复杂度制导相位恢复
Phase retrieval with complexity guidance
摘要：
基于Gerchberg-Saxton（GS）或Fienup算法的迭代相位恢复方法需要大量迭代以收敛到有意义的解。对于复值或相位对象，这些方法也遭受停滞问题，其中解在迭代之间没有太大变化，但所得解显示出诸如孪生子的存在之类的伪像。我们引入了一个复杂性参数$ζ$，可以直接从傅立叶幅度数据计算，并提供了一个衡量所需的相位恢复解决方案的波动。据观察，当开始与均匀随机相位图，Fienup解决方案的复杂性，包含停滞文物稳定在一个数值，这是远远高于$ζ$。我们提出了一种改进的Fienup算法，它使用一个受控的稀疏增强步骤，这样在每次迭代中得到的解决方案的复杂性是明确的接近$ζ$。这种方法，我们称之为复杂性引导相位检索（CGPR）被认为是显着减少收敛到一个有意义的解决方案，并自动解决停滞问题所需的相位检索迭代次数。CGPR方法可以实现迭代相位恢复的新应用，由于可靠的相位恢复所需的大量迭代，这些迭代相位恢复被认为实际上是困难的。
英文摘要：
Iterative phase retrieval methods based on the Gerchberg-Saxton (GS) or Fienup algorithm require a large number of iterations to converge to a meaningful solution. For complex-valued or phase objects, these approaches also suffer from stagnation problems where the solution does not change much from iteration to iteration but the resultant solution shows artifacts such as presence of a twin. We introduce a complexity parameter $ζ$ that can be computed directly from the Fourier magnitude data and provides a measure of fluctuations in the desired phase retrieval solution. It is observed that when initiated with a uniformly random phase map, the complexity of the Fienup solution containing stagnation artifacts stabilizes at a numerical value that is much higher than $ζ$. We propose a modified Fienup algorithm that uses a controlled sparsity enhancing step such that in every iteration the complexity of the resulting solution is explicitly made close to $ζ$. This approach which we refer to as complexity guided phase retrieval (CGPR) is seen to significantly reduce the number of phase retrieval iterations required for convergence to a meaningful solution and automatically addresses the stagnation problems. The CGPR methodology can enable new applications of iterative phase retrieval that are considered practically difficult due to large number of iterations required for a reliable phase recovery.
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