Image Reconstruction: the Sparse Way

The ability to image the inside of an object is one of the driving forces of scientific progress. Applications occur in almost all areas of science and engineering, including the whole of medical imaging, non-destructive testing, geophysics and material science. In industry imaging is frequently employed for process monitoring and quality assurance. A further important application is security monitoring like for instance airport luggage screening.Medical imaging is the application which affects the general public the most. In medicine a wide range of imaging modalities is used to assist the diagnosis. Commonly used techniques include Magnetic Resonance Imaging (MRI) and X-ray Computed Tomography (CT). Unfortunately, even using state-of-the-art imaging equipment these procedures can be either very time consuming, as in the case of an MRI scan or the patient is exposed to ionising radiation which is potentially harmful, like in CT. Both procedures would greatly benefit from reducing the number of measurements, which are necessary to reconstruct the image without compromising its diagnostic value. This almost sounds like a lost cause but it turns out it is not!Think about compression algorithms such as JPEG, which allow to significantly reduce the size of an image and later are able to restore it seemingly without visual losses. We say images are compressible. Compression standards like JPEG exploit this fact by efficiently representing images with significantly fewer numbers than the number of pixels in the original image. Mathematically, this is achieved by representing the image in a basis in which most of its coefficients are so small that they can be set to zero without visibly diminishing the quality of the image. We call such a representation sparse.Would it not be great if one could directly acquire an image in this compact representation?In recent years this question has been affirmatively answered. It turns out that under certain assumptions it is indeed possible to make such compressed measurements and to subsequently recover the image almost completely. For applications like MRI and CT this means shorter scanning times and reduced radiation exposure.However, to be able to benefit from this new sensing paradigm it is necessary to modify both, the measurement procedure and the reconstructing algorithm. This fellowship addressed exactly this problem for a wide range of imaging modalities including, CT, Tomosynthesis and Optical Tomography. It develops new ways of data acquisition and new algorithms to reconstruct the image from this data. It addresses some fundamental issues concerned with the conditions on the design of the measurement and limits of what is feasible under these conditions. It explores ways of further improving the reconstruction by incorporating prior knowledge on the object. The new Sparse Way of imaging has the potential to push boundaries of what is achievable at present in terms of resolution, data acquisition time, and radiation dose. In close collaboration with experimentalists at UCL the developed methodology will be tested on real-life applications. The research will benefit from collaboration with leading experts in the field and Rapiscan Systems, manufacturer of a wide range of security monitoring equipment.Imaging is an essential technology in science and engineering. Advances in many areas depend on a steady progress of existing imaging techniques and the development of novel approaches. The research community working on sparsity-enhanced imaging has been steadily growing over the last couple of years and it has the potential to take the lead in the more general field of imaging in the future. This fellowship will be at the forefront of this exciting research area, addressing timely and relevant real-life problems. It will strengthen the expertise of the UK in image reconstruction by delivering contributions, which will have a major impact in the field.

The applications of imaging extend to many areas of science and engineering, medical diagnosis, industrial process monitoring and quality assurance, security monitoring and many others. New acquisition and reconstruction schemes for faster and more robust imaging using substantially fewer measurements have the potential to improve upon the existing technology in many of these areas. The commercial beneficiaries are Rapiscan Systems and Dexela. Rapiscan will benefit from the development of Sparse CT. The ideas are immediately applicable to Rapiscan hardware and therefore can lead to commercial deployment in airport security CT scanners in a relatively short time. In the long run this will lead to faster and more accurate luggage screening in airports. Dexela will profit from the research on Tomosynthesis, which has the potential to significantly improve the currently achievable image quality. Advancing their technology Dexela will enhance its position against international competition. Betcke will regularly visit both companies and give presentations on the progress of the project. Under an appropriate licensing agreement the developed software will be made available and assistance in its deployment e.g. through demonstration sessions will be provided to both companies. In general manufacturers of CT, Tomosynthesis, BLT and DOT equipment will benefit from the expertise generated through the fellowship. Betcke will give presentations at mathematical, engineering and medical imaging conferences to ensure the dissemination to a wide range of audiences including the manufacturers of medical equipment to increase potential of further exploitation of the ideas. The results will be published in peer reviewed journals in those fields. The Henry Moseley X-ray Imaging Facility at the University of Manchester will benefit from the development of Sparse CT and sparsity-enhanced reconstruction algorithms. Under an appropriate licensing agreement the developed software will be made available at the facility thereby greatly increasing its exposure to other academics and the industry. Commercial exploitation of the work (patents, software licenses) will be pursued through the UCLi office who have considerable experience in such negotiations, and who have already negotiated licences for some of the previous image reconstruction software developments. Once the technology is mature enough for medical applications, the NHS will benefit from availability of more cost-efficient medical imaging equipment. Physicians and patients will benefit from new faster, more flexible and lower dose or even non-invasive diagnostic tools providing better quality results, which will increase the success rate in image assisted diagnosis. Betcke will engage in dissemination to schools and lay audiences working with the UCL Outreach office and participate in events organised by the Biomedical Optics Research Laboratory group in Medical Physics, such as e.g. the Royal Society summer exhibitions. Betcke will maintain a website documenting the progress of the project in general terms suitable for broader audiences to ensure that the research is reaching other communities for which it might be of interest. The fellowship will allow Betcke to quickly establish herself as a fully independent researcher making essential contributions at the frontiers of mathematics, science and engineering. The research visits will enable Betcke to build up long term collaborations with leading experts in the field, which will last beyond the time of the fellowship. Betcke has a very successful collaboration history with Rapiscan during her time at the University of Manchester including effective knowledge transfer to Rapiscan engineers and a filed patent application. The collaboration with Rapiscan during the fellowship will further strengthen Betcke's relationship to this important industrial partner.