CLEAN is a matching pursuit process which has two weak points: in situ
ations of astrophysical interest, the ''clean map'' is not stable in t
he corresponding object representation space, and the ''atoms'' of thi
s representation (translated versions of the ''clean beam'') are not w
ell suited for reconstructing the boundaries of the structuring entiti
es of the object at the related resolution level. As a result, CLEAN m
ust be interrupted before the best possible fit is reached. How does W
IPE wipe CLEAN clean? First, by introducing a global regularization pr
inciple based on the concept of resolution; and second, by conducting
the matching pursuit process at the level of the high-resolution basis
functions of the object space.