Statistical Inversion Theory in X-ray Tomography

In this thesis the X-ray tomography is discussed from the Bayesian statistical viewpoint. The unknown parameters are assumed random variables and as opposite to traditional methods the solution is obtained as a large sample of the distribution of all possible solutions. As an introduction to tomography an inversion formula for Radon transform is presented on a plane. The vastly used filtered backprojection algorithm is derived. The traditional regularization methods are presented sufficiently to ground the Bayesian approach. The measurements are foton counts at the detector pixels. Thus the assumption of a Poisson distributed measurement error is justified. Often the error is assumed Gaussian, altough the electronic noise caused by the measurement device can change the error structure. The assumption of Gaussian measurement error is discussed. In the thesis the use of different prior distributions in X-ray tomography is discussed. Especially in severely ill-posed problems the use of a suitable prior is the main part of the whole solution process. In the empirical part the presented prior distributions are tested using simulated measurements. The effect of different prior distributions produce are shown in the empirical part of the thesis. The use of prior is shown obligatory in case of severely ill-posed problem.

Inversion and assimilation methods with applications in geophysical remote sensing

Stratospheric ozone can be measured accurately using a limb scatter remote sensing technique at the UV-visible spectral region of solar light. The advantages of this technique includes a good vertical resolution and a good daytime coverage of the measurements. In addition to ozone, UV-visible limb scatter measurements contain information about NO2, NO3, OClO, BrO and aerosols. There are currently several satellite instruments continuously scanning the atmosphere and measuring the UVvisible region of the spectrum, e.g., the Optical Spectrograph and Infrared Imager System (OSIRIS) launched on the Odin satellite in February 2001, and the Scanning Imaging Absorption SpectroMeter for Atmospheric CartograpHY (SCIAMACHY) launched on Envisat in March 2002. Envisat also carries the Global Ozone Monitoring by Occultation of Stars (GOMOS) instrument, which also measures limb-scattered sunlight under bright limb occultation conditions. These conditions occur during daytime occultation measurements. The global coverage of the satellite measurements is far better than any other ozone measurement technique, but still the measurements are sparse in the spatial domain. Measurements are also repeated relatively rarely over a certain area, and the composition of the Earth’s atmosphere changes dynamically. Assimilation methods are therefore needed in order to combine the information of the measurements with the atmospheric model. In recent years, the focus of assimilation algorithm research has turned towards filtering methods. The traditional Extended Kalman filter (EKF) method takes into account not only the uncertainty of the measurements, but also the uncertainty of the evolution model of the system. However, the computational cost of full blown EKF increases rapidly as the number of the model parameters increases. Therefore the EKF method cannot be applied directly to the stratospheric ozone assimilation problem. The work in this thesis is devoted to the development of inversion methods for satellite instruments and the development of assimilation methods used with atmospheric models.

Development of advanced silicon radiation detectors for harsh radiation environment

This thesis describes the development of advanced silicon radiation detectors and their characterization by simulations, used in the work for searching elementary particles in the European Organization for Nuclear Research, CERN. Silicon particle detectors will face extremely harsh radiation in the proposed upgrade of the Large Hadron Collider, the future high-energy physics experiment Super-LHC. The increase in the maximal fluence and the beam luminosity up to 1016 neq / cm2 and 1035 cm-2s-1 will require detectors with a dramatic improvement in radiation hardness, when such a fluence will be far beyond the operational limits of the present silicon detectors. The main goals of detector development concentrate on minimizing the radiation degradation. This study contributes mainly to the device engineering technology for developing more radiation hard particle detectors with better characteristics. Also the defect engineering technology is discussed. In the nearest region of the beam in Super-LHC, the only detector choice is 3D detectors, or alternatively replacing other types of detectors every two years. The interest in the 3D silicon detectors is continuously growing because of their many advantages as compared to conventional planar detectors: the devices can be fully depleted at low bias voltages, the speed of the charge collection is high, and the collection distances are about one order of magnitude less than those of planar technology strip and pixel detectors with electrodes limited to the detector surface. Also the 3D detectors exhibit high radiation tolerance, and thus the ability of the silicon detectors to operate after irradiation is increased. Two parameters, full depletion voltage and electric field distribution, is discussed in more detail in this study. The full depletion of the detector is important because the only depleted area in the detector is active for the particle tracking. Similarly, the high electric field in the detector makes the detector volume sensitive, while low-field areas are non-sensitive to particles. This study shows the simulation results of full depletion voltage and the electric field distribution for the various types of 3D detectors. First, the 3D detector with the n-type substrate and partial-penetrating p-type electrodes are researched. A detector of this type has a low electric field on the pixel side and it suffers from type inversion. Next, the substrate is changed to p-type and the detectors having electrodes with one doping type and the dual doping type are examined. The electric field profile in a dual-column 3D Si detector is more uniform than that in the single-type column 3D detector. The dual-column detectors are the best in radiation hardness because of their low depletion voltages and short drift distances.

Kuormituksen vaikutus kromatografiseen erotukseen alikriittisellä vedellä

Teollisessa kromatografiassa kolonnia pyritään kuormittamaan mahdollisimman paljon, jotta saataisiin maksimoitua erotetun komponentin määrä aikayksikköä kohden. Tässä työssä kuormitusta tutkittiin nostamalla syöttöliuoksen, synteettisen melassin, näyteväkevyyttä 80-125 ºC:ssa. Eluenttina oli paineistettu kuumaa vesi ja hartsina vahva Na-muotoinen PS-DVB pohjainen vahva kationinvaihtohartsi. Lämpötilaa nostamalla piikit kapenivat ja tulivat symmetrisemmiksi, erotus nopeutui sekä suola erottui usein paremmin sokereista. Syöttöliuoksen kuiva-ainetta lisättiin asteittain 55 p-% saakka, jolloin ei vielä havaittu ongelmia erotuksessa. Lämpötilassa 125 ºC havaittiin erotuksen aikana kuormituksesta riippumatonta sakkaroosin invertoitumista. Vertailtaessa eri stationäärifaaseja havaittiin Na-muotoisen PS-DVB pohjaisen kationinvaihtohartsin erottavan yleensä sokereita, sokerialkoholeja, oligosakkarideja ja betaiinia lähes poikkeuksetta paremmin alhaisilla pitoisuuksilla kuin neutraalihartsi ja Na-muotoinen zeoliitti. Erottuminen ei yleensä parantunut lämpötilaa nostamalla, mutta piikit kapenivat ja erotus nopeutui. Monosakkaridien erotus huononi 125 ºC:ssa kationinvaihtohartsilla. Tutkittaessa terveysvaikutteisten ksylo-oligosakkaridien soveltuvuutta alikriittiseen erotukseen, niiden havaittiin huomattavasti hydrolysoituvan happamissa olosuhteissa koeputkessa 100 ºC:ssa kahdessa tunnissa. Näytteessä olevien epäpuhtauksien havaittiin katalysoineen hydrolyysiä. Hydrolysoituminen oli hitaampaa neutraaleissa olosuhteissa korotetussa lämpötilassa. Tästä voitiin tehdä johtopäätös, että alikriittiset olosuhteet eivät sovi ksylo-oligosakkaridien erotukseen.

Adaptive MCMC methods with applications in environmental and geophysical models

This work presents new, efficient Markov chain Monte Carlo (MCMC) simulation methods for statistical analysis in various modelling applications. When using MCMC methods, the model is simulated repeatedly to explore the probability distribution describing the uncertainties in model parameters and predictions. In adaptive MCMC methods based on the Metropolis-Hastings algorithm, the proposal distribution needed by the algorithm learns from the target distribution as the simulation proceeds. Adaptive MCMC methods have been subject of intensive research lately, as they open a way for essentially easier use of the methodology. The lack of user-friendly computer programs has been a main obstacle for wider acceptance of the methods. This work provides two new adaptive MCMC methods: DRAM and AARJ. The DRAM method has been built especially to work in high dimensional and non-linear problems. The AARJ method is an extension to DRAM for model selection problems, where the mathematical formulation of the model is uncertain and we want simultaneously to fit several different models to the same observations. The methods were developed while keeping in mind the needs of modelling applications typical in environmental sciences. The development work has been pursued while working with several application projects. The applications presented in this work are: a winter time oxygen concentration model for Lake Tuusulanjärvi and adaptive control of the aerator; a nutrition model for Lake Pyhäjärvi and lake management planning; validation of the algorithms of the GOMOS ozone remote sensing instrument on board the Envisat satellite of European Space Agency and the study of the effects of aerosol model selection on the GOMOS algorithm.