Quadrature Radon Transform for Smoother Tomographic Reconstruction

Abstract

Tomographic reconstruction using Radon projections taken at an angle introduce a redundancy of four. Hence the projection in one quadrant are used for tomographic reconstruction to reduce computational overheads. In this paper, we present that the though the projections at an angle do not introduce any redundancy, the achieved tomographic reconstruction is very poor. A qudrature Radon transform is further introduced as a combination of Radon transforms at projection angles. The individual back projections are computed in two parts separately; 1) considering them real and imaginary parts of a complex number 2) considering average of the individual back projections. It is observed that the quadrature Radon transform yields better results numerically and/or visually compared to conventional Radon transform.

Keywords: Single quadrant Radon transform, quadrature Radon transform, Magnitude of complex projection, average, reconstruction.