论文标题
通过量规二元性检索的近似方法
Approximate methods for phase retrieval via gauge duality
论文作者
论文摘要
我们考虑找到一个满足线性方程系统的低等级对称矩阵的问题，如相检索所示。特别是，我们求解了量规对二公式，但是使用光谱计算的快速近似来实现噪声溶液估计。然后，该估计值用作非convex rank-1矩阵分解公式的交替梯度下降方案的初始化。小问题的数值结果显示出一致的恢复，计算成本非常低。
We consider the problem of finding a low rank symmetric matrix satisfying a system of linear equations, as appears in phase retrieval. In particular, we solve the gauge dual formulation, but use a fast approximation of the spectral computations to achieve a noisy solution estimate. This estimate is then used as the initialization of an alternating gradient descent scheme over a nonconvex rank-1 matrix factorization formulation. Numerical results on small problems show consistent recovery, with very low computational cost.
