0000000000726005
AUTHOR
Charles-alban Deledalle
showing 4 related works from this author
Refitting Solutions Promoted by $$\ell _{12}$$ Sparse Analysis Regularizations with Block Penalties
2019
International audience; In inverse problems, the use of an l(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 present an efficient algorithmic method to obtain the refitted solution along with the original (biased) solution for any convex refitting block penalty. Experiments illustrate the good be…
CLEAR: Covariant LEAst-Square Refitting with Applications to Image Restoration
2017
International audience; 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 $\ell_1$ 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 a…
Characterizing the maximum parameter of the total-variation denoising through the pseudo-inverse of the divergence
2017
International audience; We focus on the maximum regularization parameter for anisotropic total-variation denoising. It corresponds to the minimum value of the regularization parameter above which the solution remains constant. While this value is well know for the Lasso, such a critical value has not been investigated in details for the total-variation. Though, it is of importance when tuning the regularization parameter as it allows fixing an upper-bound on the grid for which the optimal parameter is sought. We establish a closed form expression for the one-dimensional case, as well as an upper-bound for the two-dimensional case, that appears reasonably tight in practice. This problem is d…
Refitting solutions promoted by $\ell_{12}$ sparse analysis regularization with block penalties
2019
International audience; 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 present an efficient algorithmic method to obtain the refitted solution along with the original (biased) solution for any convex refitting block penalty. Experiments illustrate the g…