  In inverse problems, the use of an $\ell_{12}$ analysis regularizer induces a
bias in the estimated solution. We propose a general refitting framework for
removing this artifact while keeping information of interest contained in the
biased solution. This is done through the use of refitting block penalties that
only act on the co-support of the estimation. Based on an analysis of related
works in the literature, we propose a new penalty that is well suited for
refitting purposes. We also present an efficient algorithmic method to obtain
the refitted solution along with the original (biased) solution for any convex
refitting block penalty. Experiments illustrate the good behavior of the
proposed block penalty for refitting.
