Tomographic Image Reconstruction Based on Minimization of Symmetrized Kullback-Leibler Divergence
- Resource Type
- Authors
- Tetsuya Yoshinaga; Ryosuke Kasai; Yusaku Yamaguchi; Takeshi Kojima
- Source
- Mathematical Problems in Engineering, Vol 2018 (2018)
- Subject
- Kullback–Leibler divergence
Discretization
Article Subject
Differential equation
General Mathematics
02 engineering and technology
Iterative reconstruction
Computer Science::Digital Libraries
030218 nuclear medicine & medical imaging
Euler method
03 medical and health sciences
symbols.namesake
0302 clinical medicine
0202 electrical engineering, electronic engineering, information engineering
Applied mathematics
Divergence (statistics)
Mathematics
Multiplicative calculus
lcsh:Mathematics
General Engineering
Inverse problem
lcsh:QA1-939
lcsh:TA1-2040
Computer Science::Mathematical Software
symbols
020201 artificial intelligence & image processing
lcsh:Engineering (General). Civil engineering (General)
- Language
- English
- ISSN
- 1024-123X
Iterative reconstruction (IR) algorithms based on the principle of optimization are known for producing better reconstructed images in computed tomography. In this paper, we present an IR algorithm based on minimizing a symmetrized Kullback-Leibler divergence (SKLD) that is called Jeffreys’ J-divergence. The SKLD with iterative steps is guaranteed to decrease in convergence monotonically using a continuous dynamical method for consistent inverse problems. Specifically, we construct an autonomous differential equation for which the proposed iterative formula gives a first-order numerical discretization and demonstrate the stability of a desired solution using Lyapunov’s theorem. We describe a hybrid Euler method combined with additive and multiplicative calculus for constructing an effective and robust discretization method, thereby enabling us to obtain an approximate solution to the differential equation. We performed experiments and found that the IR algorithm derived from the hybrid discretization achieved high performance.