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RICT: Rotating image computed tomography with a one-to-one reversible image rotation algorithm
Chengxiang Wang1, Richard Gordon2
1School of Mathematical Sciences, Chongqing Normal University, Chongqing, China.
Background:
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.
Objective:
This study aims to reduce the actual complexity of the projection and back-projection.
Methods:
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.
Results:
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.
Conclusion:
This study demonstrates that the RIRA method has potential to be used to simplify many computed tomography image reconstruction algorithms.
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