ABSTRACT
This chapter discusses the problem of image reconstruction in modern x-ray computed tomography (CT) systems. X-ray CT aims at noninvasive visualization of structures inside a three-dimensional (3D) object using the x-ray linear attenuation coefficient (LAC) (Hubbell, 2006) as the physical parameter that distinguishes these structures from each other (Buzug, 2008; Hsieh, 2009). The LAC cannot be measured directly; access to this quantity can only be achieved indirectly by first measuring attenuation effects and then solving an inverse problem that links the desired quantity to these measurements. The solution of the inverse problem is the image reconstruction process (Defrise and Gullberg, 2006; Herman, 2009; Natterer and Wubbeling, 2007). Each measurement is a line integral of the spatial distribution of the LAC, that is, the sum of the values taken by the LAC on a line in space along which a beam of x-ray photons is transmitted through the object. The measurement is essentially obtained as the logarithm of the ratio between the number of photons that enters the object and the number of photons that exits (Buzug, 2008; Hsieh, 2009; Hubbell, 2006).
