In the problem of compressed phase retrieval, the goal is to reconstruct a sparse or approximately k-sparse vector x ∈ ℂn given access to y = |Φx|, where |v| denotes the vector obtained from taking the absolute value of v ∈ ℂn coordinate-wise. In this paper we present sublinear-time algorithms for a few for-each variants of the compressive phase retrieval problem which are akin to the variants considered for the classical compressive sensing problem in theoretical computer science. Our algorithms use pure combinatorial techniques and near-optimal number of measurements.

中文翻译：

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用于压缩相位检索的次线性时间算法


在压缩相位检索问题中，目标是在给定访问 y = |Φx| 的情况下重建稀疏或近似 k 稀疏向量 x ∈ ℂn，其中 |v|表示对 v ∈ ℂn 坐标取绝对值得到的向量。在本文中，我们提出了压缩相位检索问题的几个 for-each 变体的亚线性时间算法，这些算法类似于理论计算机科学中经典压缩传感问题所考虑的变体。我们的算法使用纯组合技术和接近最佳的测量数量。