Phase retrieval via smoothed amplitude flow
Phase retrieval via smoothed amplitude flow
复制标题
通过平滑幅度流进行相位检索
DOI：
10.1016/j.sigpro.2020.107719
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Shijian Lin
中科院分区：
文献类型：
--
作者：
Qi Luo;Hongxia Wang;Shijian Lin
相位恢复（PR）是从无相线性测量中恢复信号的逆问题。这个问题可以通过最小化基于非凸幅度的损失函数来有效解决。然而，这个损失函数是非平滑的。为了解决非平滑问题，人们提出了一系列方法，通过添加截断、重新加权和平滑操作来调整梯度或损失函数，并取得了更好的性能。但这些操作带来了额外的规则和参数，需要仔细设计。与之前的工作不同，我们提出了一种平滑幅度流（SAF）方法，该方法引入了一种新颖的平滑损失函数，以避免在梯度下降阶段检查和修改梯度分量。这种新颖的损失函数可以被视为原始基于幅度的损失函数的平滑版本。我们证明了 SAF 通过梯度算法以高概率通过精心设计的初始化阶段几何收敛到全局最优点。大量的数值测试经验表明，所提出的损失函数明显优于原始的基于幅度的损失函数。 SAF 在恢复率和收敛速度方面也优于其他最先进的方法。
Phase retrieval (PR) is an inverse problem about recovering a signal from phaseless linear measurements. This problem can be efficiently solved by minimizing a nonconvex amplitude-based loss function. However, this loss function is nonsmooth. To address the nonsmoothness, a series of methods have been proposed by adding truncating, reweighting and smoothing operations to adjust the gradient or the loss function and achieved better performance. But these operations bring about extra rules and parameters that need to be carefully designed. Unlike previous works, we present a smoothed amplitude flow (SAF) method which introduces a novel smooth loss function so as to avoid checking and modifying the gradient components in the gradient descent stage. This novel loss function can be regarded as a smoothed version of the original amplitude-based loss function. We prove that SAF converges geometrically to a global optimal point via the gradient algorithm with an elaborate initialization stage with high probability. Substantial numerical tests empirically illustrate that the proposed loss function is significantly superior to the original amplitude-based loss function. SAF also outperforms other state-of-the-art methods in terms of the recovery rate and the converging speed.
影响因子：
3
作者：
Cong Ma;Kaizheng Wang;Yuejie Chi;Yuxin Chen
通讯作者：
Cong Ma;Kaizheng Wang;Yuejie Chi;Yuxin Chen
影响因子：
2.5
作者：
Goldstein, Tom;Studer, Christoph
通讯作者：
Studer, Christoph
影响因子：
5.4
作者：
G. Wang;G. Giannakis;Y. Saad;Jie Chen
通讯作者：
G. Wang;G. Giannakis;Y. Saad;Jie Chen