A Spectral Estimation Framework for Phase Retrieval via Bregman Divergence Minimization
A Spectral Estimation Framework for Phase Retrieval via Bregman Divergence Minimization
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DOI：
10.1137/20m1388061
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发表时间：
2020-12
期刊：
影响因子：
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通讯作者：
Bariscan Yonel;B. Yazıcı
中科院分区：
文献类型：
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作者：
Bariscan Yonel;B. Yazıcı
在这篇文章中，我们提出了一个新的框架，以优化设计的频谱估计器的相位恢复给定的测量实现从一个任意的模型。我们从解构光谱方法开始，找出内在地促进估计准确性的基本机制。然后，我们提出了谱估计的一般形式，即在提升前向模型的范围内近似Bregman损失最小化，该模型可以通过在秩1，PSD矩阵上的搜索来处理。本质上，通过Bregman损失方法，我们超越了基于欧几里得意义排列的无相度量之间的相似性度量，而倾向于在$\mathbb{R}^M_+$上适当的发散度量。为此，我们导出了谱方法，通过使用元素样本化处理函数来近似最小化KL-散度和无相测量上的Itakura-Saito距离。因此，我们的公式将文献中关于最优样本处理函数的模型相关设计的现有结果联系并推广到模型无关的最优性意义上。数值模拟证实了该方法在合成数据集和真实数据集下的有效性。
In this paper, we develop a novel framework to optimally design spectral estimators for phase retrieval given measurements realized from an arbitrary model. We begin by deconstructing spectral methods, and identify the fundamental mechanisms that inherently promote the accuracy of estimates. We then propose a general formalism for spectral estimation as approximate Bregman loss minimization in the range of the lifted forward model that is tractable by a search over rank-1, PSD matrices. Essentially, by the Bregman loss approach we transcend the Euclidean sense alignment based similarity measure between phaseless measurements in favor of appropriate divergence metrics over $\mathbb{R}^M_+$. To this end, we derive spectral methods that perform approximate minimization of KL-divergence, and the Itakura-Saito distance over phaseless measurements by using element-wise sample processing functions. As a result, our formulation relates and extends existing results on model dependent design of optimal sample processing functions in the literature to a model independent sense of optimality. Numerical simulations confirm the effectiveness of our approach in problem settings under synthetic and real data sets.