Computer Simulation of the Fourier Method of Image Reconstruction from Projections in Tomography

Abstract

Nowadays, tomographic imaging methods based on various physical principles represent an attractive tool for medical diagnosis. In contemporary X-ray tomography systems the convolution filtered backprojection method still remains the leading mathematical approach implemented. However, continually increasing demands, namely computational speed in multiplanar or 3-D spatial methods and dynamic tomographic studies, have evoked a renewed interest in earlier proposed methods. One of the most promising of these has proved to be the Direct Fourier Inversion method (the so-called DFI method). This method was proposed by Ramachandran (Ramachandran and Lakshminarayanan, 1971), but unsatisfactory reconstruction quality was attained and, as a result, the method was not pursued further. Several papers were published from the late 1970s onwards (Mersereau, 1976; Stark et al., 1981; Niki et al., 1983), which exhibited a new interest in the DFI method. Although certain possibilities of error suppression were described in these papers, some important questions still remained to be tackled. We therefore considered it appropriate to re-evaluate discrete mathematical aspects of the DFI method and to develop effective computational algorithms. The Fourier spectral character of the measured data in Magnetic Resonance Tomography (Cho et al., 1982) made such research still more interesting.