Phase Retrieval by Binary Questions: Which Complementary Subspace is Closer?
Phase Retrieval by Binary Questions: Which Complementary Subspace is Closer?
复制标题
通过二元问题进行相位检索：哪个互补子空间更接近？
DOI：
10.1007/s00365-022-09582-5
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发表时间：
2022
影响因子：
2.7
通讯作者：
Bodmann, Bernhard G.
中科院分区：
文献类型：
--
作者：
Domel-White, Dylan;Bodmann, Bernhard G.
在实或复希尔伯特空间中，相位恢复的任务是从线性测量的量中恢复一个矢量，直到一个整体的单模乘法常数。在本文中，我们假设向量是归一化的，但通过与阈值进行比较，只保留有关测量值的定性二进制信息。在更具体的几何术语中，我们在实希尔伯特空间或复希尔伯特空间中选择一个子空间序列，并且只记录给定向量是否更接近子空间而不是互补子空间。子空间的维数是希尔伯特空间的一半，并且相对于正交群或酉群的作用是独立的、均匀分布的。本文的主要目标是根据这些二值问题所获得的向量信息，找到一种可行的近似恢复算法，并建立其近似恢复的误差范围。我们为固定的输入向量提供了一个点向边界和一个统一的边界来控制所有输入中的最坏情况。对于子空间的选择，这两个边界都有高概率成立。对于维数为n的实向量或复向量，点向边界要求一致的边界问题，以达到的精度。精度由归一化输入向量对应的秩一正交投影与其近似恢复之间的差的算子范数来衡量。
Phase retrieval in real or complex Hilbert spaces is the task of recovering a vector, up to an overall unimodular multiplicative constant, from magnitudes of linear measurements. In this paper, we assume that the vector is normalized, but retain only qualitative, binary information about the measured magnitudes by comparing them with a threshold. In more specific, geometric terms, we choose a sequence of subspaces in a real or complex Hilbert space and only record whether a given vector is closer to the subspace than to the complementary subspace. The subspaces have half the dimension of the Hilbert space and are independent, uniformly distributed with respect to the action of the orthogonal or unitary groups. The main goal of this paper is to find a feasible algorithm for approximate recovery based on the information gained about the vector from these binary questions and to establish error bounds for its approximate recovery. We provide a pointwise bound for fixed input vectors and a uniform bound that controls the worst-case scenario among all inputs. Both bounds hold with high probability with respect to the choice of the subspaces. For real or complex vectors of dimensionn, the pointwise bound requiresand the uniform boundbinary questions in order to achieve an accuracy of. The accuracyis measured by the operator norm of the difference between the rank-one orthogonal projections corresponding to the normalized input vector and its approximate recovery.
通过向量和投影进行相位检索
DOI：
10.1090/conm/626/12501
发表时间：
2013
期刊：
arXiv: Functional Analysis
影响因子：
--
作者：
P. Casazza
通讯作者：
P. Casazza
影响因子：
--
作者：
BLOCH, F
通讯作者：
BLOCH, F