<p>A computerized tomography scan enables the visualization of an object interior without opening it up. This technique is used in many fields e.g. in medical imaging, geology, and industry. To obtain information about an object, exterior measurements by means of X-rays are performed. Then, to reconstruct an image of the object’s interior, image-reconstructions methods are applied. The problem of reconstructing images from measurements of X-ray radiation belongs to the class of inverse problems. A class of important methods for inverse problems is Algebraic Reconstruction Techniques (ART). The performance of these methods depends on the choice of a relaxation parameter.</p> <p>In this thesis, we compare numerically various ART methods, namely Kaczmarz, symmetric Kaczmarz, randomized Kaczmarz and simultaneous ART. We perform an extensive numerical investigation of the behaviour of these methods, and in particular, study how they perform with respect to this relaxation parameter. We propose a simple heuristic for finding a good relaxation parameter for each of these methods. Comparisons of the new proposed strategy with a previously proposed one shows that our strategy has a slightly better performance in terms of relative error, relative residual and image discrepancy of the reconstructed image. Both strategies showed relatively close numerical results, but interestingly enough, for different values of this parameter.</p> / Master of Computer Science (MCS)

Research of the highest energy cosmic ray particles is in the middle of the interest of theoretical and experimental physics. Their energies are several orders of magnitude higher than energies accessible at present accelerators. In this work, the reconstruction techniques of extensive air showers measured at the Pierre Auger Observatory are studied. For this purpose, extensive air showers are modelled in the simulation tool CORSIKA. Data collected at the Pierre Auger Observatory together with simulations are used to calculate resolutions of reconstruction methods. The Multiple--eye reconstruction is the main interest of this work. It can be used for independent verification of experimental results of the Observatory.

Einleitung: Aufgrund der hohen Inzidenz der vorderen Kreuzbandverletzungen und der damit einhergehenden funktionellen Einschränkung besteht ein anhaltendes Interesse an der Verbesserung bestehender und Entwicklung neuer, besserer Techniken zur Rekonstruktion dieser Bandstruktur des Kniegelenkes. In dieser Studie wurde der Einfluss des Verankerungsniveaus (anatomisch vs. extrakortikal) und der Verankerungsart (direkt vs. indirekt) auf das mechanische Verhalten von drei exemplarischen, in der Klinik häufig angewandten Rekonstruktionstechniken, untersucht. Material & Methoden: An insgesamt 24 Kniegelenken humaner Spender mittleren Alters (40 Jahre) wurden drei Rekonstruktionstechniken (n=8 pro Gruppe) des VKB durchgeführt. Als Transplantat wurden jeweils humane Hamstringsehnen verwendet: 1.) HADBIO: anatomische und direkte Verankerung mit biodegradierbaren Interferenzschrauben, 2.) HADTIT: semi-anatomische und direkte Verankerung mit Titanschrauben, 3.) HEIButton: extrakortikale, indirekte Verankerung mit Faden-Button Verbindung. Alle rekonstruierten Kniegelenke wurden einer zyklischen, inkremental zunehmenden Belastung bis zum Versagen unterzogen. Es wurden die Parameter Konstruktsteifigkeit, absorbierte Energie, Transplantatauslenkung und Laxizitätszunahme bei Belastungen von 200, 300, 400 N, sowie die maximale Steifigkeit und Versagenskraft bestimmt. Ergebnis: Die anatomische und direkte Transplantatverankerung mit biodegradierbarer Interferenzschraube zeigt die vorteilhaftesten mechanischen Eigenschaften, während die extrakortikale und indirekte Verankerung die niedrigsten mechanischen Eigenschaften aufwies. Die tibiale Verankerungsseite ist bei Interferenzschraubenverankerung der Schwachpunkt, während die Fadenverbindungen bei der extrakortikalen Verankerungstechnik die Schwachstelle darstellten. Auch bei anatomischer und direkter Transplantatfixation findet ein nicht zu vernachlässigender permanenter Verankerungsverlust bei vergleichsweise geringer Versagenskraft statt, der vor allem auf der tibialen Verankerungsseite zu beobachten ist. Diskussion: Eine anatomische und direkte Transplantatverankerung ist von mechanischem Vorteil. Allerdings hängt die Konstruktsteifigkeit auch in erheblichem Maße vom Fixationsobjekt ab. Extrakortikale Fixationstechniken, die eine indirekte Faden-Knoten-Transplantatverbindung erfordern, unterliegen einer erheblichen nicht-reversiblen Lockerung unter zyklischer Belastung und sollten durch direkte Verankerungstechniken ersetzt werden. Aufgrund der permanenten Laxizitätszunahme auch in der anatomischen und direkten Interferenzschraubenverankerung, vor allem der tibialen Seite, sollte über Sicherungsverankerungen, so genannten Hybridfixationen nachgedacht werden, um die mechanischen Vorteile dieser Rekonstruktionsart voll zum Tragen bringen zu können. / Introduction: There is a continuous interest in the improvement and development of new techniques for the reconstruction of the anterior cruciate ligament (ACL) because of the high incidence of its injury and the resulting functional deficit. Purpose of this study was the impact of fixation level (anatomic vs. extracortical) and fixation method (direct vs. indirect) on the mechanical properties of three frequently used reconstruction techniques. Material & Methods: 24 human cadaveric knees with an average age of 40 years were used for simulation of three reconstruction techniques (n=8 per group). Human hamstring tendons were utilized as tendon grafts. 1.) HADBIO: anatomic and direct fixation with biodegradable interference screws, 2.) HADTIT: semi-anatomic and direct fixation with titanium interference screws, 3.) HEIButton: extracortical, indirect fixation with tape/button combination. All reconstructed knee joints underwent cyclic incremental loading until failure. Construct stiffness, absorbed energy, displacement and laxity increase were calculated at loads up to 200, 300, 400 N. Maximum stiffness and failure load were also recorded. Results: The anatomic and direct graft fixation with biodegradable interference screws provided the highest, while the combination of extracortical and indirect fixation showed the lowest mechanical properties. The tibial fixation site is the critical factor in interference screw fixation, while the tape/suture interfaces were the location of failure in the extracortical reconstructions. Even in the anatomic and direct reconstruction technique a considerable permanent loss of fixation, especially at the tibial fixation site and a comparably lower failure load were observed. Discussion: The combination of anatomic and direct fixation showed to be of mechanical benefit. However, construct stiffness seemed to be also affected by the fixation device. Extracortical fixation techniques, which require suture-tape/knot interfaces for graft fixation, undergo significant permanent loosening of fixation under cyclic loads and should be replaced by direct fixation techniques. Since a permanent laxity increase was still observed in the anatomic and direct interference screw reconstructions, especially on the tibial site, backup or so called hybrid fixations should be considered, which would allow to take full advantage of the mechanical improvements in these reconstruction techniques.

Fluorescence microscopy is an indispensable tool in the areas of cell biology, histology and material science as it enables non-invasive observation of specimen in their natural environment. The main advantage of fluorescence microscopy is that, it is non-invasive and capable of imaging with very high contrast and visibility. It is dynamic, sensitive and allows high selectivity. The specificity and sensitivity of antibody-conjugated probes and genetically-engineered fluorescent protein constructs allows the user to label multiple targets and the precise location of intracellular components. However, its spatial reso- lution is limited to one-quarter of the excitation wavelength (Abbe’s diffraction limit). The advent of new and sophisticated optics and availability of fluorophores has made fluorescence imaging a flourishing field. Several advanced techniques like TIRF, 4PI, STED, SIM, SPIM, PALM, fPALM, GSDIM and STORM, have enabled high resolution imaging by breaking the diffraction barrier and are a boon to medical and biological research. Invention of confocal and multi-photon microscopes have enabled observation of the specimen embedded at depth. All these advances in fluorescence microscopy have made it a much sought-after technique. The first chapter provides an overview of the fundamental concepts in fluorescence imag- ing. A brief history of emergence of the field is provided in this chapter along with the evolution of different super-resolution microscopes. An introduction to the concept of fluorophores, their broad classification and their characteristics is discussed in this chap- ter. A brief explanation of different fluorescence imaging techniques and some trending techniques are introduced. This chapter provides a thorough foundation for the research work presented in the thesis. Second chapter deals with different microscopy techniques that have changed the face of biophotonics and nanoscale imaging. The resolution of optical imaging systems are dictated by the inherent property of the system, known as impulse response or more popularly “point spread function”. A basic fluorescence imaging system is presented in this chapter and introduces the concept of point spread function and resolution. The introduction of confocal microscope and multi-photon microscope brought about improved optical sectioning. 4PI microscopy technique was invented to improve the axial resolution of the optical imaging system. Using this microscopy modality, an axial resolution of upto ≈ 100nm was made possible. The basic concepts of these techniques is provided in this chapter. The chapter concludes with a discussion on some of the optical engineering techniques that aid in improved lateral and axial resolution improvements and then we proceed to take on these engineering techniques in detail in the next chapter. Introduction of spatial masks at the back aperture of the objective lens results in gen- eration of a Bessel-like beam, which enhances our ability to see deeper inside a spec- imen with reduced aberrations and improved lateral resolution. Bessel beams have non-diffracting and self-reconstructing properties which reduces the scattering while ob- serving cells embedded deep in a thick tissue. By coupling this with the 4PI super- resolution microscopy technique, multiple excitation spots can be generated along the optical axis of the two opposing high-NA objective lenses. This technique is known as multiple excitation spot optical (MESO) microscopy technique. It provides a lateral resolution improvement upto 150nm. A detailed description of the technique and a thorough analysis of the polarization properties is discussed in chapter 3. Chapters 4 and 5 bring the focus of the thesis to the main topic of research - multi- dimensional image reconstruction for fluorescence microscopy by employing the statis- tical techniques. We begin with an introduction to filtering techniques in Chapter 4 and concentrate on an edge-preserving denoising filter: Bilateral Filter for fluorescence microscopy images. Bilateral filter is a non-linear combination of two Gaussian filters, one based on proximity of two pixels and the other based on the intensity similarity of the two. These two sub-filters result in the edge-preserving capability of the filter. This technique is very popular in the field of image processing and we demonstrate the application of the technique for fluorescence microscopy images. The chapter presents a through description of the technique along with comparisons with Poisson noise mod- eling. Chapters 4 and 5 provide a detailed introduction to statistical iterative recon- struction algorithms like expectation maximization-maximum likelihood (EM-ML) and maximum a-posteriori (MAP) techniques. The main objective of an image reconstruc- tion algorithm is to recover an object from its noisy degraded images. Deconvolution methods are generally used to denoise and recover the true object. The choice of an appropriate prior function is the crux of the MAP algorithm. The remaining of chapter 5 provides an introduction to different potential functions. We show some results of the MAP algorithm in comparison with that of ML algorithm. In chapter 6, we continue the discussion on MAP reconstruction where two new potential functions are introduced and demonstrated. The first one is based on the application of Taylor series expansion on the image. The image field is considered to be analytic and hence Taylor series produces an accurate estimation of the field being reconstructed. The second half of the chapter introduces an interpolation function to approximate the value of a pixel in its neighborhood. Cubic B-splines are widely used as a basis function during interpolation and they are popular technique in computer vision and medical imaging techniques. These novel algorithms are tested on di_erent microscopy data like, confocal and 4PI. The results are shown at the _nal part of the chapter. Tagging cell organelles with uorescent probes enable their visualization and analysis non-invasively. In recent times, it is common to tag more than one organelle of interest and simultaneously observe their structures and functions. Multicolor uorescence imaging has become a key technique to study speci_c processes like pH sensing and cell metabolism with a nanoscale precision. However, this process is hindered by various problems like optical artifacts, noise, autouorescence, photobleaching and leakage of uorescence from one channel to the other. Chapter 7 deals with an image reconstruction technique to obtain noise-free and distortion-less data from multiple channels when imaging a multicolor sample. This technique is easily adaptable with the existing imaging systems and has potential application in biological imaging and biophysics where multiple probes are used to tag the features of interest. The fact that the lateral resolution of an optical system is better than the axial resolution is well known. Conventional microscopes focus on cells that are very close to the cover-slip or a few microns into the specimen. However, for cells that are embedded deep in a thick sample (ex: tissues), it is di_cult to visualize them using a conventional microscope. A number of factors like, scattering, optical aberrations, mismatch of refractive index between the objective lens and the mounting medium and noise, cause distortion of the images of samples at large depths. The system PSF gets distorted due to di_raction and its shape changes rapidly at large depths. The aim of chapter 8 is to introduce a technique to reduce distortion of images acquired at depth by employing image reconstruction techniques. The key to this methodology is the modeling of PSF at large depths. Maximum likelihood technique is then employed to reduce the streaking e_ects of the PSF and removes noise from raw images. This technique enables the visualization of cells embedded at a depth of 150_m. Several biological processes within the cell occur at a rate faster than the rate of acquisition and hence vital information is missed during imaging. The recorded images of these dynamic events are corrupted by motion blur, noise and other optical aberrations. Chapter 9 deals with two techniques that address temporal resolution improvement of the uorescence imaging system. The _rst technique focuses on accelerating the data acquisition process. This includes employing the concept of time-multiplexing to acquire sequential images from a dynamic sample using two cameras and generating multiple sheets of light using a di_raction grating, resulting in multi-plane illumination. The second technique involves the use of parallel processing units to enable real-time image reconstruction of the acquired data. A multi-node GPU and CUDA architecture effciently reduce the computation time of the reconstruction algorithms. Faster implementation of iterative image reconstruction techniques can aid in low-light imaging and dynamic monitoring of rapidly moving samples in real time. Employing rapid acquisition and rapid image reconstruction aids in real-time visualization of cells and have immense potential in the _eld of microbiology and bio-mechanics. Finally, we conclude the thesis with a brief section on the contribution of the thesis and the future scope the work presented. Thank you for using www.freepdfconvert.com service! 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Depuis quelques années, les techniques d'imagerie de fluorescence font l'objet d'une attention particulière, celles-ci permettant d'étudier de manière non invasive un nombre important de processus cellulaires. En particulier, les techniques de fluorescence en rétrodiffusion (FRI pour Fluorescence Reflectance Imaging) présentent plusieurs avantages en termes de facilité de mise en oeuvre, de rapidité et de coût, mais elles sont aussi sujettes à des limites fortes : la pénétration des tissus reste relativement faible (quelques millimètres seulement), et il est impossible d'avoir une information quantitative du fait de la diffusion des photons. L'objectif de cette thèse a été de réduire les effets des signaux parasites afin d'améliorer les performances de la FRI aussi bien au niveau du contraste que de la résolution. Pour ce faire nous avons décidé d'utiliser de nouvelles techniques d'illumination et de détection. Contrairement aux systèmes classiques qui utilisent une illumination et une détection large champ, nous balayons l'objet d'étude avec une ligne laser, des images étant acquises à chaque position de la ligne. On a alors accès à une pile d'images contenant un nombre d'informations bien plus important que dans le cas classique. Trois axes ont été suivis pour l'exploitation de ces informations. Les méthodes développées ont été testées en simulation avec le logiciel NIRFAST et un algorithme de Monte-Carlo mais aussi expérimentalement. Les validations expérimentales ont été réalisées sur fantômes optiques et en in vivo sur petit animal en les comparant à une illumination uniforme plus classique. En améliorant à la fois le contraste et la résolution, ces différentes méthodes nous permettent d'obtenir de l'information exploitable plus loin en profondeur en réduisant les effets néfastes des signaux parasites et de la diffusion. / Intraoperative fluorescence imaging in reflectance geometry is an attractive imaging modality to noninvasively monitor fluorescence-targeted tumors. However, in some situations, this kind of imaging suffers from a lack of depth penetration and a poor resolution due to the diffusive nature of photons in tissue. The objective of the thesis was to tackle these limitations. Rather than using a wide-field illumination like usual systems, the technique developed relies on the scanning of the medium with a laser line illumination and the acquisition of images at each position of excitation. Several detection schemes are proposed to take advantage of the stack of images acquired to enhance the resolution and the contrast of the final image. These detection techniques were tested both in simulation with the NIRFAST software and a Monte-Carlo algorithm and experimentally. The experimental validation was performed on tissue-like phantoms and in vivo with a preliminary testing. The results are compared to those obtained with a classical wide-field illumination. As they enhance both the contrast and the resolution, these methods allow us to image deeper targets by reducing the negative effects of parasite signals and diffusion.