3D Image Reconstruction

This chapter outlines the fundamentals of several image reconstruction approaches currently in use in X-ray tomography at synchrotron radiation facilities and at industrial X-ray CT scanners, clarifying both their proper use and points of caution in image reconstruction. The chapter begins with the basic measurement methods for projection data, together with the basics of the projection data itself. Measurements with X-ray CT scanners can be thought of as a single set of Radon transforms collected while varying the projection angles. Similarly, X-ray tomography image reconstruction can be perceived as the inverse problem of analytically obtaining an object image by inverse Radon transform. Such fundamentals are described at the beginning including sinogram and the projection theorem. Various image reconstruction techniques, such as algebraic reconstruction technique, iterative reconstruction technique, filtered back projection, convolution back projection and cone beam reconstruction are then described. Especially image reconstruction methods for actual use are described in details such as on the shapes and equations of reconstruction filters in both the real space and frequency space, together with various schematic and real examples. Realities of image reconstruction are then introduced mainly on the practical applications of GPU-based image reconstruction. Finally, special image reconstructions, such as the offset scan, region of interest reconstruction, laminography and image reconstruction with angle constraints are introduced.