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This paper proposes a simple row-action type iterative algorithm which is appropriate to reconstruct sparse objects from a limited number of projections. The main idea is to use the L1 norm to pick up a sparse solution from a set of feasible solutions to the measurement equation. By perturbing the linear program to a quadratic program, we use the duality of the nonlinear programming to construct a row-action type iterative algorithm to find a solution, we also prove that the algorithm converges for any initial image. We show that this method works well in the 3D blood-vessel reconstruction and its computation time is shorter compared to our previous method.