Research On Mojette Transform With Non-classical Cubic Lattices

With the increasing popularity of computers, better performance of computer processing, memory and other hardware ability, more computer resources are used to calculate the projection transform. The plentiful applications of the projection transform include the image processing, coding and the medical devices as well as the network package transferring and the QoS service. All these applications are based on the performance of the used projection transform and the effect of the rebuilt data. The Radon Transform is one of the popular and basic projection transforms. And the Mojette Transform that the paper refers to is the discrete form of the Radon Transform.The ordinary Mojette Transform is based on the traditional square lattice. But the topic of the article is focused on the Mojette Transform under the hexagonal lattice. The contents are as follows:First of all, there is a brief introduction about the development of Mojette Transform as well as the illustration and comparison of the different related knowledge, which includes the approaches of Mojette Transform and the different lattices.Secondly, this article proposed a new way of computing the projection direction in hexagonal lattice coordinate system while using the Farey Series to generate the discrete directions, and we also give the transform matrix between two different coordinate system. Then we address a transform matrix between the different lattices. And also we propose an new approach as well as the algorithm to use the Dirac and Spline0Mojette Transform under the hexagonal lattice.Eventually, we compare the result of Mojette Transform under different lattices. We find that in3different testing sets, the Mojette Transform using hexagonal lattice performs better than the old traditional square lattice. And we find that during the direction between0to/2, the Correlation Coefficient value of hexagonal lattice is above99.6%, which is obviously higher than the square lattice.