ABSTRACT
This chapter describes reconstruction from noiseless projection data. This type of reconstruction is used in X-ray computed tomography. The projection, slice theorem explains how the projection data are related to the spatial frequency representation of the cross-sectional data. In X-ray computed tomography, the intensity of an X-ray beam is measured after it passes through a cross section. The beam is attenuated by the tissue in each pixel along the way. One method of reconstructing the data is to back project the ray sums to the object space. The projection, back projection operation is analogous to the original form of tomography used in radiology which is also called as the blurring tomography. Image reconstruction can also be performed in the space domain using a convolution, back projection algorithm. Fourier transform reconstruction takes advantage of the relation between the Fourier transform of the projection data and the object.
