  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 nonlinear equations and the basis material decomposition comes down to the
inverse problem of the nonlinear equations. For different spectra data,
geometric inconsistent parameters cause geometrical inconsistent rays, which
will lead to mismatched nonlinear equations. How to solve the mismatched
nonlinear equations accurately and quickly is a hot issue. This paper proposes
a general iterative method to invert the mismatched nonlinear equations and
develops Schmidt orthogonalization to accelerate convergence. The validity of
the proposed method is verified by MSCT basis material decomposition
experiments. The results show that the proposed method can decompose the basis
material images accurately and improve the convergence speed greatly.
