An accurate iterative reconstruction algorithm for sparse objects: application to 3D blood vessel reconstruction from a limited number of projections

Based on the duality of nonlinear programming, this paper proposes an accurate row-action type iterative algorithm which is appropriate to reconstruct sparse objects from a limited number of projections. The cost function we use is the L_p norm with p ≈ 1.1. This norm allows us to pick up a sparse solution from a set of feasible solutions to the measurement equation. Furthermore, since it is both strictly convex and differentiable, we can use the duality of nonlinear programming to construct a row-action type iterative algorithm to find a solution. We also impose the bound constraint on pixel values to pick up a better solution. We demonstrate that this method works well in three-dimensional blood vessel reconstruction from a limited number of cone beam projections.