Abstract: Basis material decomposition is a very essential step in dual-energy CT (DECT) reconstruction and two-material decomposition is one of the most common model whose key point is to obtain the projections of decomposition coefficient. To improve the speed of it， two-material decomposition algorithms were proposed， which are the dual-energy CT based on the error feedback gradient descent method and the Armijo-Goldstein rule gradient descent method， respectively. These two methods were able to get the projections of decomposition coefficient quickly because of the computed step size in gradient descent. Moreover， the nonlinear problem in dual-energy CT reconstruction was also effectively and efficiently solved by using the proposed methods. Simulation results indicated that compared to the projection matching method， the two proposed methods can get stable convergence and high reconstruction precision with a short span of time， which has an important significance to the clinical application. With the same reconstruction precision， the algorithm based on the Armijo-Goldstein rule gradient descent is faster， using the inexact linear search step size.

Key words: dual-energy CT, two-material decomposition, gradient descent, image reconstruction, computed step size