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

@inproceedings{Deledalle2019RefittingSP, 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}, booktitle={SSVM}, year={2019} }

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…

## 2 Citations

Block based refitting in $\ell_{12}$ sparse regularisation

- Engineering
- 2019

In many linear regression problems, including ill-posed inverse problems in image restoration, the data exhibit some sparse structures that can be used to regularize the inversion. To this end, a…

Block-Based Refitting in
$$\ell _{12}$$
ℓ
12
Sparse Regularization

- Computer ScienceJ. Math. Imaging Vis.
- 2021

This work introduces a new penalty that is well suited for refitting purposes and presents a new algorithm to obtain the refitted solution along with the original (biased) solution for any convex refitting block penalty.

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