An iterative method to deconvolve coded-mask images

Efficent astronomical imaging at energy greater than 20 keV is mainly achieved through modulation, either time (i.e. HXMT) or spatial (i.e. IBIS/INTEGRAL), techniques. Currently, the coded mask technique is widely used with the true spatial intensity distribution reconstructed from the data by the cross-correlation (CC) method. As the sensitivity of instruments increases, so must the angular resolution in order to avoid problems with source confusion. The IBIS 12’ angular resolution is clearly not sufficient to distinguish all the sources in the crowded field of the Galactic Centre. One possibility to overcome this problem is to change the deconvolution method. The objective of this thesis is to evaluate the real imaging capability of the Direct Demodulation (DD) method. It deconvolves incomplete and noisy data by iteratively solving the image formation equation under physical constraints. With the goal of exploiting the DD technique, in the early of the 1990s the HXMT mission was designed, where the imaging capability is obtained through the temporal modulation of the detected counts by a set of mechanical collimators. To achieve this goal, we developed the Lucy-Richardson (LR) code to reconstruct directly hard-X/soft- ray images. It assumes that the data and the noise follow a Poisson distribution and it guarantees the non-negativity of the restored images. For the moment, any kind of regularization or constraint was implemented in the underlying optimization problem, so this will be ill-posed yet. Due to the general nature of the DD and the fact that HXMT has still to fly, the IBIS/INTEGRAL data and its PSF were used to check our own code. The pure geometrical PSF considering only the effects due to the photon propagation from the mask to the detector was created. Our CC code implements the same balanced cross-correlation as the standard software for IBIS/INTEGRAL analysis. The CC deconvolved images are the reference for the image quality obtained with the LR. The great improvement in the theoretical angular resolution and location precision is evident. It is independent on the source position in the total FOV, the iteration number and the source flux. Within the parameters of the simulations used, the LR statistical uncertainty was found to be a factor of 10 smaller than that obtained with the CC. Furthermore, the LR deconvolved images have less fluctuating reconstructed background. The main LR drawback is the flux evaluation of the reconstructed source. It is mainly due to the choice of the correct iteration number. The use of a-priori information about the unknown object allows a complete regularization of the problem, so probably solving the problem with the flux estimation. Keywords: Coded-mask, Lucy, Richardson, INTEGRAL, IBIS