New pixellation scheme for CT algebraic reconstruction to exploit matrix symmetries

Abstract

In this article we propose a new pixellation scheme which makes it possible to speed up the time of reconstruction. This proposal consists in splitting the field of view of the scanner into as many circular sectors as rotation positions of the detector. The sectors are pixellated using circular pixels whose size is always smaller than the resolution needed. The geometry of the pixels and the arrangement on circular sectors make it possible to compute the entire matrix from only one position of the scanner. Therefore, the size of the matrix decreases as many times as the number of rotations. This results in a significant reduction of the system matrix which allows algebraic methods to be applied within a reasonable time of reconstruction and speeds up the time of matrix generation. The new model is studied by means of analytical CT simulations which are reconstructed using the Maximum Likelihood Emission Maximization algorithm for transmission tomography and is compared to the cartesian pixellation model. Therefore, two different grids of pixels were developed for the same scanner geometry: one that employs circular pixels within a cartesian grid and another that divides the field of view into a polar grid which is composed by identical sectors, with circular pixels too. The results of both models are that polar matrix is built in a few seconds and the cartesian one needs several hours, the size of the matrix is significantly smaller than the circular one, and the time of reconstruction per iteration using the same iterative method is less in the polar pixel model than in the square pixel model. Several figures of merit have been computed in order to compare the original phantom with the reconstructed images. Finally, we can conclude that both reconstructions have been proved to have enough quality but, the polar pixel model is more efficient than the square pixel model. © 2008 Elsevier Ltd. All rights reserved.