Given a linear system in a real or complex domain, linear regression aims to
recover the model parameters from a set of observations. Recent studies in
compressive sensing have successfully shown that under certain conditions, a
linear program, namely, l1-minimization, guarantees recovery of sparse
parameter signals even when the system is underdetermined. In this paper, we
consider a more challenging problem: when the phase of the output measurements
from a linear system is omitted. Using a lifting technique, we show that even
though the phase information is missing, the sparse signal can be recovered
exactly by solving a simple semidefinite program when the sampling rate is
sufficiently high, albeit the exact solutions to both sparse signal recovery
and phase retrieval are combinatorial. The results extend the type of
applications that compressive sensing can be applied to those where only output
magnitudes can be observed. We demonstrate the accuracy of the algorithms
through theoretical analysis, extensive simulations and a practical experiment.

本文研究了在输出测量值缺失相位信息的情况下，如何使用半定规划精确恢复稀疏信号。我们通过提出的升维技术，证明了只需采样频率足够高，即可通过求解简单的半定规划来恢复稀疏信号，从而扩展压缩感知技术的应用范围。