压缩采样在射电天文学中的应用II：法拉第旋转测度综合
The application of compressive sampling to radio astronomy II: Faraday rotation measure synthesis
摘要：
法拉第旋转测度（RM）综合是研究和分析银河系和河外磁场的重要工具。由于法拉第色散函数和偏振无线电发射之间存在傅立叶关系，因此色散函数的完全重建需要了解正方波长和负方波长$λ^2$处的偏振无线电发射。然而，人们只能对$λ^2 > 0$进行观察。此外，只能对有限的波长范围进行观测。因此，从这些有限的测量重构法拉第色散函数是病态的。在本文中，我们提出了三个新的重建算法的RM合成压缩感知/采样（CS）的基础上。这些算法被设计成分别适用于法拉第薄源、厚源和混合源。可视化和数值模拟结果均表明，新的RM合成方法在重建的幅度和相位信息上均优于RM-CLEAN方法
英文摘要：
Faraday rotation measure (RM) synthesis is an important tool to study and analyze galactic and extra-galactic magnetic fields. Since there is a Fourier relation between the Faraday dispersion function and the polarized radio emission, full reconstruction of the dispersion function requires knowledge of the polarized radio emission at both positive and negative square wavelengths $λ^2$. However, one can only make observations for $λ^2 > 0$. Furthermore observations are possible only for a limited range of wavelengths. Thus reconstructing the Faraday dispersion function from these limited measurements is ill-conditioned. In this paper, we propose three new reconstruction algorithms for RM synthesis based upon compressive sensing/sampling (CS). These algorithms are designed to be appropriate for Faraday thin sources only, thick sources only, and mixed sources respectively. Both visual and numerical results show that the new RM synthesis methods provide superior reconstructions of both magnitude and phase information than RM-CLEAN
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