwickelten Simulationsalgorithmus. Dadurch ist es erstmals möglich, tief liegende Delaminationen in einem 19-schichtigem Halbleiterbauelement nicht nur zu detektieren, sondern auch zu lokalisieren. Die neuen Analysemethoden ermöglichen des Weiteren eine genaue Bestimmung von elastischen Materialparametern, Schallgeschwindigkeiten, Dicken und Dichten mehrschichtiger Proben. Durch die stark verbesserte Genauigkeit der Reflexionsparameterbestimmung mittels Signalentfaltung lassen sich auch mit klassischen Analysemethoden deutlich bessere und aussagekräftigere Ergebnisse erzielen. Aus den Erkenntnissen dieser Dissertation wurde ein Ultraschall-Analyseprogramm entwickelt, das diese komplexen Funktionen auf einer gut bedienbaren Oberfläche bereitstellt und bereits praktisch genutzt wird.:Kurzfassung......................................................................................................................II Abstract.............................................................................................................................V List ob abbreviations........................................................................................................X 1 Introduction.......................................................................................................................1 1.1 Motivation.....................................................................................................................2 1.2 System theoretical description.....................................................................................3 1.3 Structure of the thesis..................................................................................................6 2 Sound field.........................................................................................................................8 2.1 Sound field measurement............................................................................................8 2.2 Sound field modeling..................................................................................................11 2.2.1 Reflection and transmission coefficients.........................................................11 2.2.2 Sound field modeling with plane waves..........................................................13 2.2.3 Generalized sound field position.....................................................................19 2.3 Receiving transducer signal.......................................................................................20 2.3.1 Calculation of the transducer signal from the sound field...............................20 2.3.2 Received signal amplitude..............................................................................21 2.3.3 Measurement of reference signals..................................................................24 3 Ultrasonic Simulation......................................................................................................27 3.1 State of the art............................................................................................................27 3.2 Simulation approach..................................................................................................28 3.2.1 Sound field measurement based simulation...................................................28 3.2.2 Reference signal based simulation.................................................................30 3.3 Determination of the impulse response.....................................................................31 3.3.1 1D ray-trace algorithm....................................................................................31 3.3.2 2D ray-trace algorithm....................................................................................33 3.3.3 Complexity reduction – optimizations.............................................................35 4 Deconvolution – Determination of reflection parameters............................................38 4.1 State of the art............................................................................................................39 4.1.1 Decomposition techniques..............................................................................39 4.1.2 Deconvolution.................................................................................................41 4.2 Analytic signal investigations for deconvolution.........................................................42 4.3 Single reference pulse deconvolution........................................................................44 4.4 Multi-pulse deconvolution..........................................................................................47 4.4.1 Homogeneous multi-pulse deconvolution.......................................................48 4.4.2 Multi-pulse deconvolution with simulated GSP profile....................................49 5 Reconstruction.................................................................................................................50 5.1 State of the art............................................................................................................50 5.2 Reconstruction approach...........................................................................................51 5.3 Direct material parameter estimation.........................................................................52 5.3.1 Sound velocities and layer thickness..............................................................52 5.3.2 Density, elastic modules and acoustic attenuation.........................................54 5.4 Iterative material parameter determination of a single layer......................................56 5.5 Reconstruction of complex specimens......................................................................60 5.5.1 Material characterization of multiple layers ....................................................60 5.5.2 Iterative simulation parameter optimization with correlation...........................62 5.5.3 Pattern recognition reconstruction of specimens with known base structure. 66 6 Applications and results.................................................................................................71 6.1 Analysis of stacked components................................................................................71 6.2 Time-of-flight and material analysis...........................................................................74 7 Conclusions and perspectives.......................................................................................78 References.......................................................................................................................82 Figures.............................................................................................................................86 Tables...............................................................................................................................88 Appendix..........................................................................................................................89 Acknowledgments.........................................................................................................100 Danksagung...................................................................................................................101

Complex spatial relationships and patterns in multivariate data are relatively simple to identify visually but di cult to detect computation- ally. For this reason, Anivis, an interactive tool for visual exploration of multivariate quantitative pure serial periodic data was developed. The data has four dimensions depth, laterality, frequency and time. The data was visualized as an animated heatmap, by mapping depth and laterality to coordinates in a pixel grid and frequency to color. Transfer functions were devised to map a single variable to color through parametric curves. Anivis implemented heatmap generation through both weighted sum and deconvolution for comparison reasons. Deconvolution exhibited a to have better theoretical and practical performance. In addition to the heatmap visualization a scatter-plot was added in order to visualize the causal relationships between data points and high value areas in the heatmap visualization. Performance and applicability of the tool were tested and verified on experimental data from the Karolinksa Institute’s Department of Neuroscience. / Komplexa spatiala mo ̈nster och fo ̈rh ̊allanden i multivariat data a ̈r rel- ativt sv ̊ara att identifiera via bera ̈kningar men simpla att identifiera vi- suellt. Att visualisera data fo ̈r denna typ av data-analys anva ̈nds ofta i m ̊anga olika typer av fa ̈lt. Detta motiverade utvecklingen av Anivis; ett interaktivt verktyg fo ̈r visuell utforskning av multivariat kvantitativ data av neural aktivitet. Anivis anva ̈nder sig av dataset baserade p ̊a experi- mentell data fr ̊an en forskningsgrupp p ̊a Karolinska Institutets Institution fo ̈r Neurovetenskap. Dessa fyrdimensionella dataset best ̊ar av ma ̈tningar fr ̊an neuroner i form av deras position, aktivitet i form av frekvens och tidpunkt. Denna data anva ̈nds fo ̈r att generera en animerad heatmap, da ̈r neuroners frekvensva ̈rden visas i form av f ̈arg. Frekvensva ̈rdena om- vandlades till fa ̈rgva ̈rden via ̈overg ̊angsfunktioner som kopplar numeriska va ̈rden till fa ̈rgva ̈rden via parametriserade kurvor. Anivis lyckades imple- mentera tv ̊a olika metoder f ̈or att generera heatmap, viktade summor och dekonvolution. Dessa tv ̊a metoder ja ̈mfo ̈rdes med varandra, varav dekon- volution visade sig vara den teoretiskt och praktiskt e↵ektivaste meto- den. Utvecklingen av Anivis visade a ̈ven behovet fo ̈r ett punktdiagram fo ̈r att visualisera f ̈orh ̊allandet mellan ma ̈tta frekvensv ̈arden och spatial frekvensfo ̈rdelning i heatmappen.

Modeling underwater acoustic propagation comes with a variety of challenges due to the need for proper characterization of the environmental conditions. These conditions include ever changing and complex water properties as well as boundary conditions. The BYU underwater acoustics open-air tank test-bed and measurement chain were developed to study underwater acoustic propagation within a controlled environment. It was also developed to provide ways to test and validate ocean models without the high cost associated with obtaining open ocean measurements. However, tank measurements require additional characterization of boundary conditions associated with the walls of the tank which would not be present in an open ocean. The characterization of BYU's underwater acoustic tank included measuring the calibrated impulse response of the tank through frequency deconvolution of sine swept signals in order to determine the frequency dependent reverberation time through reverse Schroeder integration. The reverberation time allows for calculating the frequency dependent spatially averaged acoustic absorption coefficient of the tank enclosure boundaries. The methods used for this study, common to room acoustics, also yield insights into the Schroeder frequency limit of the tank as well as validate models used for quantifying the speed of sound in the tank. The acoustic characterization was validated alongside predicted values and also applied to a tank lined with anechoic panels in order to improve the potential for modeling the tank as a scaled open ocean environment. An initial investigation into effective tank models evaluated the idealized rigid-wall and pressure-release water-air boundary model, a finite-impedance boundary model applying the measured acoustic boundary absorption and a benchmark open ocean model known as ORCA in order to determine potential tank model candidates. This study demonstrates the efficacy of the methodology for underwater acoustic tank characterization, provides a frequency dependent acoustic boundary evaluation from 5-500 kHz, and provides an initial comparison of tank models with applied characterization.

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