ABSTRACT
Tomographic data are mostly provided in the form of projections of the desirable images. As the projection data are totally incomprehensible, it is necessary to convert them into an informationally equivalent but understandable form of images. This procedure is called image reconstruction from projections. The chapter deals with different methods of the approximate reconstruction from projections under the ideal situation when all the side effects can be neglected. This should primarily provide insight into different approaches to the reconstruction problem; however, the methods are directly applicable, namely, in x-ray computed tomography, which under certain conditions approaches the ideal situation. Measured values in some modalities, namely, in gamma tomography are rather imprecise due to quantum noise, as the available measured intensities are extremely weak and therefore represented by individual photon counts with large variances. Two common tomographic modalities—Magnetic Resonance Imaging and ultrasonography—use other approaches to reconstruct the image data from the measurements.
