2019/03/02 by Charles‐Alban Deledalle, Nicolas Papadakis, Deledalle, Charles-Alban +5
Engineering · Mathematics · #FOS: Electrical engineering #FOS: Mathematics #Image and Video Processing (eess.IV) #Numerical methods in inverse problems #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1903.00741
openalex publication_date 2019/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In inverse problems, the use of an \ℓ12 analysis regularizer induces a\nbias in the estimated solution. We propose a general refitting framework for\nremoving this artifact while keeping information of interest contained in the\nbiased solution. This is done through the use of refitting block penalties that\nonly act on the co-support of the estimation. Based on an analysis of related\nworks in the literature, we propose a new penalty that is well suited for\nrefitting purposes. We also present an efficient algorithmic method to obtain\nthe refitted solution along with the original (biased) solution for any convex\nrefitting block penalty. Experiments illustrate the good behavior of the\nproposed block penalty for refitting.\n