期刊
SIAM JOURNAL ON IMAGING SCIENCES
卷 10, 期 1, 页码 243-284出版社
SIAM PUBLICATIONS
DOI: 10.1137/16M1080318
关键词
inverse problems; variational methods; refitting; twicing; boosting; debiasing
类别
资金
- Information, Signal, Image et viSion [GDR 720 ISIS]
- French State [ANR-10-IDEX-03-02]
In this paper, we propose a new framework to remove parts of the systematic errors affecting popular restoration algorithms, with a special focus for image processing tasks. Generalizing ideas that emerged for l(1) regularization, we develop an approach re-fitting the results of standard methods towards the input data. Total variation regularizations and non-local means are special cases of interest. We identify important covariant information that should be preserved by the re-fitting method, and emphasize the importance of preserving the Jacobian (w.r.t. the observed signal) of the original estimator. Then, we provide an approach that has a twicing flavor and allows re-fitting the restored signal by adding back a local affine transformation of the residual term. We illustrate the benefits of our method on numerical simulations for image restoration tasks.
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