We consider the problem of recovering a signal from the magnitudes of affine measurements, which is also known as {\em affine phase retrieval}. In this paper, we formulate affine phase retrieval as an optimization problem and develop a second-order algorithm based on Newton method to solve it. Besides being able to convert into a phase retrieval problem, affine phase retrieval has its unique advantages in its solution. For example, the linear information in the observation makes it possible to solve this problem with second-order algorithms under complex measurements. Another advantage is that our algorithm doesn't have any special requirements for the initial point, while an appropriate initial value is essential for most non-convex phase retrieval algorithms. Starting from zero, our algorithm generates iteration point by Newton method, and we prove that the algorithm can quadratically converge to the true signal without any ambiguity for both Gaussian measurements and CDP measurements. In addition, we also use some numerical simulations to verify the conclusions and to show the effectiveness of the algorithm.
翻译:我们考虑的是从石蜡测量量的大小中恢复信号的问题, 也就是所谓的“ 石蜡阶段回收量 ” 。 在本文中, 我们以优化问题的形式提出“ 石蜡阶段回收”, 并开发基于牛顿方法的二级算法来解决这个问题。 除了能够转换成一个阶段回收问题, 石蜡阶段的回收具有其独特的优势。 例如, 观测中的线性信息使得在复杂的测量条件下用二阶算法解决这个问题成为可能。 另一个好处是, 我们的算法对初始点没有任何特殊要求, 而适当的初始值对于大多数非碳素阶段的检索算法来说是必不可少的。 从零开始, 我们的算法通过牛顿方法产生迭代点, 我们证明算法可以在不含糊高斯测量量和CDP测量结果的情况下, 方形地与真实信号相融合。 此外, 我们还使用一些数字模拟来核实计算结果并显示算法的有效性。