  Multi-scale deconvolution is an ill-posed inverse problem in imaging, with
applications ranging from microscopy, through medical imaging, to astronomical
remote sensing. In the case of high-energy space telescopes, multi-scale
deconvolution algorithms need to account for the peculiar property of native
measurements, which are sparse samples of the Fourier transform of the incoming
radiation. The present paper proposes a multi-scale version of CLEAN, which is
the most popular iterative deconvolution method in Fourier space imaging. Using
synthetic data generated according to a simulated but realistic source
configuration, we show that this multi-scale version of CLEAN performs better
than the original one in terms of accuracy, photometry, and regularization.
Further, the application to a data set measured by the NASA Reuven Ramaty High
Energy Solar Spectroscopic Imager (RHESSI) shows the ability of multi-scale
CLEAN to reconstruct rather complex topographies, characteristic of a real
flaring event.
