Fast iterative reconstruction for multi-spectral CT by a Schmidt orthogonal modification algorithm (SOMA)

Multi-spectral CT (MSCT) is increasingly used in industrial non-destructive testing and medical diagnosis because of its outstanding performance like material distinguishability. The process of obtaining MSCT data can be modeled as a nonlinear system and the basis material decomposition comes down to the inverse problem of the nonlinear system. For different spectra data, geometric inconsistent parameters cause geometrical inconsistent rays, which will lead to the mismatched nonlinear system. How to solve the mismatched nonlinear equations accurately and quickly is a hot issue. This paper proposes a general iterative method (SOMA) to invert the mismatched nonlinear equations. The SOMA method gives different equations different confidence and searches along the more accurate hyperplane by Schmidt orthogonalization, which can get the optimal solution quickly. The validity of the SOMA method is verified by MSCT basis material decomposition experiments. The results show that the SOMA method can decompose the basis material images accurately and improve the convergence speed greatly.