利用复学生t分布和Wirtinger导数进行射电干涉校准
Radio Interferometric Calibration Using a Complex Student's t-distribution and Wirtinger Derivatives
摘要：
不完整的天空模型和射频干扰会使无线电干涉测量增益校准产生偏差，从而导致校准伪影，这会限制所得到的图像的动态范围。有人建议，采用重尾似然函数的校准算法不太容易受到这种影响，因为它们对数据中的离群值具有鲁棒性。我们提出了一种算法的基础上，学生的t分布，利用复杂的优化和Wirtinger演算的框架，有效和强大的干涉增益校准。我们将此算法作为一个选项集成在新发布的校准软件包CubiCal中。我们证明，该算法可以减轻不完整的天空模型和射频干扰引入的一些偏见，通过将其应用到模拟和真实数据。我们的研究结果表明显着的改进相比，传统的最小二乘求解器，假设高斯似然函数。此外，我们提供了一些见解，为什么该算法优于传统的求解器，并讨论具体的情况下（方向无关和方向相关的自校准），这是预期的情况。
英文摘要：
Radio interferometric gain calibration can be biased by incomplete sky models and radio frequency interference, resulting in calibration artefacts that can restrict the dynamic range of the resulting images. It has been suggested that calibration algorithms employing heavy-tailed likelihood functions are less susceptible to this due to their robustness against outliers in the data. We present an algorithm based on a Student's t-distribution which leverages the framework of complex optimisation and Wirtinger calculus for efficient and robust interferometric gain calibration. We integrate this algorithm as an option in the newly released calibration software package, CubiCal. We demonstrate that the algorithm can mitigate some of the biases introduced by incomplete sky models and radio frequency interference by applying it to both simulated and real data. Our results show significant improvements compared to a conventional least-squares solver which assumes a Gaussian likelihood function. Furthermore, we provide some insight into why the algorithm outperforms the conventional solver, and discuss specific scenarios (for both direction-independent and direction-dependent self-calibration) where this is expected to be the case.
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