The inverse source problem arising in Photoacoustic Tomography
Lead Research Organisation:
University College London
Department Name: Mathematics
Abstract
The project addresses fundamental analytical questions on the acoustic wave
equation. The questions arise in, but are not limited to the context of
Photoacoustic Tomography (PAT).
PAT is a medical imaging technique that combines the high contrast in
electromagnetic absorption, say between healthy and cancerous tissue, with the
high resolution of ultrasound. The existing PAT image reconstruction methods
based on time-reversal arguments do not work when photoacoustic measurements
are obtained by using an array of detectors that reflects acoustic waves.
However, the use of detector arrays significantly speeds up the data
acquisition in practice. One of the main objectives of the project is to
develop a comprehensive analytical theory for PAT in a reflecting cavity
formed by detector arrays.
The mathematical results to be obtained have applications beyond PAT in the
fields of Control Theory for Partial Differential Equations and Inverse
Problems. These applications will be explored. In particular, the results
allow us to understand better the stability properties of hyperbolic inverse
boundary value problems. These problems occur in a large number of
applications including medical ultrasound tomography, seismology, oceanology,
process monitoring and non-destructive testing. In terms of these
applications, our focus is on seismic imaging.
equation. The questions arise in, but are not limited to the context of
Photoacoustic Tomography (PAT).
PAT is a medical imaging technique that combines the high contrast in
electromagnetic absorption, say between healthy and cancerous tissue, with the
high resolution of ultrasound. The existing PAT image reconstruction methods
based on time-reversal arguments do not work when photoacoustic measurements
are obtained by using an array of detectors that reflects acoustic waves.
However, the use of detector arrays significantly speeds up the data
acquisition in practice. One of the main objectives of the project is to
develop a comprehensive analytical theory for PAT in a reflecting cavity
formed by detector arrays.
The mathematical results to be obtained have applications beyond PAT in the
fields of Control Theory for Partial Differential Equations and Inverse
Problems. These applications will be explored. In particular, the results
allow us to understand better the stability properties of hyperbolic inverse
boundary value problems. These problems occur in a large number of
applications including medical ultrasound tomography, seismology, oceanology,
process monitoring and non-destructive testing. In terms of these
applications, our focus is on seismic imaging.
Planned Impact
The analytical theory for Photoacoustic Tomography (PAT) in a reflecting
cavity to be developed will immediately benefit the practitioners of this
imaging technique. Collaboration with the experimentalists in the
Photoacoustic Imaging Group in the Department of Medical Physics and
Bioengineering at University College London (UCL) guarantees that the results
of the project will directly improve the use of PAT in clinical and
preclinical imaging. Via this pathway, the results will translate, for example,
to the UCL Centre for Advanced Biomedical Imaging, which has a small animal
PAT scanner that is used in a variety of in vivo preclinical imaging studies.
We will prove new stability results on the hyperbolic inverse boundary value
problems. The mathematical theory of these problems has not been applied to
real-life measurements. However, motivated by the increased computational
power, there is an emerging interest in the theory in the field of seismic
imaging. Collaboration with the Geo- Mathematical Imaging Group at Purdue
University offers a pathway for the results to disseminate to the
practitioners of seismic imaging.
cavity to be developed will immediately benefit the practitioners of this
imaging technique. Collaboration with the experimentalists in the
Photoacoustic Imaging Group in the Department of Medical Physics and
Bioengineering at University College London (UCL) guarantees that the results
of the project will directly improve the use of PAT in clinical and
preclinical imaging. Via this pathway, the results will translate, for example,
to the UCL Centre for Advanced Biomedical Imaging, which has a small animal
PAT scanner that is used in a variety of in vivo preclinical imaging studies.
We will prove new stability results on the hyperbolic inverse boundary value
problems. The mathematical theory of these problems has not been applied to
real-life measurements. However, motivated by the increased computational
power, there is an emerging interest in the theory in the field of seismic
imaging. Collaboration with the Geo- Mathematical Imaging Group at Purdue
University offers a pathway for the results to disseminate to the
practitioners of seismic imaging.
Organisations
People |
ORCID iD |
Lauri Oksanen (Principal Investigator) |
Publications
Burman E
(2020)
A Fully Discrete Numerical Control Method for the Wave Equation
in SIAM Journal on Control and Optimization
Burman E
(2019)
A fully discrete numerical control method for the wave equation
De Hoop M
(2018)
An Exact Redatuming Procedure for the Inverse Boundary Value Problem for the Wave Equation
in SIAM Journal on Applied Mathematics
Helin T
(2016)
Correlation based passive imaging with a white noise source
Helin T
(2018)
Correlation based passive imaging with a white noise source
in Journal de Mathématiques Pures et Appliquées
Burman E
(2018)
Data assimilation for the heat equation using stabilized finite element methods.
in Numerische mathematik
Lassas M
(2015)
Determination of the spacetime from local time measurements
in Mathematische Annalen
Lassas M
(2014)
Determination of the Spacetime from Local Time Measurements
Description | We have developed a new algorithm for photoacoustic tomography reconstructions that applies to the measurement configuration used by the experimental group at the biomedical imaging department at UCL. The new reconstruction method that is guaranteed to converge at an exponential rate, for example, when the data is gathered using three array detectors forming a corner. |
Exploitation Route | We plan to help the biomedical imaging group at UCL to implement the algorithm in practice. |
Sectors | Healthcare |
URL | https://doi.org/10.1088/0266-5611/32/12/125004 |
Description | EPSRC fellowship |
Amount | £629,463 (GBP) |
Funding ID | EP/P01593X/1 |
Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
Sector | Public |
Country | United Kingdom |
Start | 03/2017 |
End | 02/2022 |
Description | Inverse Problems, Imaging and PDEs at HKUST Institute for Advanced Study |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Other audiences |
Results and Impact | Talk at a scientific conference |
Year(s) Of Engagement Activity | 2016 |
Description | Meeting for Young Mathematicians in Finland |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Postgraduate students |
Results and Impact | A networking event for PhD students, recent postdocs and master students close to graduation. The aim was to allow networking of young researchers among themselves and with top figures in the academic as well as the industrial worlds. |
Year(s) Of Engagement Activity | 2015 |
Description | Simons MATH+X symposium on Seismology and Inverse Problems |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Other audiences |
Results and Impact | Workshop for seismologists, mathematicians and computer scientists presenting the state of the art and emerging directions of research on the one hand and expose key challenges on the other hand, with the goal of bridging seismology, the analysis of inverse problems and machine learning, and data from ever-expanding, modern networks. |
Year(s) Of Engagement Activity | 2017 |
Description | Summer Preschool on Inverse Problems |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Postgraduate students |
Results and Impact | I gave lectures in a summer school on inverse problems. |
Year(s) Of Engagement Activity | 2015 |
Description | Talk at Applied Inverse Problem conference |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Professional Practitioners |
Results and Impact | Scientific conference, gave a talk on my research related to microlocal analysis of ray transforms in Lorentzian geometry. |
Year(s) Of Engagement Activity | 2015 |
Description | Talk at Poincare institute |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Professional Practitioners |
Results and Impact | Scientific conference, gave a talk on my research related to microlocal analysis of ray transforms in Lorentzian geometry. |
Year(s) Of Engagement Activity | 2015 |
Description | Workshop on Carleman estimates, unique continuation and applications |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Other audiences |
Results and Impact | I organized a scientific workshop at UCL |
Year(s) Of Engagement Activity | 2016 |
URL | https://sites.google.com/site/carlemanuniquecontinuation/ |