Superiorization-based multi-energy CT image reconstruction. (English) Zbl 1367.65033
In multi-energy computer-tomography (CT) image reconstruction one has to find the image \(X\) by minimizing the objective function \(\phi(X)=\|X\|_*+\lambda r(X)\), subject to \(AX=G\) where \(r\) is a total variation (TV) term for smoothing purpose and the norm is the nuclear norm. The prior rank intensity and sparsity model (PRISM) essentially assumes that \(X\) is a superposition of a low rank and a sparse matrix. The simultaneous algebraic reconstruction technique (SART) is an iterative method to solve \(AX=G\) using a relaxation parameter to control the step size. In a superiorizated version of an iterative algorithm, the usual iterations are perturbed to get better performance. Inspired by Y. Censor et al. [J. Optim. Theory Appl. 160, No. 3, 730–747 (2014; Zbl 1298.90104)], this paper proposes a superiorized version of the SART subject to the PRISM prior. The superiorization consists in modifying the iteration by adding an appropriate matrix to the SART iterate \(X^{(k)}\) to force a descend of the objective function \(\phi\). The method is compared numerically with the split-Bregman algorithm (see [T. Goldstein and S. Osher, SIAM J. Imaging Sci. 2, No. 2, 323–343 (2009; Zbl 1177.65088)]).
Reviewer: Adhemar Bultheel (Leuven)
MSC:
| 65D18 | Numerical aspects of computer graphics, image analysis, and computational geometry |
| 68U10 | Computing methodologies for image processing |
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
Keywords:
x-ray spectral CT; simultaneous algebraic reconstruction technique; superiorization; split-Bregman; computer-tomography image reconstruction; rank intensity and sparsity model; iterative algorithmReferences:
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