An accurate iterative reconstruction algorithm for sparse objects: Application to 3D blood vessel reconstruction from a limited number of projections
An accurate iterative reconstruction algorithm for sparse objects: Application to 3D blood vessel reconstruction from a limited number of projections
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DOI：
10.1088/0031-9155/47/15/303
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发表时间：
2002-08-07
影响因子：
3.5
通讯作者：
Kudo, H
中科院分区：
文献类型：
--
作者：
Li, MH;Yang, HQ;Kudo, H
基于非线性规划的对偶性，本文提出了一种精确的行作用型迭代算法，该算法适用于从有限数目的投影重建稀疏目标。我们使用的成本函数是L-p范数，p近似为1.1。这个范数允许我们从测量方程的一组可行解中选择一个稀疏解。此外，由于它是严格凸的和可微的，我们可以利用非线性规划的对偶性构造一个行作用型迭代算法来求解。我们还对像素值施加边界约束，以获得更好的解决方案。我们证明了这种方法在有限数量的锥束投影的三维血管重建中效果良好。
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 approximate to 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.