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| Truncated projections can arise from a detector with limited field of view (LFOV). Truncation artifacts can be reduced through extrapolation methods; however the reconstructed images 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 extrapolation method alone. This paper builds a theoretic foundation for the above iterative reconstruction-reprojection algorithm. The theoretic foundation is suitable to parallel-beam fan-beam cone-beam computed tomography(CT). Two pre-assumptions are summarized from CT system. 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 consists of the general inverse of the sub-matrices of the matrix. The solution can be approximately implemented as the iterative reconstruction-reprojection algorithm mentioned above.
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| Keywords:artifact, truncation, image, reconstruction, projection, extrapolation, LFOV, tomography, local, inverse, CT, SPECT, PET |
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