论文标题
非常打结的镜头：使用高斯过程回归探索正则化在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
论文作者
论文摘要
重建晶状体电位和镜头源很容易成为一个不受限制的问题，即使自由度较低，由于变性，尤其是当包括在光滑的镜头上叠加到平滑镜头上的潜在扰动时。传统上，正则化已被用来限制数据未能做到的解决方案，例如在源的未保证部分中。在这项探索性工作中，我们超越了正规化的通常选择，并采用了以观察动机的先验来亮度。当重建晶状体电势扰动时，我们还进行了类似的比较，该镜头的扰动被认为是固定的，即渗透到整个视野。我们发现，在所有考虑的示例中，在贝叶斯定量框架内，在贝叶斯定量框架内毫无疑问地优选了出于身体动机的先验，避免过度拟合。对于扰动，选择错误的正则化可能会产生有害的效果，即使高质量的数据也无法纠正，而使用纯光滑的透镜模型可以将它们吸收到很高的程度并导致偏置溶液。最后，我们对半线性反演技术的新实现为测量源与潜在扰动之间的脱糖性提供了第一个定量框架。
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.
