  We present a new method of removing PSF artifacts and improving the
resolution of multidimensional data sources including imagers and
spectrographs. Rather than deconvolution, which is translationally invariant,
this method is based on sparse matrix solvers. This allows it to be applied to
spatially varying PSFs and also to combining observations from instruments with
radically different spatial, spectral, or thermal response functions (e.g.,
SDO/AIA and RHESSI). It was developed to correct PSF artifacts in Solar Orbiter
SPICE, so the motivation, presentation of the method, and the results revolve
around that application. However, it can also be used as a more robust (e.g.,
WRT a varying PSFs) alternative to deconvolution of 2D image data and similar
problems, and is relevant to more general linear inversion problems.
