Abstract. Clean is a matching pursuit process which has two weak points: in situations of astrophysical interest, the "clean map" is not stable in the corresponding object representation space, and the "atoms" of this representation (translated versions of the "clean beam") are not well suited for reconstructing the boundaries of the structuring entities of the object at the related resolution level. As a result, Clean must be interrupted before the best possible fit is reached. How does Wipe wipe Clean clean? First, by introducing a global regularization principle 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.

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