PhaseMax: Convex Phase Retrieval via Basis Pursuit
PhaseMax: Convex Phase Retrieval via Basis Pursuit
复制标题
DOI：
10.1109/tit.2018.2800768
复制
发表时间：
2018-04-01
影响因子：
2.5
通讯作者：
Studer, Christoph
中科院分区：
文献类型：
--
作者：
Goldstein, Tom;Studer, Christoph
我们认为恢复（实值或复值）信号的幅度只有测量，称为相位恢复。我们制定相位恢复作为一个凸优化问题，我们称之为PhaseMax。与使用半定松弛并将相位恢复问题提升到更高维度的其他凸方法不同，PhaseMax是在原始信号维度中操作的“非提升”松弛。我们表明，对偶问题的PhaseMax是基础的追求，这意味着可以使用最初设计用于稀疏信号恢复的算法进行相位恢复。我们开发了一个广泛的随机测量合奏的成功概率的PhaseMax急剧下界，我们分析了测量噪声对解决方案的精度的影响。我们使用数值结果来证明我们的恢复保证的准确性，并展示了PhaseMax在实践中的有效性和局限性。
We consider the recovery of a (real-or complex-valued) signal from magnitude-only measurements, known as phase retrieval. We formulate phase retrieval as a convex optimization problem, which we call PhaseMax. Unlike other convex methods that use semidefinite relaxation and lift the phase retrieval problem to a higher dimension, PhaseMax is a "non-lifting" relaxation that operates in the original signal dimension. We show that the dual problem to PhaseMax is basis pursuit, which implies that the phase retrieval can be performed using algorithms initially designed for sparse signal recovery. We develop sharp lower bounds on the success probability of PhaseMax for a broad range of random measurement ensembles, and we analyze the impact of measurement noise on the solution accuracy. We use numerical results to demonstrate the accuracy of our recovery guarantees, and we showcase the efficacy and limits of PhaseMax in practice.