Thursday 18 November 2010

Break for now at least

Andy has not yet managed to make an EIDORS video a tutorial. I suggest we take a break for now. But I am open to suggestions. Reply in comments with things you would like me to talk about, or find someone else to talk about. Applications springs to mind for one thing. Some of us are learning about lung EIT and lung mechanics. Others geophysical EIT.

Thursday 11 November 2010

EIDORS playtime at 11 today

Instead of a lecture today I have booked the small computer cluster downstairs in the Alan Turing Building. I intend we shall have a play with EIDORS. I am currently faffing about getting netgen etc working on windoze!

If you are looking for it go past Pi in The Sky and take the second door on right.

Thursday 4 November 2010

No lecture tomorrow

I had been planning a demo of EIDORS but as my laptop has died it is proving too difficult to set up. Locals may be interested in The Numerical Analysis and Scientific Computing Seminar tomorrow (Friday 5th Nov)

Paul Childs (Schlumberger Cambridge Research)
Challenges in seismic imaging
3pm Frank Adams 1 Alan Turing Building

Friday 29 October 2010

Lecture 6 Sharp changes

This lecture concentrated on reconstruction algorithms for sharp changes. I concentrated mainly on Monotonicity method and Factorization. I referred to the slides for a talk given in Korea in 2006, so you will need this open to follow as it is not easy to see on the video.

There are references at the end of the slides, but for factorization method there are some more recent work that might be a better place to start.

I did not go in to TV that much but there are more details on the slides.

Videos All in one file, Or in chunks part 1, part 2, part 3, part 4.


Here is the web interface Brühl's factorization code.

Sunday 24 October 2010

Lecture 5: drive and measurement patterns

This was a bit unplanned but following a phone call to Andy Adler on Thursday I decided to talk about drive and measurement patterns, so it if it seems a bit rambling and unplanned it was.

Videos here part1, part2, part3,part4.

Some links mentioned in the notes

Friday 15 October 2010

Lecture 4 Solving the forward problem

Today's topic is solving the forward problem. For the discussion of FEM I will refer to my book chapter in Holder's book with Nick Polydorides and Andrea Borsic (see preprint version). Theses are also useful, Marko Vaukhonen's and Nick Polydorides' (see reading list)

The video (a single AVI) download here

The "cot formula" that relates FEM to resistor networks in 3D appears in our paper from the Florida EIT meeting William R. B. Lionheart and Kyriakos Paridis, Finite Elements and Anisotropic EIT reconstruction. Journal of Physics: Conference Series, vol. 224, no. 1, p. 012022, 2010

Monday 11 October 2010

Lecture 3 videos now here

This is just here to trigger your RSS feed or whatever, I'll delete it when people have noticed...I am not yet convinced of this "email lists are so last century" idea and new fangled things like RSS feeds and blogger followers, well we will see how it works.

Yes it is Friday at 11am

We are continuing on Fridays at 11-12, in the same room, except for Nov 26th. We probably wont have a lecture then as the room is booked by someone else and one of my students is being viva'd. We will endeavour to put the lectures on the web the same day but some times (eg this time) it might slip to Monday

Friday 8 October 2010

Lecture 3

Time for some vector calculus and linear algebra. I started by explaining the so-called Louiville transformation between the conductivity and stationary Schrödinger equation. Then we went on to least squares solution of over determined linear systems, Tikhonov regularization and the SVD.

This material is covered in more detail in my lecture notes for a course we used to teach use the username inverse and the password crime to access this page and look at chapter 3 of the notes.

Video as one avi file, or
part1 part2 part3 part4 part5

Or on YouTube Part 1,

Tuesday 5 October 2010

Updates

We have added links to the lectures in avi files split up in to (less than) 15 min chunks. I am experimenting with Youtube. Please post in comments to let us know if this works for you. Also I have put up some homework problems on the blog post for lecture 2.

Monday 4 October 2010

Lecture 2 the linearization

In this lecture we go through Calderón's Born Neumann series for the forward problem and the linearization that results from truncating the higher order terms. The Fréchet derivative of the Neuman-to-Dirichlet map is derived from Calderón's calculation of the Fréchet derivative of the Dirichlet-toNeumann map with respect to conductivity.

The (high resolution) video is here Lower resolution in chunks part1, part2,part3,part4.

Some helpful resources:
Some homework suggestions
  1. Have a go at deriving the Born-Neumann series and directly the linearization for the Neumann-to-Dirichlet case. To make it simpler assume that the conductivity does not change in a neighbourhood of the boundary
  2. How does the argument change for the case of complex conductivity? Clearly you need some complex conjugates around.
  3. Find the sensitivity/Fréchet derivative for the stationary Schrödinger/variable wave speed Helmholtz equation -∇2 u + c u=0. If c is allowed to be negative you have to assume that it is "non resonant", that is you avoid eigenvalues, then there is a well defined Green's operator. This problem is relevant to ultrasound/seismic imaging, diffuse optical tomography, quantum scattering etc.

Friday 24 September 2010

Lecture 1 Introduction to the Forward Problem

The video of the first lecture is available as a download (about 628MBytes). Kyriakos has made a smaller avi file or you can see it in 15min chunks part1, part2,part3,part4. We are trying Youtube (not yet sure resolution is enough) part1

There is a home work exercise implicit in the lecture. That is to check the calculation of the Dirichlet to Neumann map for the concentric anomaly by separation of variables. Another interesting thing to do is do some calculations of current and voltage patterns, and see how they change with rho and mu.

If you get anywhere with this post it in the comments too!

Thursday 23 September 2010

Initial reading list

So here is a short reading list for people just starting out in EIT reconstruction

  • The book chapter W Lionheart, N.Polydordes and A Borsic, The reconstruction problem, Part 1 of Electrical Impedance Tomography: Methods, History and Applications, (ed) D S Holder, Institute of Physics, p3-64, 2004. It is available as a preprint MIMS e-print: 2006.421>but you might encourage your library to buy the whole book especially if you want to read about medical applications. This chapter is aimed especially and engineering PhD students jsut starting out in EIT.
  • Andy Adler, Romina Gaburro, William Lionheart, EIT, chapter in Handbook of Mathematical Methods in Imaging, O Scherzer, Springer-Verlag, 2010. This chapter is more aimed at maths PhD students thinking of working in EIT, especially the sections on uniqueness. The introductory part and the numerical methods towards the end are suited to engineering students. An excerpt from the this chapter serves as notes for my first lecture.
  • Marko Vauhkonen's PhD thesis PhD thesis: Electrical impedance tomography and prior information (PDF) , 1997. It is still a good place to learn about practical numerical impelementation of EIT reconstruction algorithms.
(To be continued......)

  • Nick Polydorides thesis Image Reconstruction Algorithms for Soft-Field Tomography is still useful especially for the 3D problem.
  • Welcome

    With two new PhD students starting here in Manchester on Electrical Impedance Tomography reconstruction I have to get them quickly up to speed with the basics of reconstruction. My idea was to try to share this as much as possible with others starting out on learning EIT reconstruction (for medical, process or geophysical imaging) around the world.

    I have not yet figured out how to do video streaming or video conferenceing in an easy way, so my first shot is to give a lecture (the first is today Thursday 23/09/2010 at 4pm in the Alan Turing Building Frank Adams Room 2), video it and post it on something like youtube.

    Hopefully people following our impromptu course will be able to see the video and post queries and comments here on the blog.

    Please introduce yourself as a comment to this post. Say at least your name, if you are a PhD student, postdoc or whatever and at what institution, and roughly what you are working on (or planning to work on)

    Bill Lionheart