Image Reconstruction Based On Hilbert And Hybrid Filtered Algorithms With Inverse Distance Weight And No Backprojection Weight

Filtered backprojection (FBP) reconstruction algorithms are very popular in the field of X-ray computed tomography (CT) because they give advantages in terms of the numerical accuracy and computational complexity. Ramp filter based fan-beam FBP reconstruction algorithms have the position dependent weight in the backprojection which is responsible for spatially non-uniform distribution of noise and resolution, and artifacts. Many algorithms based on shift variant filtering or spatially-invariant interpolation in the backprojection step have been developed to deal with this issue. However, these algorithms are computationally demanding. Recently, fan-beam algorithms based on Hilbert filtering with inverse distance weight and no weight in the backprojection have been derived using the Hamaker’s relation. These fan-beam reconstruction algorithms have been shown to improve noise uniformity and uniformity in resolution. In this thesis, fan-beam FBP reconstruction algorithms with inverse distance back-projection weight and no backprojection weight for 2D image reconstruction are presented and discussed for the two fan-beam scan geometries -equi-angular and equispace detector array. Based on the proposed and discussed fan-beam reconstruction algorithms with inverse distance backprojection and no backprojection weight, new 3D cone-beam FDK reconstruction algorithms with circular and helical scan trajectories for curved and planar detector geometries are proposed. To start with three rebinning formulae from literature are presented and it is shown that one can derive all fan-beam FBP reconstruction algorithms from these rebinning formulae. Specifically, two fan-beam algorithms with no backprojection weight based on Hilbert filtering for equi-space linear array detector and one new fan-beam algorithm with inverse distance backprojection weight based on hybrid filtering for both equi-angular and equi-space linear array detector are derived. Simulation results for these algorithms in terms of uniformity of noise and resolution in comparison to standard fan-beam FBP reconstruction algorithm (ramp filter based fan-beam reconstruction algorithm) are presented. It is shown through simulation that the fan-beam reconstruction algorithm with inverse distance in the backprojection gives better noise performance while retaining the resolution properities. A comparison between above mentioned reconstruction algorithms is given in terms of computational complexity. The state of the art 3D X-ray imaging systems in medicine with cone-beam (CB) circular and helical computed tomography scanners use non-exact (approximate) FBP based reconstruction algorithm. They are attractive because of their simplicity and low computational cost. However, they produce sub-optimal reconstructed images with respect to cone-beam artifacts, noise and axial intensity drop in case of circular trajectory scan imaging. Axial intensity drop in the reconstructed image is due to the insufficient data acquired by the circular-scan trajectory CB CT. This thesis deals…