论文标题
仿射相通过二阶方法检索
Affine Phase Retrieval via Second-Order Methods
论文作者
论文摘要
在本文中，我们研究了仿射期检索问题，该问题旨在从仿射测量的幅度中恢复信号。我们基于牛顿和高斯 - 纽顿迭代的二阶优化方法开发了二阶优化方法，并确定在特定的先验条件下，该问题表现出很强的凸度。从理论上讲，我们证明具有重采样的牛顿方法在无噪声设置中实现了高斯测量和可接受的编码衍射模式（CDP）的全局二次收敛。此外，我们证明了相同的理论框架自然扩展到高斯 - 纽顿方法，这意味着其二次收敛。为了验证我们的理论发现，我们进行了广泛的数值实验。结果证实了二阶方法的二次收敛，而其计算效率仍然与一阶方法相媲美。此外，我们的实验表明，二阶方法可以通过相对较少的测量来实现精确的恢复，从而突出了它们的实际可行性和鲁棒性。
In this paper, we study the affine phase retrieval problem, which aims to recover signals from the magnitudes of affine measurements. We develop second-order optimization methods based on Newton and Gauss-Newton iterations and establish that, under specific a priori conditions, the problem exhibits strong convexity. Theoretically, we prove that the Newton method with resampling achieves global quadratic convergence in the noiseless setting for both Gaussian measurements and admissible coded diffraction patterns (CDPs). Furthermore, we demonstrate that the same theoretical framework naturally extends to the Gauss-Newton method, implying its quadratic convergence. To validate our theoretical findings, we conduct extensive numerical experiments. The results confirm the quadratic convergence of second-order methods, while their computational efficiency remains comparable to that of first-order methods. Additionally, our experiments demonstrate that second-order methods achieve exact recovery with relatively few measurements, highlighting their practical feasibility and robustness.
