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MATS577 MA1: Multiwave Imaging (JSS23), 2 op [kotisivu]

Matematiikan ja tilastotieteen laitos

Kurssille ei voida ilmoittautua, koska se on jo vanhennettu.
Kurssin ilmoittautumisaika päättyi 30.4.13 klo 23:59.

Yleisiä tietoja

Kotisivu: http://www.jyu.fi/summerschool
Alkaa - päättyy: 19.8.13 - 23.8.13
Ilmoittautumisaika: 1.2.13 klo 0:00 - 30.4.13 klo 23:59
Ilmoittautuminen voidaan perua 25.6.2013 klo 00:00 mennessä.
Opettaja(t): Tommi Brander (tommi.brander@gmail.com)
Yliopistotutkija Joonas Ilmavirta (joonas.ilmavirta@jyu.fi)
Professori Mikko Salo (mikko.j.salo@jyu.fi)
Laajuus: 2 op
Kielet: opetuskielet: English; suorituskielet: English
Ilmoittautuneita: 39
Organisaatiot:Kansainvälinen kesäkoulu - Jyväskylä Summer School (JSS), Matemaattis-luonnontieteellinen tiedekunta (MLTK), Matematiikan ja tilastotieteen laitos (MATHS), Matematiikka (MAT)
  • Lecturer: Prof. Gunther Uhlmann (University of Washington)
  • The course is a part of the 23rd international Jyväskylä Summer School programme

Multi-wave imaging methods, also called hybrid methods, attempt to combine the high resolution of one imaging method with the high contrast capabilities of another through a physical principle. One important medical imaging application is breast cancer detection. Ultrasound provides a high (sub-millimeter) resolution, but suffers from low contrast. On the other hand, many tumors absorb much more energy of electromagnetic waves (in some specific energy bands) than healthy cells. Photoacoustic tomography (PAT) consists of sending relatively harmless optical radiation into tissues that causes heating which results in the generation of propagating ultrasound waves (the photo-acoustic effect). Such ultrasonic waves are readily measurable. The inverse problem then consists of reconstructing the optical properties of the tissue from these measurements. In Thermoacoustic tomography (TAT) low frequency microwaves, with wavelengths on the order of $1m$, are sent into the medium. The rationale for using the latter frequencies is that they are less absorbed than optical frequencies. Transient Elastography (TE) images the propagation of shear waves using ultrasound.

Multi-wave imaging methods lead to a rich supply of new mathematical questions that involve elliptic and hyperbolic partial differential equations. We will discuss some of the inverse problems arising in these imaging techniques with emphasis on PAT.


The course is aimed at graduate students, but strong advanced undergraduate students with the appropriate background might find it suitable. Basic knowledge of linear partial differential equations and Sobolev spaces will be useful. A good reference for the background topics is the book by L.C. Evans: Partial Differential Equations and in particular the chapters in this book which deal with linear second order partial differential equations.


Obligatory attendance at lectures and completing the exercises.



Kurssin työmäärä:

10 h lectures (2 x 45 min/day and consultations/day)

[Tiivistä opetusryhmien aika- ja paikkatiedot]

Lecture [ryhmien tarkat tiedot ja ilmoittautuminen]

Lecture [ryhmätiedot ja ilmoittautuminen]; ilmoittautuneita 39, maksimi 200
ilm.aika: 1.2.2013 00:00 - 30.4.2013 23:59
 PaikkaViikkoPäiväPvmKloOhjaajaLisätietojaURITapahtuman tiedot
1MaD 20234ma19.8.201310:00-12:00SaloTapahtuman tiedot
2MaD 20234ti20.8.201310:00-12:00SaloTapahtuman tiedot
3MaD 20234ke21.8.201310:00-12:00SaloTapahtuman tiedot
4MaD 20234to22.8.201310:00-12:00SaloTapahtuman tiedot
5MaD 20234pe23.8.201310:00-12:00SaloTapahtuman tiedot