Modified Polar Grid-based Accelerated Image Reconstruction Technique for X-ray CT

Abstract

Image reconstruction by projections is basically a mathematical problem. The speed and accuracy of the reconstruction mainly depend upon, (1) discretization scheme (2) solution technique. Solution by Algebraic Method (AM) is the most promising technique for manufacturing the low-cost (few detectors arrangement) X-ray CT set-up. Slow converging rate and huge memory requirement are the two major drawbacks of the AM algorithms. Projection coefficient calculations and their storages are major time and storage-consuming processes of the algebraic methods. Among all algebraic methods, the Multiplicative Algebraic Reconstruction Technique (MART) is more effective because it maximizes the entropy of the image space. The conventional MART algorithm uses square grids (SG) in the discretization process of the image reconstruction. In the present work, we employed a modified polar grid to cope with the shortcomings of the MART method. In this new discretization scheme, only the projection coefficients of the first view, need to be calculated. Projection coefficients for other views can be easily calculated by using the symmetries of the modified polar grid. This method significantly reduces the reconstruction time and storage requirement of the MART algorithm. In addition, we also presented the direct method of polar to square grid transformation for the visualization of the reconstructed images. We tested the proposed method to fan-beam geometry for 2D image reconstruction. Structural similarity index(SSIM) and L2 error are used for quality assessment of the reconstructed images.