使用Shapard进行反卷积
Deconvolution with Shapelets
摘要：
我们试图找到一个基于shapelet的方案，从PSF的星系图像去卷积，导致无偏剪切测量。基于Shapelet空间中卷积的解析公式，在点扩展函数完全已知的假设下，我们构造了一个恢复未卷积Shapelet系数的过程。使用特定的模拟，我们测试这种方法，并将其与其他已公布的方法进行比较。我们发现，卷积shapelet空间导致一个shapelet模型的顺序$n_{max}^h = n_{max}^g + n_{max}^f$与$n_{max}^f$和$n_{max}^g$是最大的订单的内在星系和PSF模型，分别。因此，去卷积是将一定数量的卷积系数映射到通常较少数量的去卷积系数上的变换。通过从数据中推断后一个数字，我们构造了这种变换的最大似然解，并获得了无偏剪切估计与显着的降噪量相比，建立的方法。这一发现是特别有效的复杂PSF模型和低$S/N$图像，这使得我们的方法适用于典型的弱透镜条件。
英文摘要：
We seek to find a shapelet-based scheme for deconvolving galaxy images from the PSF which leads to unbiased shear measurements. Based on the analytic formulation of convolution in shapelet space, we construct a procedure to recover the unconvolved shapelet coefficients under the assumption that the PSF is perfectly known. Using specific simulations, we test this approach and compare it to other published approaches. We show that convolution in shapelet space leads to a shapelet model of order $n_{max}^h = n_{max}^g + n_{max}^f$ with $n_{max}^f$ and $n_{max}^g$ being the maximum orders of the intrinsic galaxy and the PSF models, respectively. Deconvolution is hence a transformation which maps a certain number of convolved coefficients onto a generally smaller number of deconvolved coefficients. By inferring the latter number from data, we construct the maximum-likelihood solution for this transformation and obtain unbiased shear estimates with a remarkable amount of noise reduction compared to established approaches. This finding is particularly valid for complicated PSF models and low $S/N$ images, which renders our approach suitable for typical weak-lensing conditions.
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