Tiny a priori knowledge solves the interior problem in computed tomography.
Based on the concept of differentiated backprojection (DBP) (Noo et al 2004 Phys. Med. Biol. 49 3903, Pan et al 2005 Med. Phys. 32 673, Defrise et al 2006 Inverse Problems 22 1037), this paper shows that the solution to the interior problem in computed tomography is unique if a tiny a priori knowledge on the object f(x, y) is available in the form that f(x, y) is known on a small region located inside the region of interest. Furthermore, we advance the uniqueness result to obtain more general uniqueness results which can be applied to a wider class of imaging configurations. We also develop a reconstruction algorithm which can be considered an extension of the DBP-POCS (projection onto convex sets) method described by Defrise et al (2006 Inverse Problems 22 1037), where we not only extend this method to the interior problem but also introduce a new POCS algorithm to reduce computational cost. Finally, we present experimental results which show evidence that the inversion corresponding to each obtained uniqueness result is stable.
Kudo
Hiroyuki
H
Department of Computer Science, Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Japan. kudo@cs.tsukuba.ac.jp
Courdurier
Matias
M
Noo
Frédéric
F
Defrise
Michel
M
D000465:Algorithms; D003201:Computers; D006801:Humans; D007091:Image Processing, Computer-Assisted; D021621:Imaging, Three-Dimensional; D015233:Models, Statistical; D010363:Pattern Recognition, Automated; D019047:Phantoms, Imaging; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D012984:Software; D015898:Tomography Scanners, X-Ray Computed; D014057:Tomography, X-Ray Computed / Q000295:instrumentation* / Q000379:methods*