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Inverse Problems - follow-up meeting


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10th February 2014 to 14th February 2014

Organisers: Malcolm Brown (Cardiff), Thanasis Fokas (Cambridge), Yaroslav Kurylev (UCL), Bill Lionheart (Manchester), William Symes (Rice) and Adrian Nachman (Toronto)

Workshop Theme

The 2011 programme included two highly successful workshops Analytic and Geometric Methods in Medical Imaging and Inverse Problems in Science and Engineering. In this Follow-up Meeting we propose to focus on recent developments in the mathematical problems associated with, and generated by, these workshops.

In the two yeas since the end of the programme there has been much progress in these areas. Representative examples include:

  • Breakthrough on the local X-ray transform by Uhlmann and Vasy
  • Important work of Singer and Wu on 2-D tomography from noisy projections taken at unknown random directions
  • Recovery of SPECT images from minimal data

A particularly important and advancing area in the medical imaging of tissue is the use of hybrid imaging. These methods combine high-contrast imaging methods, such as those found in Electrical Impedance Tomography or Optical Tomography, with high-resolution methods such as magnetic resonance imaging or ultrasound.

A new Diffusion Tensor Current Density Imaging method (Hoell, Moradifam and Nachman) addressees a problem that arrises in Current Density Impedance Imaging while the recent theoretical work of Guillaume Bal, Chenxi Guo and Francois Monard provides a way of improving the image from the ill-posed problem.

In Image Analysis, recent progress has been made on fast MRI using Matrix Completion and new Algorithms, to quantify the geometric similarity of anatomical surfaces which do not require the marking of special features or landmarks by the user.

In the area of Industrial Seismology, the seismic inverse problem is now central to major commercial efforts, while remaining a source of very difficult computational and mathematical problems. There is ongoing work to quantify the need for very low frequency data acquisition, the possibility of effective quality control, and the very difficult problems associated with shallow geological waveguides which are prevalent in some parts of the world. Developments in this area include de Hoop's Banach space analysis of the basic inverse problem, and Plessix's techniques for estimating more than one mechanical parameter as function of position along with reliability measures. These topics will continue to grow in sophistication and economic importance in the next few years.

Another area of remote geophysical sensing in which progress has been made is landmine detection and security screening. Especially noteworthy are recent work by Ammari, Volkov, and Kang, and the initiative by the Bobby Charlton Charity to develop new landmine detection equipment.

These and related problems will form the basis of the meeting.

Participation is by invitation only.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons