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The gradient-flow-based explicit and semi-implicit finite element methods proposed in our earlier papers have been applied to solve various variational models for image reconstruction in cryo-electron microscopy and X-ray computed tomography, respectively. In this paper, we develop a gradient-flow-based blended finite element method for solving the variational model of three-dimensional image reconstruction. The method can be regarded as a linear combination of the explicit and semi-implicitdoi:10.4310/cms.2014.v12.n6.a1 fatcat:32o6y7kbhfa55fyuybuvkye4t4