Interior tomography with continuous singular value decomposition.
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.
Xin
X
Jin
Alexander
A
Katsevich
Hengyong
H
Yu
Ge
G
Wang
Liang
L
Li
Zhiqiang
Z
Chen
D000465:Algorithms; D003198:Computer Simulation; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D019047:Phantoms, Imaging; D012815:Signal Processing, Computer-Assisted; D014057:Tomography, X-Ray Computed / Q000379:methods*