The projection equations in the research of discrete tomography are obtained by either counting the number of points that each line passes or computing the fractional areas of the intersection of each strip and the grid. In this work, a system of linear equations for strip-based projections with rational slopes is obtained. The linear dependency number of these equations is derived.
In this paper, we perform numerical studies on Feldkamp-type and Katsevich-type algorithms for cone-beam reconstruction with a nonstandard spiral locus to develop an electron-beam micro-CT scanner. Numerical results are obtained using both the approximate and exact algorithms in terms of image quality. It is observed that the two algorithms produce similar quality if the cone angle is not large and/or there is no sharp density change along the z-direction. The Katsevich-type algorithm is generally preferred due to its nature of exactness.