Inverse Problems and Imaging Seminars
material
1st Semester, 2013/14

9th
December
2013 Characterising the shape and material properties of hidden targets from magnetic induction data
Dr Paul Ledger (Swansea University)
Time 4:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractThis talk will review some recent developments that confirm the engineering prediction of H^T . ( M H^M) for the sensitivity of measurements of the perturbed magnetic field to the presence of a general conducting object placed in a low frequency background field is correct. Explicitly, H^T is the background field generated by the transmitter coil, H^M is the background field generated by the receiving coil as if it was used as a transmitter and M is rank 2 polarization or polarizability tensor that describes the shape and material properties of the object. We will discuss how a recently derived asymptotic formula for the perturbed magnetic field due to the presence of a conducting object that involves a rank 4 tensor does in fact reduce to a formula involving a complex symmetric rank 2 tensor with at most 6 independent coefficients. For objects with rotational or reflectional symmetries the number of independent coefficients is still smaller. The talk will also show how the new tensors for different objects can be accurately computed by solving a vector valued transmission problem by hpversion finite elements. The ability to compute these tensors for different objects holds great promise for applications that involve the location and characterisation of conducting objects such as landmine detection, ensuring food safety and security screening.

2nd
December
2013 Tensor tomography of Strain
Bill Lionheart (School of Mathematics, University of Manchester)
Time 4:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractWe have been working for many years on measuring stress and strain with polarized light which results in the inverse problem for the Truncated Transverse Ray Transform. Recently however we have been considering the measurement of strain using xray diffraction and this results in the Transverse Ray Transform. I will explain how this arises in the physical problem and how the explicit inverse might be used with limited data. The classical Pascal's theorem in projective geometry will make a guest appearance. I will go on to explain a filtered back projection inversion for the complete data Transverse Ray Transform, including a intriguing bit of abstract algebra. I will conclude with a proof that "Bragg Edge Tomography" cannot determine strain.

18th
November
2013 Uniqueness results for the inverse conductivity problem
Michael Crabb (School of Mathematics, University of Manchester)
Time 4:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractSome uniqueness results for the inverse conductivity problem will be discussed. I will describe how complex geometric optics (CGO) solutions were used in the 1980s to prove uniqueness of solution for the complete data problem in three or more dimensions. I will briefly discuss how these methods have been extended to tackle some partial data problems, as well as some recent developments for the local partial data problem that are most relevant in practical applications.

11th
November
2013 Characterization of objects by weakly electric fish through the first order polarization tensor
Taufiq Ahmad Khairrudin (School of Mathematics, University of Manchester)
Time 4:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractAccording to previous studies by Ammari (2007) and Nelson (2009), electrosensing by a weakly electric fish has some similarities with the electrical impedance tomography (EIT) system. Because of this we adapted the polarization tensor from EIT into the electrosensing context. Our aim is to investigate object characterization by the fish through the first order polarization tensor without actually reconstructing an image of the object. In this talk, I will discuss the mathematical background of the polarization tensor in electrosensing. After that, some examples of object characterization through the tensor by the fish will be given.

4th
November
2013 GPU accelerated algebraic iterative reconstruction for cone beam xray micro CT
Will Thompson (School of Mathematics, University of Manchester)
Time 4:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractCone beam xray micro CT is a technique for imaging objects from their xray projections, using a single xray source and a flat panel detector. Wellknown analytical methods exist for reconstruction, but these perform poorly under less than ideal data acquisition conditions, such as limited numbers of projections or reduced exposure time. Algebraic iterative reconstruction methods offer the potential for much better image quality under such conditions, but are generally considered unfeasible for reconstruction of real data sets due to their high computational demands. The talk will discuss a new algorithm for calculating the key discrete forward and back projection steps, and its efficient implementation on GPU.

28st
October
2013 Katsevich Reconstruction for Helical Scan CT
Henry Tregidgo (School of Mathematics, University of Manchester)
Time 4:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractTwo major considerations in Xray Computed Tomography are the required acquisition time and Xray dose for the scans. In helical scan CT, scans are taken by moving source and detector in one continuous helix relative to the object rather than taking several separate circular scans. This not only reduces the acquisition time and dosage, but also allows faster processes to be captured and artefacts to be reduced at large cone angles. One theoretically exact reconstruction method for helical cone beam microCT is the Katsevich reconstruction algorithm. In this paper we look at two implementations of the derivatives required for the Katsevich reconstruction algorithm on flat detectors, both the original implementation suggested by Noo and a formulation proposed by Katsevich.

21st
October
2013 Combining xray scatter and tomographic information: A collaboration with Rapiscan Systems Ltd and the Home Office.
Nicola Wadeson (School of Mathematics, University of Manchester)
Time 4:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractRapiscan System's Real Time Tomography (RTT) xray cone beam CT machine used in airport security records a high level of scattered photons due to an unconventional geometry. Here we discuss the effects and possible uses of the scattered signal, followed by a description of the Geant4 Monte Carlo simulation used to emulate the system and the proposed scatter correction methods.

15th
March
2012 Adjoint Techniques in Optical Tomography
Kernel Prieto (School of Mathematics, University of Manchester)
Time 2:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstract 
8th
March
2012 Level Set Methods for Inverse Scattering (II): Shape evolution by level set functions.
Oliver Dorn (School of Mathematics, University of Manchester)
Time 2:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractI plan to continue the discussion from last week's seminar and present more details on how to choose level set functions and how to evolve these in order to solve shape reconstruction problems.

1st
March
2012 Level Set Methods for Inverse Scattering (I): Shape representation by level set functions.
Oliver Dorn (School of Mathematics, University of Manchester)
Time 2:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractI will give a brief and very informal introduction in the use of level set functions for inverse scattering and image reconstruction. The 'classical level set representation of shapes' is presented and motivated this week which has been used intensively in the literature for different shape evolutions problems, such as shape reconstruction, shape optimization and image segmentation applications. This is the first of a few talks which I plan to present on this topic based on interest and feedback of the audience. These talks are in a completely 'ad hoc' style presented mainly at the blackboard.

23rd
February
2012 The generalised Radon transform on ellipses: strain measurement and seismic imaging
Bill Lionheart (School of Mathematics, University of Manchester)
Time 2:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractThe Radon transform can be generalized to the integral on families of curves  often called the FunkRadon transform. Integrals over families of ellipses arise in two dimensional seismic reflection imaging (and similar techniques such as ground penetrating radar) where the wave speed is assumed constant. The extraction of strain measurements from diffraction patterns of polycrystaline materials also involves the ellipse Radon transform. We shall consider cases in which an explicit inversion formula is available as well as a PDE that characterizes the range.

3rd
Nov
2011 Permeability estimation using twophase flow equations and 4D seismics
Salomao Chissonde, CEAS and SEAES, University of Manchester
Time 2:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractIn this work the equations of fluid flow in porous media are used in combination with timelapse changes in pressure and saturation and 4D seismic results for estimating the absolute permeability in reservoirs. The derived fluid flow differential equations are discretized and solved using Matlab, additional parameters such as mobility, and fractional flow are also considered. This work integrates different disciplines, mathematics, computer programming, geophysics and reservoir engineering. These together serve as tools to predict reservoir performance and to optimize the hydrocarbon recovery and field profit by reducing the uncertainty and by generating updated integrated models.

27nd
Oct
2011 On seismic travel times, Xrays and magic squares
Oliver Dorn (School of Mathematics, University of Manchester)
Time 2:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractIn the seminar, I will give an example of an inverse problem which occurs in three different applications where it asks for three different solutions!

6th
Oct
2011 Factorization method in Electrical Impedance Tomography
Russel Miller (School of Mathematics)
Time 2:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractTBA

29th
Sept
2011 We will try to arrange for a Live Video Broadcast of the External Event: Inverse Problems Seminar at Newton Institute, Cambridge. (Gunther Uhlmann, University of Irvine, will talk about 'Cloaking: Science meets Science Fiction').
Time 5:00pm, Frank Adam Room 2, School of Mathematics, Alan Turing BuildingAbstractCloaking: science meets science fiction
Uhlmann, G (Washington)
Thursday 29 September 2011, 17:0018:00
Seminar Room 1, Newton Institute, Cambridge
Abstract
We describe recent theoretical and experimental progress on making objects invisible to detection by electromagnetic waves, acoustic waves and quantum waves. We emphasize the method of transformation optics. For the case of electromagnetic waves, Maxwell's equations have transformation laws that allow for design of electromagnetic materials that steer light around a hidden region, returning it to its original path on the far side. Not only would observers be unaware of the contents of the hidden region, they would not even be aware that something was being hidden. The object, which would have no shadow, is said to be cloaked. We recount some of the history of the subject and discuss some of the issues involved. 
22nd
Sept
2011 The Sensitivity in Electrical Impedance Tomography
Michael Crabb (School of Mathematics)
Time 2:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractTBA

27th
May
2010 High Performance Visualizing (and tightly coupling high performance reconstruction) for the Next Generation of 3D volumes
Martin Turner and George Leaver
Time 2:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractThe EPSRC funded "Multiscale xray imaging facility for monitoring and modelling structural evolution in situ" project has created the multiscale from macro to nano Henry Moseley XRay Imaging Facility, launched in June 2009. A multitude of different objects have been scanned creating new insights across the faculties. To build the next generation of visualization system Research Computing have looked at bids from IBM, HP and Dell. "These three bids represent three creative ways to construct the next generation of tightly connected HPC and HPV over highly interconnected datasets for the $ 4K^3 $ models required." We will present hardware options and software available for developing and building this system and ask for use cases from researchers to help them exploit their algorithms to the next stage. Details will be given of the preproject that has just completed with the development of a scalable visualization package built on the UK National supercomputing facility run by NAG, a CRAY XT5 (www.hector.ac.uk).

20th
May
2010 xtremeEnd Remote Scientific Visualization ShowandTell
External event, see abstract.
Time 2:004:00pm, Kilburn Building, Room 1:10.AbstractNo Inverse Problems and Imaging seminar in the Alan Turing Bldg this day. Instead: Invitation to participate in the related workshop/showandtell event with company AVS Europe organized by M. Turner in the Kilburn Bldg.
Abstract for that event: With the company AVS Europe we will present and discuss recent work including: CRAY HECToR integration of remote visualization, ParaFEMViewer, Erasmus funded Unstructured Volume rendering, and EU IP training and reports back from AVS user group in Switzerland and AVS in the CS Advanced MSc course. 
29th
April
2010 MultiSheet Rebinning Methods for Real Time Tomography
Marta Betcke (University College London)
Time 2:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractThe high speed of data acquisition in the new cone beam scanners, like Rapiscan RTT, is achieved through using a stationary ring of sources, which replaces the slowly rotating gantry. To accommodate the stationary ring of sources in the design, it was necessary to divert from the 4th generation CT geometry. The resulting new geometry requires new different reconstruction algorithms than those devised for the standard cone beam CT. In this talk I present a novel type of rebinning methods for the RTT scanner geometry. The new methods generalise the idea of rebinning to a single surface to rebinning to multiple surfaces and provide a family of provably optimal methods. The multisheet surface is a natural fit for the RTT scanner geometry. The new methods utilise this property along with the linearity of the Radon transform to reconstruct superimposed images on the multisheet surface, which are subsequently deconvolved in the axial direction through solving of a series of small systems of equations for each transaxial pixel independently, therewith constituting a highly parallelisable and efficient method. I will discuss a simplified variant of the multisheet method, which can be implemented in a more efficient way while its performance remains very close to the optimal method. Finally, I will show performance of the twosheet rebinning method on the RTT80 data.

22nd
April
2010 CO2 injection and characterization of compartmentalized reservoirs
Rossmary Villegas (School of Chemical Engineering, University of Manchester)
Time 2:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractOne popular technique for enhanced oil recovery is to inject CO2 through injection wells into an active reservoir in order to enhance hydrocarbon production rates at the production wells. During this process, it is important to simulate and monitor the gas or fluid flow in the reservoir from the available data. We present a new approach for the simulation of such CO2 injection processes. This approach is in particular useful in those cases where channels of certain rock types are present in the reservoir. Our algorithm is able to reconstruct complicated channels and the corresponding permeability distributions simultaneously from production and CO2 injection data. For the characterization we use a compositional model which takes into account the interaction between the injected CO2 and the gas or fluid in the reservoir. Also the incorporation of additional 4D seismic data is discussed. In the shape reconstruction approach, an implicit representation of the shapes (channels) by a level set technique is used in order to be able to incorporate interfaces in the model. Numerical results are presented which demonstrate the performance and main concepts of this algorithm.

18th March
2010 Scatter in an uncollimated xray CT machine based on a Geant4 Monte Carlo simulation
Nicola Wadeson (University of Manchester)
Time 2:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractA highspeed motionlessgantry xray CT machine has been developed by Rapiscan Systems Ltd. to eliminate mechanical rotation, allowing for 3D images to be collected in real time. The nature of the design limits the possibility of detector collimation which has implications in the reconstructed image due to scattered photons. A Monte Carlo computer simulation of the xray machine has been developed, using the Geant4 software toolkit, to analyse the behaviour of both Rayleigh and Compton scattered photons. An overview of the system and the simulation will be presented along with results obtained for typical airport baggage and medical applications.

11th March
2010 Passive mmwave/THz radiometric imaging and inverse problems in electronic beamforming
Neil Salmon (QinetiQ)
Time 2:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractPassive millimetre wave (20 to 300 GHz) and THz (0.1 THz to 30 THz) imaging radiometry offers capabilities for realtime all weather imaging, personnel security screening and remote atmospheric sounding. Examples of imagery to demonstrate these capabilities will be presented together with the fundamentals of radiometry. However, the deployment scenarios for these applications require the use of planar geometry electronic beamforming technology, as conventional quasioptical systems are too bulky and heavy. Fortunately, recent advances in electronic technology mean this architecture of imager can now be realised and collaborative work with QinetiQ in the Alan Turing building of the Physics and Astronomy department now sets out to demonstrate this experimentally. This shift in technology brings new requirements for algorithm innovation to create images from directly sampled and correlated radiometric electric fields from aperture arrays. Some basics of how this inversion problem is currently viewed will be presented.

4th
March
2010 Can Fritz John help with Laminography?
Bill Lionheart (School of Mathematics)
Time 2:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractIn 1939 Fritz John wrote an influential paper that set the scene for 3D xray CT and drew the attention of the world to Radon's earlier work. In this paper he shows how the integrals of a function over lines satisfy a partial differential equation (John's equation) and hence how if data is known on some sets of lines it can be deduced for a larger set by solving a boundary value problem. This paper deserves to be revisited. In problems such as laminography where a thin sheet is xrayed from limited range of directions and other limited data problems the paper certainly shows that some data sets are nonredundant. I expect this has implication to a range of limited data problems, for example tomography using a transmission electron microscope and who knows perhaps astronomy or other problems.That is where the audience participation comes in. The talk will only use advanced calculus so should be reasonably accessible.

25th February
2010 Early breast cancer detection using microwaves and a level set inversion strategy
Oliver Dorn (School of Mathematics)
Time 2:00pm, Frank Adams Room 1, School of Mathematics, Alan Turing BuildingAbstractDuring recent years, the use of microwaves has been discussed as a tool for the early detection of breast cancer. The gold standard for breast screening is still mammography, even though it suffers from wellknown limitations: lack of sensitivity (it misses up to 15% of tumors), low specificity (it gives rise to a large amount of false positive readings), and the exposure to potentially dangerous radiation. The use of microwaves as a complementary screening tool might help to avoid or improve some of these limitations. However, even though antenna development for this new technology has been advancing well, and several prototypes have been built worldwide, the development of efficient inversion algorithms for reliably extracting the desired information from the gathered microwave data has not kept pace. Major difficulties are the potentially low contrast in electromagnetic parameters between a malignant or benign tumor and the surrounding fibroglandular tissue in a dense breast, and the comparatively long wavelength of microwaves which both challenge the mathematical tools which are employed for the inversion. In the talk, we will present a recently developed structural inversion technique which makes use of a level set representation of shapes for estimating simultaneously the main structure of the complex breast and giving information regarding the existence, location and size of a hidden tumour from microwave data. Numerical experiments in 2D are presented which show that this technique is able to provide stable reconstructions for realistic breast phantoms (based on MRI images) from simulated 2D data. Some criteria are given on size and characteristics of a hidden tumour to be reliably detected by this technique. This is joint work with N. Irishina, M. Moscoso and D. Alvarez, Universidad Carlos III de Madrid, Spain.

2006  2008

29Lab based Xray Nanotomography system for non invasive multiscale imaging from composite materials to biological samples with resolution from mm to sub 50 nm
Apr
2008
S. H . Lau, Xradia Inc
3  4pm, D13 Material Science Centre

28Inverse problems in Positron Emission Tomography
Apr
2008
Julian Matthews
2  3pm, Frank Adams 1, Alan Turing Building

20The development of Tomographic Energy Dispersive Diffraction Imaging
Mar
2008
Bob Cernik
10  11am, Frank Adams 2, Alan Turing Building

23Dissecting Dinosaurs
Nov
2007
Phil Manning
11  12pm, Frank Adams 1, Alan Turing Building

23Intreatment Xray Conebeam Tomography for Guiding Radiotherapy: Developments at the Christie Hospital
Oct
2007
Chris Moore and Tom Marchant
3  4pm, Frank Adams 2, Alan Turing Building

10Ultrafast tomography using offtheshelf graphics cards
Sept
2007
Guillem Pratx
3:304:30 pm, Frank Adams room 1, Alan Turing Building

12Truncated Projections and RegionofInterest Reconstruction in Classical XRay Computed Tomography
June
2007
Rolf Clackdoyle
1:452:45 pm, M12, MSS Building
This forum will be part of a British Inverse Problems Society one day meeting on "Challenges in tomography: Medical Imaging, Material Science and Airport Security". More informationAbstract ( click to view)In computed tomography, an xray projection is truncated if the detector is not large enough to capture the image of the sample being scanned. In certain cases it is possible to accurately reconstruct a subset of the sample (a regionofinterest) even if some of the projections are truncated. The current understanding of regionofinterest reconstruction will be presented.

20Hough transform for severely limited data in industrial tomography
March
2007
Eugenio P. A. Constantino
2  3 pm, M12, MSS Building.

12Image analysis for computerised tomography
Feb
2007
Dan Öberg
2  3 pm, M12, MSS Building.

8Nanotomography and diffraction contrast tomography at the European synchrotron
Nov
2006
Greg Johnson
1  2 pm, M12, MSS Building.

20New Dynamic (4D) Image Reconstruction Methods for Positron Emission Tomography
Sep
2006
Andrew Reader
2  3pm, O10, MSS Building