Synthetic direct demodulation method and its applications in Insight-HXMT data analysis

TL;DR

The paper introduces the synthetic direct demodulation (synDD) method, which reduces computational complexity in solving modulation equations for X-ray data analysis, enabling efficient detection of transients and variable objects in Insight-HXMT observations.

Contribution

The synDD method reduces the dimensionality of modulation equations using PCA and clustering, improving efficiency in analyzing Insight-HXMT data for transient detection.

Findings

Reduces matrix multiplication complexity from polynomial to linear-logarithmic time.

Enables simultaneous analysis of multiple datasets from different epochs and instruments.

Improves detection of X-ray transients and monitoring of variable objects.

Abstract

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.