Richardson-Lucy deconvolution with a spatially Variant point-spread function of Chandra: Supernova Remnant Cassiopeia A as an Example

Richardson-Lucy (RL) deconvolution is one of the classical methods widely used in X-ray astronomy and other areas. Amid recent progress in image processing, RL deconvolution still leaves much room for improvement under a realistic situations. One direction is to include the positional dependence of a point-spread function (PSF), so-called RL deconvolution with a spatially variant PSF (RL$_{\rm{sv}}$). Another is the method of estimating a reliable number of iterations and their associated uncertainties. We developed a practical method that incorporates the RL$_{\rm{sv}}$ algorithm and the estimation of uncertainties. As a typical example of bright and high-resolution images, the Chandra X-ray image of the supernova remnant Cassiopeia~A was used in this paper. RL$_{\rm{sv}}$ deconvolution enables us to uncover the smeared features in the forward/backward shocks and jet-like structures. We constructed a method to predict the appropriate number of iterations by using statistical fluctuation of the observed images. Furthermore, the uncertainties were estimated by error propagation from the last iteration, which was phenomenologically tested with the observed data. Thus, our method is a practically efficient framework to evaluate the time evolution of the remnants and their fine structures embedded in high-resolution X-ray images.