Phaseless inverse scattering problems appear often in practical applications since phaseless data are relatively easier to measure than the phased data, but they are also numerically more difficult to solve due to the translation invariance property. Based on three distinct noisy measurements of phaseless far-field data, the phase information can be approximately reconstructed by formulating it as a single source localization problem, for which many efficient algorithms are readily available. In this paper, we numerically compare several source localization algorithms based on different norm formulations in the context of inverse scattering. As one major contribution, we propose an improved phase retrieval algorithm, which addresses some pitfalls of the original phase retrieval algorithm in [X. Ji, X. Liu, B. Zhang, SIAM J. Imaging Sci. 12 (1) (2019) 372–391.] Moreover, a simple criterion of minimizing the condition number of the underlying linear least square system is advocated for optimizing the choices of scattering strengths (or sensors’ locations). Extensive numerical results are shown to illustrate the similarity and difference among the tested algorithms.

无相逆散射问题在实际应用中经常出现，因为无相数据比有相数据更容易测量，但由于平移不变性，它们在数值上也更难求解。基于对无相远场数据的三个不同噪声测量，可以通过将其表述为单源定位问题来近似重建相位信息，为此可以使用许多有效的算法。在本文中，我们在数值上比较了在逆散射背景下基于不同范数公式的几种源定位算法。作为一个主要贡献，我们提出了一种改进的相位检索算法，它解决了 [X. Ji, X. Liu, B. Zhang, SIAM J. Imaging Sci. 12 (1) (2019) 372–391.] 此外，提倡最小化基础线性最小二乘系统的条件数的简单标准，以优化散射强度（或传感器位置）的选择。大量的数值结果显示了测试算法之间的相似性和差异。