论文标题
通过Bregman Divergence最小化的相位检索的光谱估计框架
A Spectral Estimation Framework for Phase Retrieval via Bregman Divergence Minimization
论文作者
论文摘要
在本文中，我们开发了一个新颖的框架，以最佳的设计光谱估计量，用于从任意模型中实现的测量值。我们首先解构光谱方法，并确定固有地促进估计准确性的基本机制。然后，我们提出了一种频谱估计的一般形式主义，因为近似Bregman的损失最小化在提升的正向模型的范围内，该模型可以通过搜索rank-1，PSD矩阵进行搜索。从本质上讲，通过Bregman损失方法，我们超越了欧几里得意识对准的相似性度量，在无量音测量之间，有利于$ \ Mathbb {r}^m _+$的适当差异指标。为此，我们得出了通过使用元素的样品处理函数来实现KL差异近似最小化的光谱方法，并且在无音测量的情况下进行了iTakura-Saito距离。结果，我们的公式将文献中最佳样本处理功能的模型依赖性设计关联并扩展到了独立的最佳意义。数值模拟证实了我们在综合和真实数据集中问题设置中方法的有效性。
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.
