综合直接解调法及其在Insight-HXMT数据分析中的应用
Synthetic direct demodulation method and its applications in Insight-HXMT data analysis
摘要：
目的。调制方程将观测数据与对象联系起来，其中观测值由线性系统近似。因此，从观测数据重建物体相当于求解调制方程。在这项工作中，我们提出了合成直接解调（synDD）的方法来降低一般调制方程的维数，并解决其稀疏表示的方程。方法.主成分分析用于降低核矩阵的维数，k-均值聚类应用于其稀疏表示，以将核矩阵分解为一系列循环矩阵的加权和。因此，矩阵-向量和矩阵-矩阵乘法的复杂性从多项式时间减少到线性对数时间。本文导出了稀疏表示下调制方程的一般统计解。针对硬X射线调制望远镜（Insight-HXMT）设计了基于synDD方法的数据分析流水线。结果在这种方法中，可以在合成观测模型中同时减少来自同一物体但不规则采样和/或在多个时期用不同仪器观测的大量数据。我们建议在Insight-HXMT数据分析中使用所提出的synDD方法，特别是用于检测X射线瞬变和监测具有扫描观测的时变对象。
英文摘要：
Aims. A modulation equation relates the observed data to the object where the observation is approximated by a linear system. Reconstructing the object from the observed data is therefore is equivalent to solving the modulation equation. In this work we present the synthetic direct demodulation (synDD) method to reduce the dimensionality of a general modulation equation and solve the equation in its sparse representation. Methods. A principal component analysis is used to reduce the dimensionality of the kernel matrix and k-means clustering is applied to its sparse representation in order to decompose the kernel matrix into a weighted sum of a series of circulant matrices. The matrix- vector and matrix-matrix multiplication complexities are therefore reduced from polynomial time to linear-logarithmic time. A general statistical solution of the modulation equation in sparse representation is derived. Several data-analysis pipelines are designed for the Hard X-ray modulation Telescope (Insight-HXMT) based on the synDD method. Results. In this approach, a large set of data originating from the same object but sampled irregularly and/or observed with different instruments in multiple epochs can be reduced simultaneously in a synthetic observation model. We suggest using the proposed synDD method in Insight-HXMT data analysis especially for the detection of X-ray transients and monitoring time-varying objects with scanning observations.
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