Significant progress has been made in recent years in the ability to perform advanced 3D X-ray imaging for scientific, industrial and medical applications. To obtain high quality images, complex experimental equipment must be combined with advanced algorithms for processing the data obtained using the instruments. The main goal of this Lorentz Workshop was to bring together active researchers from the experimental and computational communities involved in 3D X-ray imaging (= tomography) to provide an updated view on the state-of-the-art in the respective fields and to setup a roadmap for a joint research effort that combines state-of-the-art X-ray imaging abilities with tailored algorithm development for these techniques.

The workshop brought together around 60 participants from different communities (mathematical, computational, experimental) involved in tomography. The participants were very eager to interact and learn, resulting in a very active group. Three discussion groups on selected topics developed in different ways during the week:

- The in-vivo Phase Contrast tomography group identified several small groups of participants where solutions from one side could be matched to concrete problems from the other side, laying the basis for further joint research. Setting up specific examples of the potential of new algorithms on experimental datasets is considered as the first step to the adoption of such new methods.

- The 4D imaging group laid a foundation for making problems and datasets available to the broader community, and also matched skills and expertise from various participants.

- The fluorescence tomography group spent considerable effort in discussing the problem/model that should be solved. After several days of intensive discussion, consensus was reached and plans were made for a joint effort including experiment and computation.

A particular successful item in the program was the speeddating session, where participants were teamed up in pairs for 3-minute discussions. Although no one knew what to expect, it was highly valued by most participants as a good means of creating new contacts.

As a platform for shaping the newly formed collaborations, several web repositories were set up for the different topics treated during the workshop, which can be found at

https://confluence.aps.anl.gov/display/XSD4DIC/Home

https://confluence.aps.anl.gov/display/XSDIVPCI/Home

https://confluence.aps.anl.gov/display/XSDXFT/Home

This workshop was partially funded by the EU EXTREMA COST Action, a network grant for advanced tomography. As a result of this Lorentz Workshop, five short term exchanges of participating PhD students (visiting a foreign institute for collaborative research) have already been carried out in the months following the workshop.

The discussions on the roadmap have resulted in a concrete plan to have a follow-up workshop at the European Synchrotron (ESRF) in Grenoble, which will take place in December 2014. This will include simultaneous availability of four experimental beamlines and a large computing cluster, creating a unique experimental/computational event.

One important conclusion of the discussions during this workshop was the fact that the mismatch between the experiments and the available physics models is often a major obstacle for making advanced algorithms work well in practice. To deal with these challenges, various new aspects and communities should be involved in the discussion, which could be a very interesting topic for a future Lorentz Workshop, following a similar format.

Overall, the workshop was received in a very positive way. Some (even senior!) participants described it as the best workshop they had attended in many years. We expect that in the coming year, several publications will emerge from the collaborations initiated at this Lorentz Workshop.