Refitting Solutions Promoted by ℓ _12 Sparse Analysis Regularizations with Block Penalties

  title={Refitting Solutions Promoted by ℓ \_12 Sparse Analysis Regularizations with Block Penalties},
  author={Charles-Alban Deledalle and Nicolas Papadakis and Joseph Salmon and Samuel Vaiter},
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… 

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