Truncation studies using the generalized naturalized natural pixel bases for parallel beam geometry

For natural pixel basis, the image equation can be described as Mq=p, where p is the projection measurement, q is the unknown estimation, and matrix M is the backprojection-projection operation. Without considering photon scatter, geometric response, and attenuation, the natural pixel representation of the projection operator for parallel beam geometry is a unit strip perpendicular to the collimation bin. Since the backprojection operator can be different from the adjoint projection operator, a backprojection operator which does not truncate the image can be found to reduce the artifacts in truncation studies. In this study, two computer simulated phantoms and physical Hoffman brain phantom are reconstructed and evaluated. Non-truncated, 25% truncated and 50% truncated projections are generated from the above projections. Nine different combinations of the matrix M are studied for parallel beam geometry. The singular value decomposition (SVD) reconstruction method is used to solve q in this inverse problem, and the final image is obtained by backprojecting this q into a discrete array of points. Without truncation, we observe that different backprojection geometries can reconstruct almost the same image. In truncation studies, estimation of more the projection bins is more effective to reduce the ring artifact than changing the projection bin width. Since the backprojection operator does not truncate the image, the ring artifact is reduced.