Rich and Nonlinear Tomography - a multidisciplinary approach
RNT
4 January 2023 to 30 June 2023
Programme theme
Tomographic imaging provides the ability to image properties in the interior of an object from measurements taken on its surface or in the far field. It is vital in medicine, manufacturing, geophysics, advanced material and security, to mention only few of its applications. Sensor technology is increasingly extending not only in the number of detector elements and the speed of acquisition but also by adding capability to resolve frequency, energy, polarisation state, transient response, resulting not only in higher data rates but also in richer data. Even though this holds the promise of imaging vector or tensor properties, the highly coupled and often non-linear nature of the underlying inverse problem means that new mathematical and computational methods are needed.
Analytical and geometrical tools in inverse problems are fundamental for understanding the issues of uniqueness and stability of the solution of such ill-posed problems in terms of the data. These, in turn, are key to unearth useful subsets of possible data we can gather, transmit and store and to understand what a-priori information is needed to stabilize the problem. Where data is missing due to physical limitations of transmitter and receiver locations, microlocal analysis can provide information about the directions one can expect to be able to reconstruct singularities (abrupt changes in material properties). Solving an inverse problem also requires an efficient forward solver.
Numerical analysis is key to efficient forward solution. In particular, for non-linear problems, the forward solver is computed repeatedly with only slightly different parameters. Efficient paralleization, including both CPU and GPU cases are key to being able to solve rich tomography problems efficiently. Regularization penalty terms (e.g. total variation and its generalizations) are increasingly being applied to tomographic inverse problems. This requires the use of a new generation of primal-dual optimization algorithms, which, coupled with the non-linearity and the rich data sets, leads to challenging optimization problems. Often in inverse problems and imaging the goal is not simply the best picture. What is required is a diagnosis, location and identification of a physical property that requires a quantification of uncertainty. This might range from the quantity of oil that can be extracted from a reservoir to the detection of a land mine or threat object in a bag.
The Bayesian approach, specifically sampling schemes that are effective in high dimensional spaces, provides a tool to explore the posterior distribution in the Bayesian formulation of an inverse problem. With fast forward solvers and efficient sampling schemes, together with dimension reduction methods, this is becoming feasible for imaging inverse problems. Calibration problems where the geometry and characteristics of detectors for example are imprecisely known (which is typical in most real problems) can also benefit from a Machine Learning (ML) approach. The programme, organised around the four overlapping themes of
- analysis and geometry;
- numerical analysis;
- optimisation; and
- Bayesian statistics,
aims at stimulating close engagement between mathematicians and statisticians working on inverse problems and instrument scientists, engineers, physicists and image users to focus on the right problems both in the mathematical formulation and the end-user’s requirements. The main objective is to produce step changes in the capabilities of rich and non-linear tomography through application of mathematical sciences to the system design, reconstruction and interpretation of images. By identifying rich and non-linear tomographic methods as a large cluster of emergent techniques and by throwing a spotlight on their mathematical similarities, the programme aims to catalyse rapid development of new tomographic imaging methods. By employing the above mathematical and statistical themes to work across diverse application areas from medical imaging to geophysics, security, defence, materials and non-destructive testing, the programme aims at breaking down the barriers to communication across discipline areas. By bringing together end-users and instrument scientists with mathematical scientists, the programme will encourage the development of shared software platforms reflecting the underlying general structure of the mathematical problems.
By encouraging the sharing of representative data sets, it is also hoped that mathematical scientist can benefit from these when they do not have a direct collaboration with experimental groups. Finally, the programme aims at creating an open and diverse forum of researchers that includes early career researchers, women in science and, more generally, researchers coming from under-represented groups.
Click here to download the programme's final scientific report
Preprints
| Title | Year | Programme | |
|---|---|---|---|
Broken ray transform for twisted geodesics on surfaces with a reflecting obstacleAuthors: Shubham Jathar, Manas Kar, Jesse Railo |
2022 | RNT | 20 September 2023 |
Model-corrected learned primal-dual models for fast limited-view photoacoustic tomographyAuthors: Andreas Hauptmann, Jenni Poimala |
2022 | RNT | 11 April 2023 |
Workshops
Rich and Nonlinear Tomography (RNT) in Radar, Astronomy and Geophysics
30 January 2023 to 3 February 2023
New Mathematical Frontiers for Multi-Dimensional Radar Systems
21 February 2023 to 23 February 2023
Rich and non-linear tomography in medical imaging, materials and non destructive testing
27 March 2023 to 31 March 2023
New tomographic methods using particles
15 May 2023 to 19 May 2023
Seminars
| Wednesday 11th January 2023 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Misha Kilmer Tufts University |
Room 2 | 
|
| Wednesday 18th January 2023 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Bill Lionheart University of Manchester |
Room 2 |
|
| Tuesday 24th January 2023 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Suman Sahoo University of Jyväskylä |
Room 2 | |
| Wednesday 25th January 2023 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Paul Ledger Keele University |
Room 2 | |
| Wednesday 8th February 2023 | |||
|---|---|---|---|
| 15:10 to 16:10 |
Francis Watson University of Manchester |
Room 2 |
|
| Wednesday 15th February 2023 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Chris Wensrich University of Newcastle, Australia |
Room 2 |
|
| Wednesday 1st March 2023 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Jakob Jørgensen Technical University of Denmark; University of Manchester |
Room 2 |
|
| Tuesday 7th March 2023 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Florencia Malamud Paul Scherrer Institut |
Room 2 |
|
| Wednesday 8th March 2023 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Jana de Wiljes Universität Potsdam |
Room 2 |
|
| Monday 20th March 2023 | |||
|---|---|---|---|
| 13:30 to 17:30 |
Jakob Jørgensen Technical University of Denmark; University of Manchester |
Centre for Mathematical Sciences | |
| Tuesday 21st March 2023 | |||
|---|---|---|---|
| 09:00 to 12:30 |
Jakob Jørgensen Technical University of Denmark; University of Manchester |
Centre for Mathematical Sciences | |
| 13:30 to 17:30 |
Jakob Jørgensen Technical University of Denmark; University of Manchester |
Centre for Mathematical Sciences | |
| Wednesday 22nd March 2023 | |||
|---|---|---|---|
| 09:00 to 12:30 |
Jakob Jørgensen Technical University of Denmark; University of Manchester |
Centre for Mathematical Sciences | |
| 13:30 to 17:30 |
Jakob Jørgensen Technical University of Denmark; University of Manchester |
Centre for Mathematical Sciences | |
| Thursday 23rd March 2023 | |||
|---|---|---|---|
| 09:00 to 12:30 |
Jakob Jørgensen Technical University of Denmark; University of Manchester |
Centre for Mathematical Sciences | |
| Tuesday 4th April 2023 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Nick Polydorides University of Edinburgh |
Room 2 | |
| Wednesday 5th April 2023 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Silvia Gazzola University of Bath |
Room 2 | |
| Wednesday 12th April 2023 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Daniel Andre Cranfield University |
Room 2 |
|
| Wednesday 19th April 2023 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Bill Lionheart University of Manchester |
Room 2 |
|
| Wednesday 26th April 2023 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Sean Holman University of Manchester |
Room 2 |
|
| Wednesday 3rd May 2023 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Ben Cox University College London |
Room 2 |
|
| Thursday 4th May 2023 | |||
|---|---|---|---|
| 15:15 to 16:15 |
Victoria Nockles The Alan Turing Institute; Defence Science and Technology Laboratory |
Room 2 | |
| Thursday 11th May 2023 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Peter Kuchment Texas A&M University |
Room 1 |
|
| Tuesday 23rd May 2023 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Simon Hubmer Austrian Academy of Sciences |
Room 2 |
|
| Wednesday 24th May 2023 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Anna Polyakova Sobolev Institute of Mathematics; Novosibirsk State University |
Room 2 |
|
| Thursday 25th May 2023 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Andy Adler Carleton University |
Room 2 |
|
| Friday 26th May 2023 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Venky Krishnan Tata Institute of Fundamental Research |
Room 2 |
|
| Friday 2nd June 2023 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Misha Kilmer Tufts University |
Room 1 |
|
| Wednesday 7th June 2023 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Ivan Svetov Sobolev Institute of Mathematics; Novosibirsk State University |
Room 2 |
|
| Tuesday 13th June 2023 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Stephen Hobbs Cranfield University |
Room 2 |
|
| Wednesday 14th June 2023 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Andrea Arnold Worcester Polytechnic Institute |
Room 2 |
|
| Wednesday 28th June 2023 | |||
|---|---|---|---|
| 15:00 to 17:00 |
Shari Moskow Drexel University |
Room 2 |
|
| Thursday 29th June 2023 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Francis Watson University of Manchester |
Room 2 | |
Organisers
- Marta Betcke University College London
- Romina Gaburro University of Limerick
- Silvia Gazzola University of Bath
- Sean Holman University of Manchester
- Paul Ledger Keele University
- Bill Lionheart University of Manchester
- Tanja Tarvainen University of Eastern Finland
- Francis Watson University of Manchester
Speakers
- Andy Adler Carleton University
- Daniel Andre Cranfield University
- Andrea Arnold Worcester Polytechnic Institute
- Ben Cox University College London
- Jana de Wiljes Universität Potsdam
- Silvia Gazzola University of Bath
- Stephen Hobbs Cranfield University
- Sean Holman University of Manchester
- Simon Hubmer Austrian Academy of Sciences
- Jakob Jørgensen Technical University of Denmark; University of Manchester
- Misha Kilmer Tufts University
- Venky Krishnan Tata Institute of Fundamental Research
- Peter Kuchment Texas A&M University
- Paul Ledger Keele University
- Bill Lionheart University of Manchester
- Florencia Malamud Paul Scherrer Institut
- Shari Moskow Drexel University
- Victoria Nockles The Alan Turing Institute
- Anna Polyakova Sobolev Institute of Mathematics; Novosibirsk State University
- Nick Polydorides University of Edinburgh
- Suman Sahoo University of Jyväskylä
- Ivan Svetov Sobolev Institute of Mathematics; Novosibirsk State University
- Francis Watson University of Manchester
- Chris Wensrich University of Newcastle, Australia
Participants
- Andy Adler Carleton University
- Amal Alghamdi Technical University of Denmark
- Rehman Ali University of Rochester
- Daniel Andre Cranfield University
- Simon Arridge University College London
- Marta Betcke University College London
- Ander Biguri University of Cambridge
- Liliana Borcea University of Michigan
- Tatiana Alessandra Bubba University of Bath
- Luca Calatroni CNRS (Centre national de la recherche scientifique)
- Daniela Calvetti Case Western Reserve University
- Miguel Carcamo Universidad de Santiago de Chile
- Margaret Cheney Colorado State University
- Julianne Chung Emory University
- Matias Courdurier Pontificia Universidad Católica de Chile
- Ben Cox University College London
- Evelyn Cueva Escuela Politécnica Nacional de Quito
- Jana de Wiljes Universität Potsdam
- Naeem Desai Defence Science and Technology Laboratory; University of Manchester
- Yiqiu Dong Technical University of Denmark
- Niall Donlon University of Limerick
- Vladimir Druskin Worcester Polytechnic Institute
- Nebojsa Duric University of Rochester
- James Elgy Keele University
- Florian Faucher INRIA Bordeaux - Sud-Ouest
- Romina Gaburro University of Limerick
- Silvia Gazzola University of Bath
- Holly George-Samuels University of Manchester; QinetiQ
- Sarah Hamilton Marquette University
- Andreas Hauptmann University of Oulu; University College London
- Joshua Hellier Defence Science and Technology Laboratory
- Sean Holman University of Manchester
- Simon Hubmer Austrian Academy of Sciences
- Victoria Hutterer Johannes Kepler Universität
- Alexei Iantchenko Malmö University
- Shubham Jathar Indian Institute of Science Education and Research (IISER)
- Jakob Jørgensen Technical University of Denmark; University of Manchester
- Misha Kilmer Tufts University
- Kim Knudsen Technical University of Denmark
- Alexander Korsunsky University of Oxford; European Synchrotron Radiation Facility ESRF
- Venky Krishnan Tata Institute of Fundamental Research
- Peter Kuchment Texas A&M University
- Leonid Kunyansky University of Arizona
- Kody Law University of Manchester
- Paul Ledger Keele University
- Daniel Lesnic University of Leeds
- Bill Lionheart University of Manchester
- Florencia Malamud Paul Scherrer Institut
- Marco Marletta Cardiff University
- Marco Martorella University of Birmingham
- David McMahon University of Limerick
- Sayed Miah Keele University
- Shari Moskow Drexel University
- Victoria Nockles The Alan Turing Institute
- Clifford Nolan University of Limerick
- Roman Novikov CNRS & École polytechnique; Russian Academy of Sciences
- Xiaochuan Pan University of Chicago
- Vaggelis Papoutsellis UKRI
- Mirjeta Pasha Tufts University
- Anna Polyakova Sobolev Institute of Mathematics; Novosibirsk State University
- Nick Polydorides University of Edinburgh
- Clarice Poon University of Bath
- Todd Quinto Tufts University
- Jesse Railo University of Cambridge
- Ronny Ramlau Johannes Kepler Universität; Austrian Academy of Sciences
- Rosemary Renaut Arizona State University
- Audrey Repetti Heriot-Watt University
- Andreas Rieder Karlsruhe Institute of Technology (KIT)
- Malena Sabaté Landman Emory University
- Suman Sahoo University of Jyväskylä
- Mikko Salo University of Jyväskylä
- Søren Schmidt European Spallation Source ERIC
- Carola-Bibiane Schönlieb University of Cambridge; Cambridge Mathematics of Information in Healthcare
- Ekaterina Sherina University of Vienna
- Samuli Siltanen University of Helsinki
- Manuch Soleimani University of Bath
- Ivan Svetov Sobolev Institute of Mathematics; Novosibirsk State University
- Katy Tant University of Strathclyde
- Tanja Tarvainen University of Eastern Finland
- Tristan van Leeuwen Centrum voor Wiskunde en Informatica (CWI); Universiteit Utrecht
- Francis Watson University of Manchester
- Chris Wensrich University of Newcastle, Australia
- Mikhail Zaslavskiy Southern Methodist University
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