非常棘手的Lenser：探索正则化在使用高斯过程回归的源和潜在重建中的作用
The Very Knotty Lenser: exploring the role of regularization in source and potential reconstructions using Gaussian Process Regression
摘要：
重建透镜的潜力和透镜源可以很容易地成为一个约束不足的问题，即使当自由度低，由于退化，特别是当潜在的扰动叠加在一个光滑的透镜包括在内。正则化传统上用于约束数据未能这样做的解决方案，例如在源的非透镜部分。在这项探索性工作中，我们超越了通常的正则化选择，并采用了源亮度的观测驱动先验。我们还进行了类似的比较时，重建透镜潜在的扰动，这被假定为是固定的，即渗透到整个视场。我们发现，物理动机的先验会导致较低的残差，避免过拟合，并在贝叶斯定量框架内的所有考虑的例子中是决定性的首选。对于扰动，选择错误的正则化可能会产生有害影响，即使是高质量的数据也无法校正，而使用纯光滑透镜模型可以在很大程度上吸收它们并导致有偏差的解决方案。最后，我们的新实现的半线性反演技术提供了第一个定量的框架来测量源和潜在的扰动之间的简并。
英文摘要：
Reconstructing lens potentials and lensed sources can easily become an underconstrained problem, even when the degrees of freedom are low, due to degeneracies, particularly when potential perturbations superimposed on a smooth lens are included. Regularization has traditionally been used to constrain the solutions where the data failed to do so, e.g. in unlensed parts of the source. In this exploratory work, we go beyond the usual choices of regularization and adopt observationally motivated priors for the source brightness. We also perform a similar comparison when reconstructing lens potential perturbations, which are assumed to be stationary, i.e. permeate the entire field of view. We find that physically motivated priors lead to lower residuals, avoid overfitting, and are decisively preferred within a Bayesian quantitative framework in all the examples considered. For the perturbations, choosing the wrong regularization can have a detrimental effect that even high-quality data cannot correct for, while using a purely smooth lens model can absorb them to a very high degree and lead to biased solutions. Finally, our new implementation of the semi-linear inversion technique provides the first quantitative framework for measuring degeneracies between the source and the potential perturbations.
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