Review of Tomographic Imaging Methods Applied to Medical Imaging

Abstract

With the introduction of X-ray CT it became possible to produce con- trasty sectional images of the human body free of superimpositions. The indisputable successes of this new radiographic techniaue prompted the extension of it to other types of radiation used in medical diagnosis as well. But even the elementary requirements for adequate penetration capacity on the one hand and sufficient interaction with the tissue on the other hand exclude the majority of known types of radiation. Although basically applicable to corpuscular radiation of high energy or - after modification - to ultrasound waves, the principle will in the near future first of all conquer the field of extremely long waves in the shape of NMR (nuclear magnetic resonance) . Therefore, the reconstruction ap-proaches which have become known for X-ray CT are presented primarily, these being the algebraic and here in particular the iterative as well as the integral transformation procedures, which have achieved greater importance. Two-dimensional display is preferred here. Using NMR as an example, where three-dimensional (3D) image reconstruction appears more likely to be achievable, marked differences between the 3D-reconstruction problem and the 2D-problem can be demonstrated. This is in particular the local character in the 3D case of the convolution operation, which is an important part of image reconstruction, and the derivability of the reconstruction method from principles of potential theory. For wavelength ranges where the nature of the waves may not be neglected, in recent years there have arisen approaches which in a natural way associate themselves with those already known from CT.