Uniformly sampled polar and cylindrical grid approach for 2D, 3D image reconstruction using algebraic algorithm

Image reconstruction by Algebraic Methods (AM) outperforms the transform methods in situations where the data collection procedure is constrained by time, space, and radiation dose. AM algorithms can also be applied for the cases where these constraints are not present but their high computational and storage requirement prohibit their actual breakthrough in such cases. In the present work, we propose a novel Uniformly Sampled Polar/Cylindrical Grid (USPG/USCG) discretization scheme to reduce the computational and storage burden of algebraic methods. The symmetries of USPG/USCG are utilized to speed up the calculations of the projection coefficients. In addition, we also offer an efficient approach for USPG to Cartesian Grid (CG) transformation for the visualization. The Multiplicative Algebraic Reconstruction Technique (MART) has been used to process the projections data in order to determine the field function of the suggested grids. We first use cyber phantoms of various shapes, sizes and densities to test the USPG/USCG-based MART algorithm. Experimental projections data of a frog and Cu-Lump have been further exercised to validate the proposed approach. A variety of image quality measures have been evaluated to check the accuracy of the reconstruction. Results indicate that the current strategies speed up (when compared to CG-based algorithms) the reconstruction process by a factor of 2.5 and reduce the memory requirement by the factor p, the number of projections used in the reconstruction.