Volume 620, December 2018
|Number of page(s)||10|
|Section||Numerical methods and codes|
|Published online||11 December 2018|
Synthetic direct demodulation method and its applications in Insight-HXMT data analysis⋆
1 Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology, Beijing, 100094, PR China
2 Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
3 Leibniz Institute for Solid State and Materials Research, IFW Dresden, 01069 Dresden, Germany
4 Tsinghua Center for Astrophysics, Department of Physics, Tsinghua University, Beijing, 100084, PR China
Accepted: 21 August 2018
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 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.
Key words: methods: data analysis / methods: numerical / techniques: image processing / X-rays: general
© ESO 2018
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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