论文标题
仿射相检索的强凸度
Strong convexity of affine phase retrieval
论文作者
论文摘要
从强度测量值中恢复信号的某些条目被称为{\ em仿射相检索}。在本文中，我们证明，在某些温和条件下，在整个空间上，天然最小二乘的配方在整个空间上强烈凸出，前提是测量值是复杂的高斯随机vecotrs，并且测量数$ m \ gtrsim d \ log d \ log d $ d $ d $ d $ d $ d $是信号的尺寸。基于结果，我们证明了仿射相检索的简单梯度下降方法线性收敛到目标解，从任意初始点起很高的可能性。这些结果表明，仿射相的检索与经典相位检索之间有一个本质差异，其中经典相位检索的最小二乘配方是非凸。
The recovery of a signal from the intensity measurements with some entries being known in advance is termed as {\em affine phase retrieval}. In this paper, we prove that a natural least squares formulation for the affine phase retrieval is strongly convex on the entire space under some mild conditions, provided the measurements are complex Gaussian random vecotrs and the measurement number $m \gtrsim d \log d$ where $d$ is the dimension of signals. Based on the result, we prove that the simple gradient descent method for the affine phase retrieval converges linearly to the target solution with high probability from an arbitrary initial point. These results show an essential difference between the affine phase retrieval and the classical phase retrieval, where the least squares formulations for the classical phase retrieval are non-convex.
