Computed tomography is the process of reconstructing the interiors of objects from data collected based on transmitted or emitted radiation. The problem occurs in a wide range of application areas. Here we discuss the computer algorithms used for achieving the reconstructions. The Reconstruction Problem We want to solve the following general problem. There is a three-dimensional structure whose internal composition is unknown to us. We subject this structure to some kind of | Gabor T. Herman. Algorithms for Computed Tomography 2000 CRC Press LLC. http . Algorithms for Computed Tomography Gabor T. Herman University of Pennsylvania Introduction The Reconstruction Problem Transform Methods Filtered Backprojection FBP The Linogram Method Series Expansion Methods Algebraic Reconstruction Techniques ART Expectation Maximization EM Comparison of the Performance of Algorithms References Introduction Computed tomography is the process of reconstructing the interiors of objects from data collected based on transmitted or emitted radiation. The problem occurs in a wide range of application areas. Here we discuss the computer algorithms used for achieving the reconstructions. The Reconstruction Problem We want to solve the following general problem. There is a three-dimensional structure whose internal composition is unknown to us. We subject this structure to some kind of radiation either by transmitting the radiation through the structure or by introducing the emitter of the radiation into the structure. We measure the radiation transmitted through or emitted from the structure at a number of points. Computed tomography CT is the process of obtaining from these measurements the distribution of the physical parameter s inside the structure that have an effect on the measurements. The problem occurs in a wide range of areas such as x-ray CT emission tomography photon migration imaging and electron microscopic reconstruction see . 1 2 . All of these are inverse problems of various sorts see . 3 . Where it is not otherwise stated we will be discussing the special reconstruction problem of estimating a function of two variables from estimates of its line integrals. As it is quite reasonable for any application we will assume that the domain of the function is contained in a finite region of the plane. In what follows we will introduce all the needed notation and .
