| Abstrakt: |
The empirical two-step data-domain-decomposition (DDD) method has been shown to be effective in yielding accurate image reconstruction from discrete data collected in multispectral computed tomography. The key step in the DDD method is to estimate accurately basis sinograms from discrete data by basing upon the nonlinear discrete-to-discrete (DD)-data model. From the basis sinograms, basis images and subsequently virtual monochromatic images at energies of interest can readily be reconstructed. In this work, we carry out theoretical and numerical analyses of the existence, uniqueness, and stability of the solution to the nonlinear DD-data model for accurately estimating the discrete basis sinograms. More precisely, we derive a sufficient condition on that the mapping in the nonlinear DD-data model is a local homeomorphism and also a necessary condition on that it is a proper mapping and further a homeomorphism, demonstrating the existence of the solution. We also obtain a sufficient condition on the global injectivity of the nonlinear mapping, revealing the uniqueness condition on the solution. Furthermore, we identify some bounded regions for specific stability estimates of the nonlinear DD-data model. Finally, we conduct numerical studies to demonstrate quantitatively the validity extent of conditions derived. Under the solution conditions derived, results of the numerical study confirm that unique truth basis sinograms can numerically accurately be recovered from noise-free data and that the solution stability is demonstrated using noisy data. [ABSTRACT FROM AUTHOR] |
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