CLEAR: Covariant LEAst-square Re-fitting with applications to image restoration

Abstract :

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. Extending ideas that emerged for 1 regularization, we develop an approach that can help 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 to 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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Submitted on : Friday, September 13, 2019 - 4:52:30 PM
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  • HAL Id : hal-02287337, version 1


Charles-Alban Deledalle, Nicolas Papadakis, Joseph Salmon, Samuel Vaiter. CLEAR: Covariant LEAst-square Re-fitting with applications to image restoration. SIAM J. Imaging Sci., 2017, 10 (1), pp.243-284. ⟨hal-02287337⟩



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