The long-standing interior problem has important mathematical and practical implications.
The recently developed interior tomography methods have produced encouraging results.
A particular scenario for theoretically exact interior reconstruction from truncated
projections is that there is a known sub-region in the ROI. In this paper, we improve
a novel continuous singular value decomposition (SVD) method for interior reconstruction
assuming a known sub-region. First, two sets of orthogonal eigen-functions are calculated
for the Hilbert and image spaces respectively. Then, after the interior Hilbert data
are calculated from projection data through the ROI, they are projected onto the eigen-functions
in the Hilbert space, and an interior image is recovered by a linear combination of
the eigen-functions with the resulting coefficients. Finally, the interior image is
compensated for the ambiguity due to the null space utilizing the prior sub-region
knowledge. Experiments with simulated and real data demonstrate the advantages of
our approach relative to the POCS type interior reconstructions.