ABSTRACT
Development of a good model of the data collection process is a large part of the task of understanding reconstruction. Use of a priori information can markedly improve the accuracy of reconstruction. Use of eigenfunctions greatly simplifies the description of reconstruction. The separation of the reconstruction process into back projection, exact reconstruction, and noise reduction aids understanding of reconstruction. This chapter reviews these themes. The major task in understanding computed tomographic reconstruction is to understand the relation of the projection data to the cross-sectional object. The linear systems approach was used in explaining nuclear magnetic resonance imaging, X-ray computed tomography, and the multi-detector scanner. Linear algebra was used to explain deconvolution in first pass radionuclide angiocardiography and reconstruction in single photon emission computed tomography. More generally, it can be used to solve nonshift invariant problems which arise in any of these applications.
