参数不确定信息场论中未知谱信号的重构
Reconstruction of signals with unknown spectra in information field theory with parameter uncertainty
摘要：
宇宙度规扰动和其他信号的最佳重建需要知道它们的功率谱和其他参数。如果这些不是先验已知的，则必须从用于信号重建的相同数据同时测量它们。在信息场论的框架内，我们制定了存在未知参数的信号推理的一般问题。我们开发了一个通用的参数不确定性重整化估计（PURE）技术，并解决了重建高斯信号与未知功率谱的问题，有五种不同的方法：（i）单独的最大后验功率谱测量和随后的重构，（ii）具有边缘化功率谱的最大后验功率重构，（iii）最大化信号和谱的联合后验，（iv）从维纳滤波器映射中的方差猜测频谱，以及（v）提供PURE滤波器的场论问题的重整化流分析。在所有情况下，重建可以被描述或近似为维纳滤波器操作，其中假定的信号频谱根据相同的配方从数据导出，但具有不同的系数。所有这些过滤器，除了重整化的一个，表现出感知阈值的情况下，Jeffreys之前的未知光谱。方差低于该阈值的数据模式根本不影响信号重构。过滤器（iv）似乎是类似于所谓的Karhune-Loeve和Feldman-Kaiser-Peacock估计的星系功率谱在宇宙学中使用，因此也应该表现出一个边际感知阈值，如果正确实施。我们提出了统计性能测试，并表明，纯过滤器是优于其他。
英文摘要：
The optimal reconstruction of cosmic metric perturbations and other signals requires knowledge of their power spectra and other parameters. If these are not known a priori, they have to be measured simultaneously from the same data used for the signal reconstruction. We formulate the general problem of signal inference in the presence of unknown parameters within the framework of information field theory. We develop a generic parameter uncertainty renormalized estimation (PURE) technique and address the problem of reconstructing Gaussian signals with unknown power-spectrum with five different approaches: (i) separate maximum-a-posteriori power spectrum measurement and subsequent reconstruction, (ii) maximum-a-posteriori power reconstruction with marginalized power-spectrum, (iii) maximizing the joint posterior of signal and spectrum, (iv) guessing the spectrum from the variance in the Wiener filter map, and (v) renormalization flow analysis of the field theoretical problem providing the PURE filter. In all cases, the reconstruction can be described or approximated as Wiener filter operations with assumed signal spectra derived from the data according to the same recipe, but with differing coefficients. All of these filters, except the renormalized one, exhibit a perception threshold in case of a Jeffreys prior for the unknown spectrum. Data modes, with variance below this threshold do not affect the signal reconstruction at all. Filter (iv) seems to be similar to the so called Karhune-Loeve and Feldman-Kaiser-Peacock estimators for galaxy power spectra used in cosmology, which therefore should also exhibit a marginal perception threshold if correctly implemented. We present statistical performance tests and show that the PURE filter is superior to the others.
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