Presentation by Dr Thomas Blumensath
Dr Blumensath came to give a presentation on his work in x-ray computed tomography - the process of reconstructing the interior structure of objects using x-ray's. We were introduced to the basic model of x-ray absorption that allows for reconstruction to take place. This model is based on a mathematical transformation know as the radon transform. With a knowledge of how x-rays are absorbed ("forward problem") we are able to use this understanding to find methods for inverting the process and reconstructing the interior of an object ("inverse problem").
There exist many standard algorithms for reconstructing objects, such as filtred back-projection and algebraic reconstruction technique (ART). However these standard methods need large amounts of input measurements in order to produce an accurate reconstruction. This is not always feasible; for instance if the object to be imaged is very large or if we wish to minimise exposure to x-ray radiation. It is hoped that the use of sparse methods will enable acurate reconstruction from limited measurements.
Many standard methods also make assumptions about the forward models linearity in order to invert - although this leads to a decent reconstruction in most instances there are situations in which issues may arise. Dr Blumensath is working on models that take into account the true non-linearitys in the forward problem in order to develop better reconstruction methods.
Results of various reconstruction methods