Programme theme
Many important real world problems give rise to an Inverse problem (IP). These include medical imaging, non-destructive testing, oil and gas exploration, land-mine detection and process control. For example, in the exploration for oil and gas, one needs to assess the structure of the interior of the earth from observations made at the surface. Typically, an explosion is created and the resulting shockwaves together with their reflections are used to build a model of the structure of the earth. In magnetoencephalography one needs to determine the electric current in the neurones from the measurement of the magnetic field outside the head. In the field of medical imaging IP forms an important tool in diagnostic investigations. For example, PET and SPECT are two modern imaging techniques whose success is dependent on solving IPs.
At their simplest level IP are concerned with obtaining information about the interior of a body from data which is available at its surface. Mathematically, this is a parameter identification problem: given a set of data representing the behaviour of solutions, identify the unknown parameters of the model.
The mathematical machinery needed for solving various IPs is mainly founded in mathematical analysis and uses tools from functional analysis, function theory, conformal maps, spectral theory, theory of PDEs, integral equations, and micro-local and global analysis. In recent years tools from differential geometry, stochastic analysis, etc., are becoming important. Moreover, in order to realise the solution to many applied problems in a useful way, the tools of numerical analysis and scientific computing are needed.
We intend this programme to help cross-fertilise ideas between scientists by providing them with the opportunity to work on important problems with experts from other groups. We intend to focus on the following topics during the period of the programme: Inverse spectral problems, Analytic and geometric methods for IP, Stochastic methods, Numerical methods, and Application of IP to industry, medicine, finance, biology, and exploration seismology; and plan to organise several workshops which focus on these highlighted areas, as well as a tutorial meeting.
Click here to download the programme's final scientific report
Preprints
| Title | Year | Programme | |
|---|---|---|---|
Uniqueness results for one-dimensional Schrödinger operators with purely discrete spectraAuthors: Jonathan Eckhardt, Gerald Teschl |
2011 | INV | 21 October 2016 |
Singular Weyl-Titchmarsh-Kodaira theory for Jacobi operatorsAuthors: Jonathan Eckhardt, Gerald Teschl |
2011 | INV | 21 October 2016 |
Cracks with impedance, stable determination from boundary dataAuthors: Giovanni Alessandrini, Eva Sincich |
2011 | INV | 21 October 2016 |
Weyl-Titchmarsh Theory for Sturm-Liouville operators with distributional coefficientsAuthors: Jonathan Eckhardt, Fritz Gesztesy, R Nichols, Gerald Teschl |
2011 | INV | 21 October 2016 |
Monodromy evolving deformations and confluent Halphen's systemsAuthors: Yousuke Ohyama |
2011 | INV | 21 October 2016 |
Workshops
Introductory workshop
25 July 2011 to 29 July 2011
Inverse problems in analysis and geometry
1 August 2011 to 5 August 2011
Analytic and geometric methods in medical imaging
22 August 2011 to 26 August 2011
Inverse spectral problems in one dimension
17 October 2011 to 21 October 2011
Inverse problems in science and engineering
12 December 2011 to 16 December 2011
Sparse regularisation for inverse problems
7 February 2014 to 7 February 2014
Inverse problems - follow-up meeting
10 February 2014 to 14 February 2014
Seminars
| Tuesday 9th August 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Gregory Eskin University of California, Los Angeles |
Room 2 | 
|
| Tuesday 16th August 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Alexander Its |
Room 2 |
|
| Tuesday 30th August 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Lassi Päivärinta University of Helsinki |
Room 2 | |
| Tuesday 6th September 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Heinz Langer Vienna University of Technology |
Room 2 |
|
| Tuesday 13th September 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Matias Dahl Aalto University School of Science and Technology (TKK) |
Room 2 | |
| Tuesday 20th September 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Gen Nakamura Hokkaido University |
Room 1 |
|
| Tuesday 27th September 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Daniel Faraco Universidad Autonoma de Madrid |
Room 2 |
|
| 15:30 to 16:30 |
Sergei Ivanov Steklov Mathematical Institute, Russian Academy of Sciences |
Room 2 |
|
| Thursday 29th September 2011 | |||
|---|---|---|---|
| 17:00 to 18:00 |
Gunther Uhlmann University of Washington |
Room 1 |
|
| Tuesday 4th October 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Alexandru Tamasan University of Central Florida |
Room 1 |
|
| Tuesday 11th October 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 | Room 2 |
|
|
| Tuesday 25th October 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Bill Rundell Texas A&M University |
Room 2 |
|
| Wednesday 26th October 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Guillaume Bal Columbia University |
Room 2 | |
| Thursday 27th October 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Jan Boman Stockholm University |
Room 2 |
|
| Monday 31st October 2011 | |||
|---|---|---|---|
| 15:00 to 17:00 | Discussion Room | ||
| Tuesday 1st November 2011 | |||
|---|---|---|---|
| 15:00 to 17:00 | Discussion Room | ||
| Thursday 3rd November 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Bill Lionheart University of Manchester |
Room 1 |
|
| Tuesday 8th November 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Peter Perry University of Kentucky |
Room 2 |
|
| Thursday 10th November 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Joyce McLaughlin Rensselaer Polytechnic Institute |
Room 2 |
|
| Tuesday 15th November 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Raluca Felea Rochester Institute of Technology |
Room 2 | |
| Thursday 17th November 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
On the scattered field generated by a ball inhomogeneity of constant index |
Room 2 |
|
| Tuesday 22nd November 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Samuli Siltanen University of Helsinki |
Room 2 |
|
| Wednesday 23rd November 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Delio Mugnolo Universität Ulm |
Room 2 |
|
| Thursday 24th November 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Chris Budd University of Bath |
Room 2 | |
| Monday 28th November 2011 | |||
|---|---|---|---|
| 15:00 to 18:00 | Discussion Room | ||
| Tuesday 29th November 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Alexander Kachalov Pereslavl-Zalessky of the Russian Academy of Sciences |
Room 2 |
|
| Thursday 1st December 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Otmar Scherzer Technische Universität Wien |
Room 2 |
|
| Tuesday 6th December 2011 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Daniel Lesnic University of Leeds |
Room 2 |
|
| Friday 7th February 2014 | |||
|---|---|---|---|
| 10:15 to 10:55 | No Room Required | ||
| 10:55 to 11:00 | Room 1 | ||
| 13:45 to 14:30 |
A statistical perspective on sparse regularization and geometric modelling |
Room 1 |
|
| 14:30 to 15:00 |
A primal dual method for inverse problems in MRI with non-linear forward operators |
Room 1 |
|
| 15:30 to 16:00 |
Restoration of images with blur and noise - effective models for known and unknown blurs |
Room 1 |
|
| 16:00 to 16:30 | Room 1 | ||
| 17:00 to 18:00 | No Room Required | ||
| Monday 10th February 2014 | |||
|---|---|---|---|
| 08:30 to 09:35 | No Room Required | ||
| 09:35 to 09:45 | No Room Required | ||
| 09:45 to 10:30 | Room 1 |
|
|
| 10:30 to 11:00 | No Room Required | ||
| 11:00 to 11:45 |
Conjugate gradient iterative hard thresholding for compressed sensing and matrix completion |
Room 1 |
|
| 11:45 to 12:30 | Room 1 |
|
|
| 12:30 to 13:30 | No Room Required | ||
| 13:30 to 14:15 |
Reconstruction of the wave speed in a geophysical inverse problem |
Room 1 |
|
| 14:15 to 15:00 | Room 1 |
|
|
| 15:00 to 15:30 | No Room Required | ||
| 15:30 to 16:15 |
A Data-Driven Edge-Preserving D-bar Method for Electrical Impedance Tomography |
Room 1 | |
| 16:15 to 17:00 | Room 1 |
|
|
| 17:00 to 18:00 | No Room Required | ||
| Tuesday 11th February 2014 | |||
|---|---|---|---|
| 09:00 to 09:45 | Room 1 | ||
| 10:30 to 11:00 | No Room Required | ||
| 11:00 to 11:45 | Room 1 |
|
|
| 12:30 to 13:30 | No Room Required | ||
| 13:30 to 14:15 | Room 1 |
|
|
| 15:00 to 15:30 | No Room Required | ||
| 15:30 to 16:15 | Room 1 | ||
| 16:15 to 17:00 | Room 1 | ||
| 17:00 to 18:00 | No Room Required | ||
| Wednesday 12th February 2014 | |||
|---|---|---|---|
| 10:30 to 11:00 | No Room Required | ||
| 11:00 to 11:45 |
On Convex Finite-Dimensional Variational Methods in Imaging Sciences, and Hamilton-Jacobi Equations |
Room 1 |
|
| 11:45 to 12:30 | Room 1 |
|
|
| 12:30 to 13:30 | No Room Required | ||
| 13:30 to 14:15 |
Alternating Projection, Ptychographic Imaging and connection graph Laplacian |
Room 1 |
|
| Thursday 13th February 2014 | |||
|---|---|---|---|
| 10:30 to 11:00 | No Room Required | ||
| 11:45 to 12:30 | Room 1 |
|
|
| 12:30 to 13:30 | No Room Required | ||
| 13:30 to 14:15 | Room 1 | ||
| 19:30 to 22:00 | No Room Required | ||
| Friday 14th February 2014 | |||
|---|---|---|---|
| 09:00 to 09:45 | Room 1 |
|
|
| 09:45 to 10:30 | Room 1 |
|
|
| 10:30 to 11:00 | No Room Required | ||
| 11:45 to 12:30 |
Optimizing the optimizers - what is the right image and data model? |
Room 1 |
|
| 12:30 to 13:30 | No Room Required | ||
Organisers
- Malcolm Brown Cardiff University
- Yaroslav Kurylev University College London
- Bill Lionheart University of Manchester
Speakers
- Guillaume Bal Columbia University
- Jan Boman Stockholm University
- Chris Budd University of Bath
- Matias Dahl Aalto University School of Science and Technology (TKK)
- Gregory Eskin University of California, Los Angeles
- Daniel Faraco Universidad Autonoma de Madrid
- Raluca Felea Rochester Institute of Technology
- Alexander Its
- Sergei Ivanov Steklov Mathematical Institute, Russian Academy of Sciences
- Alexander Kachalov Pereslavl-Zalessky of the Russian Academy of Sciences
- Heinz Langer Vienna University of Technology
- Daniel Lesnic University of Leeds
- Bill Lionheart University of Manchester
- Joyce McLaughlin Rensselaer Polytechnic Institute
- Delio Mugnolo Universität Ulm
- Gen Nakamura Hokkaido University
- Peter Perry University of Kentucky
- Lassi Päivärinta University of Helsinki
- Bill Rundell Texas A&M University
- Otmar Scherzer Technische Universität Wien
- Samuli Siltanen University of Helsinki
- Alexandru Tamasan University of Central Florida
- Gunther Uhlmann University of Washington
Supported By
