Abstract
Modelling the forward projection or reprojection, that is defined as the operation that transforms a 3D volume into series of 2D set of line integrals, is of interest in several medical imaging applications as iterative tomographic reconstruction (X-ray, Computed Tomography [CT], Positron Emission Tomography [PET], Single Photon Emission Computed Tomography [SPECT]), dose-calculation in radiotherapy and 3D-display volume-rendering. As forward projection is becoming widely used, iterative reconstruction algorithms and their characteristics may affect the reconstruction quality; its accuracy and performance needs more attention. The aim of this chapter is to show the importance of the modelling of the forward projection in the accuracy of medical tomographic data (CT, SPECT and PET) reconstructed with iterative algorithms. Therefore, we first present a brief overview on the iterative algorithms used in tomographic reconstruction in medical imaging. Second, we focus on the projection operators. Concepts and implementation of the most popular projection operators are discussed in detail. Performance of the computer implementations is shown using the well-known Shepp_Logan phantom. In order to avoid possibly confounding perspective effects implied by fan or cone-beam, this study is performed in parallel acquisition geometry.
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