Affiliations: Doubletask North York, Ontario, Canada | University of Toronto, Toronto, Canada | Xi'an Jiao Tong University, Xi'an, China | Northwestern Poly Technical University Xi'an, Xi'an,
China
Note: [] Corresponding author: Shuangren Zhao, 113 Mintwood Dr., North
York, Ontario M2M 3A6, Canada. E-mail: [email protected]
Abstract: Truncated projections can arise from a detector with a limited field
of view (LFOV). Truncation artifacts can be reduced through extrapolation
methods; however the reconstructed images with extrapolation are often
over-corrected or under-corrected. Recently, an iterative
reconstruction-reprojection algorithm was developed, which incorporated
extrapolation with iterative algorithm. It gave the possibility to better
reduce truncation artifacts compared to using the extrapolation method alone.
This article builds a theoretic foundation for the above iterative
reconstruction-reprojection algorithm. The theoretic foundation is suitable to
parallel-beam, fan-beam and cone-beam computed tomography(CT). Two assumptions
are summarized from the CT system. Then, a truncation-artifact-free solution
for the problem of LFOV is derived from these assumptions. The solution
contains a "local inverse" of matrix. The local inverse of a matrix is defined
using the sub-matrix and its general inverse. The solution can be approximately
implemented as the iterative reconstruction-reprojection algorithm which is
just the algorithm mentioned above.
