Abstract
Significant research and development have been made on various kinds of CT's such as the Xβray, the MRI and the positron, which are applied widely in practice. The CT device is divided into the measurement system and the image reconstruction system. Efforts are still being made at present to improve the resolution and speed of those systems. This paper discusses the 2βD Fourier transform method, which is one of the image reconstruction methods that have been investigated and applied in the image reconstruction in various types of CT's.
Traditionally, the 2βD Fourier transform method has been considered as suffering from low image quality, although the image can be reconstructed with a high speed. The reason for image degradation is the lack of accuracy in the interpolation in the 2βD Fourier transform domain, which can be remedied by improving the accuracy.
A problem then is that the coordinate transformation in the Fourier domain depends on the individual CT. From such a viewpoint, this paper analyzes the relation between the coordinate transformation and the reconstructed image to indicate the reason for the image degradation.
A systematic analysis is made of the reconstructed image when the linear interpolation is applied to each coordinate transformation, to indicate the reason for the image degradation and to describe the artifact appearing in the reconstructed image. Based on the result of this analysis, an algorithm is constructed which can eliminate the artifact from the reconstructed image. The algorithm is composed of the normalization algorithm for the interpolation characteristics, the interpolation by the fastβFourier transform and the inverse 2βD Fourier transform enlarging the reconstructed image region. The effectiveness of the method is demonstrated by applying the method to the transformation from the polar to the Cartesian coordinate.