Parallelisation of Tomographic Reconstruction Methods

In medicine, there is a still growing interest in non-invasive examination techniques which can depict anatomical structures. Amongst these methods are Magnetic Resonance Imaging (MRI), Positron Emission Tomography (PET) and Computerised Tomography (CT). These are all based on the same principle: under a number of angles, a set of line integrals in a plane is measured resulting in a set of prooles. This set of prooles is called the Radon transform of the object. The problem now is to reconstruct a two-dimensional image from its Radon transform. It is possible to derive reconstruction algorithms from the so-called Fourier slice theorem. This theorem links the one-dimensional Fourier transform of a proole to the two-dimensional Fourier transform of the object which is to be reconstructed. Three diierent reconstruction methods, based on this theorem, are considered in this thesis: the rst one is the ltered backprojection algorithm, the second one is direct Fourier reconstruction, and the last method is a multiresolution reconstruction algorithm based on the wavelet transform and ltered backprojection. The multiresolution algorithm results in the two-dimensional wavelet transform of the object. This thesis deals with the parallelisation of the above mentioned reconstruction methods and of the wavelet transform on a Connection Machine CM-5. It is known that ltered backprojection gives far better reconstructions than the direct Fourier method, whereas the latter is the fastest to compute. Of the algorithms considered, the ltered backprojection algorithm is the most diicult to parallelise. Because the CM-5 has a distributed memory, the reconstruction equations cannot be translated into a program in a straightforward manner. Several optimisations depending on the architecture of the CM-5 have to be made in order to get a satisfactory performance. This also holds for the multiresolution algorithm, as it uses the backprojection part of the ltered backprojection algorithm. Direct Fourier reconstruction on the contrary is very easy parallelised on the CM-5. The implementation of the wavelet transform has led to an eecient algorithm.