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 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.