This paper introduces a multiscale maximum entropy (MSME) algorithm for image restoration of the Hard X-ray Modulation Telescope (HXMT), which is a collimated scan X-ray satellite mainly devoted to a sensitive all-sky survey and pointed observation in 1-250 keV. The novelty of the MSME method is to use wavelet decomposition and multiresolution support to control noise amplification in the different scales. And our work is focused on the application and modification of this method to restore diffuse sources detected by HXMT scanning observation. And an improved method, ensemble multiscale maximum entropy (EMSME) algorithm, is proposed to alleviate the problem of mode mixing exiting in MSME. Simulation have been performed on the detection of the diffuse source Cen A by HXMT in the all-sky survey mode. The results show that the MSME method is adapted to the deconvolution task of HXMT for diffuse source detection and the improved method could suppress noise and improve the correlation and signal-to-noise ratio, thus proving itself a better algorithm for image restoration. Through one all-sky survey, HXMT could reach a capacity of detecting a diffuse source with maximum differential flux of 0.5 mCrab.
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