RICT: Rotating image computed tomography with a one-to-one reversible image rotation algorithm.

Abstract

The Mueller, Siddon and Joseph weighting algorithms are frequently used for projection and back-projection, which are relatively complicated when they are implemented in computer code. This study aims to reduce the actual complexity of the projection and back-projection. First, we neglect the exact shape of the pixel, so that its shadow is a rectangle projecting precisely to a detector bin, which implies that all the pixel weights are exactly 1 for each ray through them, otherwise are exactly 0. Next, a one-to-one reversible image rotation algorithm (RIRA) is proposed to compute the projection and back-projection, where two one-to-one mapping lists namely, U and V, are used to store the coordinates of a rotated pixel and its corresponding new coordinates, respectively. For each 2D projection, the projection is simply the column sum in each orientation according to the lists U and V. For each 2D back-projection, it is simply to arrange the projection to the corresponding column element according to the lists U and V. Thus, there is no need for an interpolation in the projection and back-projection. Last, a rotating image computed tomography (RICT) based on RIRA is proposed to reconstruct the image. Experiments show the RICT reconstructs a good image that is close to the result of filtered back-projection (FBP) method according to the RMSE, PSNR and MSSIM values. What's more, our weight, projection and back-projection are much easier to be implemented in computer code than the FBP method. This study demonstrates that the RIRA method has potential to be used to simplify many computed tomography image reconstruction algorithms.