Fundamental limits of phasemax for phase retrieval: A replica analysis
Fundamental limits of phasemax for phase retrieval: A replica analysis
复制标题
DOI：
10.1109/camsap.2017.8313210
复制
发表时间：
2017-08
期刊：
影响因子：
--
通讯作者：
Oussama Dhifallah;Yue M. Lu
中科院分区：
文献类型：
--
作者：
Oussama Dhifallah;Yue M. Lu
我们考虑最近提出的一种解决相位恢复问题的凸公式，称为PhaseMax方法。利用统计力学中的复制方法，分析了PhaseMax算法在高维极限下的性能。我们的分析预测了PhaseMax的精确渐近性能。特别地，我们发现了一个尖锐的相变现象，用一个简单的解析式描述了相变边界。这一结果表明，文献中现有性能界限所要求的过采样率可以进一步降低。数值结果证实了复制分析的有效性，表明理论预测与算法的实际性能非常吻合，即使在中等信号维度的情况下也是如此。
We consider a recently proposed convex formulation, known as the PhaseMax method, for solving the phase retrieval problem. Using the replica method from statistical mechanics, we analyze the performance of PhaseMax in the high-dimensional limit. Our analysis predicts the exact asymptotic performance of PhaseMax. In particular, we show that a sharp phase transition phenomenon takes place, with a simple analytical formula characterizing the phase transition boundary. This result shows that the oversampling ratio required by existing performance bounds in the literature can be further reduced. Numerical results confirm the validity of our replica analysis, showing that the theoretical predictions are in excellent agreement with the actual performance of the algorithm, even for moderate signal dimensions.