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.

Educatio publica praestantissimum est vitiorum submovendorum auxilium

Invocatio: D.F.G.

De publica juventutis institutione

Variantti A.

Educatio juventutis publica in scholis inferioribus 1

Invokaatio: D.F.G.

Catalogus librorum, quos possedit b. m. vir Henr. Gabr. Porthan, cancellar. Reg. Svec. consiliar. profess. eloqu. ad Acad. Aboënsem, [et] ord. reg. Svec. de Stella Polari eques: subhastatione publica, die mensis octobris 14 et sqq. anni 1812 Aboae divendendorum

Arkit: 1 arkintunnukseton lehti, A-2E8 2F3.

Catalogus librorum, beate defuncti domini Christierni Herkepaei, qvorum auctio publica habebitur Holmiae d [ ] a:o 1738

Arkit: A8 B5[-?].

Bibliotheca Caroli Frider. Mennander, olim s. s. theol. doctoris, archiepiscopi atque Academiae Upsaliens. pro-cancellarii, nec non membri regii ord. de Stella Polari. Publica auctione vendenda Upsaliae, d. 2. Februarii, 1788

Arkit: 1 arkintunnukseton lehti, )(2, A-T4. - S. [150] tyhjä.