Continuous analog of multiplicative algebraic reconstruction technique for computed tomography

2016 ◽  
Author(s):  
Kiyoko Tateishi ◽  
Yusaku Yamaguchi ◽  
Omar M. Abou Al-Ola ◽  
Takeshi Kojima ◽  
Tetsuya Yoshinaga
2008 ◽  
Vol 18 (04) ◽  
pp. 1219-1225 ◽  
Author(s):  
TETSUYA YOSHINAGA ◽  
YOSHIHIRO IMAKURA ◽  
KEN'ICHI FUJIMOTO ◽  
TETSUSHI UETA

Of the iterative image reconstruction algorithms for computed tomography (CT), the power multiplicative algebraic reconstruction technique (PMART) is known to have good properties for speeding convergence and maximizing entropy. We analyze here bifurcations of fixed and periodic points that correspond to reconstructed images observed using PMART with an image made of multiple pixels and we investigate an extended PMART, which is a dynamical class for accelerating convergence. The convergence process for the state in the neighborhood of the true reconstructed image can be reduced to the property of a fixed point observed in the dynamical system. To investigate the speed of convergence, we present a computational method of obtaining parameter sets in which the given real or absolute values of the characteristic multiplier are equal. The advantage of the extended PMART is verified by comparing it with the standard multiplicative algebraic reconstruction technique (MART) using numerical experiments.


2008 ◽  
Vol 8 (3) ◽  
pp. 11853-11877 ◽  
Author(s):  
D. A. Degenstein ◽  
A. E. Bourassa ◽  
C. Z. Roth ◽  
E. J. Llewellyn

Abstract. The OSIRIS instrument onboard the Odin spacecraft routinely measures vertical profiles of spectrally dispersed, limb scattered sunlight from the upper troposphere into the lower mesosphere. These measurements are used to retrieve the ozone number density vertical profile over the altitude range from 10 to 60 km using the SaskMART Multiplicative Algebraic Reconstruction Technique, which is a one dimensional modification of an existing two-dimensional tomographic retrieval algorithm. This technique allows for the consistent merging of the absorption information from radiance measurements at wavelengths in the Chappuis and the Hartley-Huggins bands at each iteration of the inversion. The effectiveness of the retrieval is demonstrated using a set of coincident SAGE II occultation measurements that show a mean bias of less than 2% from 18 to 53 km.


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