Array imaging using intensity-only measurements
Array imaging using intensity-only measurements
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DOI：
10.1088/0266-5611/27/1/015005
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发表时间：
2011-01-01
期刊：
影响因子：
2.1
通讯作者：
Papanicolaou, George
中科院分区：
文献类型：
--
作者：
Chai, Anwei;Moscoso, Miguel;Papanicolaou, George
我们介绍了一种新的方法，窄带阵列成像的局部散射体强度只测量考虑重建的位置和反射率的散射体的可能性，正是从只有部分知识的阵列数据，因为我们假设相位信息是不可用的。我们重新制定这个强度只有成像问题作为一个非凸优化问题，并表明，我们可以通过最小化与未知的反射率的半正定矩阵的秩有确切的恢复。由于这个优化问题是NP-难的，计算上是难以处理的，我们用它的核范数，它的奇异值之和来代替矩阵的秩，这是一个可以在多项式时间内解决的凸规划问题。数值实验探讨了该方法的鲁棒性，它恢复稀疏的反射率向量精确的凸优化问题的解决方案。
We introduce a new approach for narrow band array imaging of localized scatterers from intensity-only measurements by considering the possibility of reconstructing the positions and reflectivities of the scatterers exactly from only partial knowledge of the array data, since we assume that phase information is not available. We reformulate this intensity-only imaging problem as a non-convex optimization problem and show that we can have exact recovery by minimizing the rank of a positive semidefinite matrix associated with the unknown reflectivities. Since this optimization problem is NP-hard and is computationally intractable, we replace the rank of the matrix by its nuclear norm, the sum of its singular values, which is a convex programming problem that can be solved in polynomial time. Numerical experiments explore the robustness of this approach, which recovers sparse reflectivity vectors exactly as solutions of a convex optimization problem.