... Determine the net instrument response desired. ... Use a numerical algorithm, the convolution network (discussed in detail below), to search for the solution that provides the desired mapping of the observed data to the desired form. ... We first made preliminary studies investigating recovery of images that have been broadened by the HST's mirror by modeling its PSF as shown in Fig. ... Our recovery procedure was applied also to spectral data, in this case to a tunable diode laser (TDL) spectrum. ...