ylös hierarkiassa

Mat-1.218 Inversio-ongelmien seminaari

Vanhojen esitelmien aiheita

Syksy 2005

ti 22.11. klo 15-17 TKK U322 Yaroslav V. Kurylev (Loughborough University): Eskin's solution to the inverse problem of the wave equation
ti 29.11. klo 9-11 TKK E Tapio Helin: Image segmentation and working with Mumford-Shah functional

Syksy 2004

to 5.8. klo 12 HY C323 Roberto de la Prieta (Universidad Rey Juan Carlos, Espanja): PET (Positron emission tomography) reconstruction
pe 13.8. klo 12 TKK U356 Roberto de la Prieta (Universidad Rey Juan Carlos, Espanja): Regularized statistical Positron emission tomography (PET) image reconstruction
Abstract: Statistical methods offer a better modeling of the process of data acquisition in PET. Some choices for these models will be reviewed, and also some numerical algorithm to carry out the reconstruction. However, statistical data fitting criterion leads to an ill-posed problem. Several Bayesian penalization strategies had been proposed to date in order to deal with this difficulty. Also Total Variation regularization can be used to regularize this inverse problem in an edge-preserving fashion.
ma 27.9. klo 10 TKK U322 Sari Lasanen (Oulun yliopisto): Converging posterior means in Gaussian statistical inversion
ma 4.10. klo 10 TKK U322 Mikko Salo (Helsingin yliopisto): Introduction to complex geometrical optics solutions
Abstract: Many inverse problems for elliptic operators, such as Calderón's inverse conductivity problem and inverse scattering problems at fixed energy, have been given satisfactory answers using so called complex geometrical optics (CGO) solutions. These are solutions which look like harmonic exponentials, and they date back to Faddeev, Calderón, Sylvester and Uhlmann. I will review the construction of CGO solutions for different operators, starting with the fundamental estimates of Sylvester-Uhlmann and heading all the way to first order perturbations of Laplace. The results may be used to solve several inverse problems in three or higher dimensions.
ma 11.10. klo 10 TKK U322 Nuutti Hyvönen (Helsingin yliopisto): Diffusiivisia tomografiamenetelmiä inkluusioiden kera, osa I (Diffusive tomography methods with inclusions, part I)
ma 18.10. klo 10 HY C321 Pekka Tietäväinen (TKK): Existence and Uniqueness for the Exterior Helmholtz Problem with Layer Potential Techniques
Abstract: We use the jump relations and functional analytical properties of the single and double layer operators to prove existence and uniqueness for the exterior Helmholtz problem with Dirichlet boundary conditions.
ma 25.10. klo 10 TKK U322 Nuutti Hyvönen (Helsingin yliopisto): Diffusiivisia tomografiamenetelmiä inkluusioiden kera, osa II (Diffusive tomography methods with inclusions, part II)
Esitelmässä ei oleteta, että kuulijat olisivat seuranneet maanantaina 11.10. pidetyn ensimmäisen osan.
ma 1.11. klo 10 HY C321 Sampsa Pursiainen (TKK): Digitaalisen Curvelet-muunnoksen perusteet (Digital Curvelet Transform : Back to Basics)
ma 8.11. klo 9 TKK U322 Teemu Pennanen (Helsingin kauppakorkeakoulu): Stochastic programming - optimization under stochastic uncertainty
Ensiksi klo 9.15-9.35 on koeluento dosenttuuria varten. Sen jälkeen tilaisuus jatkuu inversio-ongelmien seminaarina.
ma 15.11. klo 10 HY C321 Juha-Matti Perkkiö (HY): Generalization of the continuous curvelet transform into higher dimensions (Jatkuvan käyräkemuunnoksen useampiulotteinen vastine)
ma 22.11. klo 10 TKK U322 Sanna Kaasalainen (HY): Sironta satunnaisesta aineesta
ma 29.11. klo 10 HY C321 Petteri Piiroinen (HY): Suslin-avaruuksista
ma 6.12. klo 10 TKK U322 Seminaari peruttu: Itsenäisyyspäivä
ma 13.12. klo 10 HY C321 Seminaari peruttu: Stokastiikka Suomessa -tapahtuma

Kevät 2004

Keväällä 2004 tutustumme Dirac-operaattoreihin.
26.1.P722 Petri Ola: Johdatus Dirac-operaattoreihin: Euklidinen Dirac
2.2.U322 Petri Ola: Johdatus Dirac-operaattoreihin: Euklidinen Dirac (osa 2, vielä pääsee kärryille)
9.2.P722 Matti Lassas: An introduction to Dirac operator and differential forms
16.2.U322 Ricardo Weder: Inverse spectral-scattering problem with two sets of discrete spectra
18.2.U356 (keskiviikko, klo 12.15, ylimääräinen esitelmä, inversio-ongelmien ja Finsler-geometrian seminaari)
Alexander Katchalov: Gaussian beams in anisotropic electromagnetic media
23.2.P722 Matti Lassas: An introduction to Dirac operator and differential forms (continued),
Yaroslav V. Kurylev: Dirac and connections
1.3. S I Matti Lassas: Inversio-ongelmat ja geometria
(huom. klo 16, Suomen matemaattisen yhdistyksen vuosikokouksen yhteydessä,
Helsingin yliopiston matematiikan ja tilastotieteen laitoksen salissa S I, os. Yliopistonkatu 5, Helsinki, 4. krs.)
8.-29.3. Ei seminaaria
5.4.U322 Juha-Matti Perkkiö: Miksi ääriviivat ovat ohuita
19.4. Juha-Matti Perkkiö: Miksi ääriviivat ovat ohuita, osa 2 Siirretty. (Uusi paikka ja aika ilmoitetaan myöhemmin.)
26.4. Ei seminaaria
3.5.P722 Pekka Tietäväinen: Kerrospotentiaalit Helmholtz-yhtälölle
10.5. Ei seminaaria
17.5.U322 Sampsa Pursiainen: Diracin yhtälö ja spin-ryhmä

2003

28.1. Maaria Salo: Reunat säilyttävä dekonvoluutio: jatkuvan ongelman teoriaa
4.2. Maaria Salo: Reunat säilyttävä dekonvoluutio: diskreetti ongelma ja sovelluksia
11.2. Viktoria Sofieva (Ilmatieteen laitos): Information theoretical approach to optimal selection of measurements
19.2. Mikko Viinikainen: Reaaliaikainen EEG-inversio
24.2. Prof. Robert Kotiuga: The Appearance of Helicity in the Solution of Various 3-D Inverse Problems
11.3. Matti Lassas: Inversio-ongelmien stabiilisuus
18.3. Kirsi Peltonen: Onko rationaalifunktioita korkeammissa dimensioissa
8.4. Kenrick Bingham: Blagovetshenskin identiteetti hyperbolisessa käänteisongelmassa
15.4. ks. Prof. Leonid Kalachevin tiiviskurssi
22.4. Pääsiäisloma
29.4. Hanna Pikkarainen: Sähköinen prosessitomografia; deterministinen maailma
5.5. Hanna Pikkarainen: Sähköinen prosessitomografia; stokastinen maailma
13.5. Jukka Liukkonen: An Electric Integral Equation for a Resistive Host
29.9. Juha-Matti Perkkiö: Diplomityöesitelmä: Radiative transfer problem on Riemannian manifolds (12.15 - n. 12.35)
29.9. Stephen McDowall: Infinite order boundary determination of material parameters for Maxwell's equations (n. klo 12.35)
13.10. Stephen McDowall: Infinite order boundary determination of material parameters for Maxwell's equations
20.10. Mikko Salo: The Nakamura-Uhlmann intertwining method
27.10. Sampsa Pursiainen: Numerical methods in statistical EIT, part I (abstract)
3.11. Sampsa Pursiainen: Numerical methods in statistical EIT, part II (abstract)
17.11. Juha-Matti Perkkiö: Radiative transfer problem on Riemannian manifolds; preliminaries
24.11. Juha-Matti Perkkiö: Radiative transfer problem on Riemannian manifolds
1.12. Stephen McDowall: An inverse problem for the radiative transport equation in the presence of a Riemannian metric

2002

23.9. klo 14.15 - 16, sali U322 (huom. maanantai) Matti Lassas: Introduction to inverse conductivity problem
Abstract: We give a review on classical results for inverse conductivity problem started by Alberto Calderón. We pay special attention to relation of Riemannian geometry and inverse problem. Also, we discuss some recent counterexamples.
9.10. klo 12.30, sali Y307 Matti Lassas: Introduction to inverse conductivity problem: some recent counterexamples
(ks. tiivistelmä yllä)
16.10. kello 12.15, sali U358 Matias Dahl: Kontakti- ja symplektigeometria sähkömagnetiikassa
Abstract: The present work is divided into two parts. In the first part, we show that, by working in Fourier space, the Bohren decomposition and the Helmholtz's decomposition can be combined into one decomposition. This yields a completely mathematical decomposition, which decomposes an arbitrary vector field on R3 into three components. The most important properties of this decomposition is that it commutes with both the curl operator and with the time derivative. We can therefore apply this decomposition to Maxwell's equations without assuming anything about the media. When we apply this decomposition to the traditional Maxwell's equations (for E, D, B, H) on R3, we will see that Maxwell's equations split into three completely uncoupled sets of equations. Also, when a medium is introduced, the decomposed Maxwell's equations either remain uncoupled, or become coupled depending on the complexity of the medium. As a special case, the decomposed Maxwell's equations contain the Bohren decomposition.

In the second part of this work, we begin with an introduction to contact and symplectic geometry and then study their relation to electromagnetism. By studying examples, we show that the decomposed fields in the decomposed Maxwell's equations always seem to induce contact structures. For instance, for a planewave, the decomposed fields are the right and left hand circulary polarized components and each of these induce their own contact structure. Moreover, we show that each contact structure induces its own Carnot-Carathéodory metric, and the path traversed by the circularly polarized waves seem to coincide with the geodesics of these metrics.

23.10. klo 12.15, sali U358 Matti Lassas: Mikrolokaali analyysi ja inversio-ongelmat
30.10. klo 12.15, sali U358 Matti Lassas: Mikrolokaali analyysi ja inversio-ongelmat - osa 2
6.11. klo 12.15, sali U358 Nuutti Hyvönen: Impedanssitomografian elektrodimalli: approksimaatio-ominaisuudet ja inkluusioiden karakterisointi
13.11. klo 12.15, sali U358 Teemu Pennanen, HKKK: Calibrated option bounds
20.11. klo 12.15 - n. 13.30, sali U358 Teemu Pennanen, HKKK: Calibrated option bounds - osa 2
27.11. klo 12.15, sali U358 Nuutti Hyvönen: Impedanssitomografian elektrodimalli: approksimaatio-ominaisuudet ja inkluusioiden karakterisointi - osa 2
11.12. Inversiopäivät Tahkovuoressa


Kenrick Bingham 3.1.2006
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