Speaker: Fred Noo

Title: Data requirements in X-ray computed tomography

This talk will discuss the amount and location of measurements required to obtain accurate images in x-ray computed tomography (CT). To simplify the discussion I will initially focus on single-slice imaging. Also, I will use the observation that each measurement in CT provides information on a line in space, namely the line that connects the x-ray source focus to the detector center. Following the 1917 theory of the mathematician Johan Radon, it was observed that the measurements should represent a uniform coverage of all possible lines passing through the object within the slice of interest. In other words, accurate reconstruction is not possible if a large angle of measurement orientations is missing. This fact is often called "the limited angle problem", and I will illustrate the difficulties inherent to this problem that make accurate reconstruction impossible. After the limited angle problem, I will discuss two additional problems: the interior and the exterior problems. These problems appear when all measurement orientations are nicely covered, but for each orientation, there is a significant amount of lines not covered by the measurements while passing through the object under study. This amount is found near the edges of the object in the interior problem, and near the center of the object in the exterior problem. I will show that in some ways the interior problem is more easily manageable than the others. Putting together all these problems, it has been often declared that CT is "all or nothing", that is whether we are interested in the full slice or just a region-of-interest in it, measurements must cover the entire slice. This principle has driven developments in CT since its beginning. However, researches initiated and pursued at UCAIR are showing more and more that CT is not "all or nothing": regions-of-interest can be imaged accurately with limited radiation exposure. I will discuss these findings, which, quoting C. Crawford from Analogic Corporation forces a completely rethinking of the concept of CT. Following the trend of my talk last year, I will be avoiding most equations, focussing on the fundamental aspects.