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• W2336136902 endingPage "014002" @default.
• W2336136902 startingPage "014002" @default.
• W2336136902 abstract "The seminal paper of Daubechies, Defrise, DeMol made clear that $ell^p$ spaces with $pin [1,2)$ and $p$-powers of the corresponding norms are appropriate settings for dealing with reconstruction of sparse solutions of ill-posed problems by regularization. It seems that the case $p=1$ provides the best results in most of the situations compared to the cases $pin (1,2)$. An extensive literature gives great credit also to using $ell^p$ spaces with $pin (0,1)$ together with the corresponding quasinorms, although one has to tackle challenging numerical problems raised by the non-convexity of the quasi-norms. In any of these settings, either super, linear or sublinear, the question of how to choose the exponent $p$ has been not only a numerical issue, but also a philosophical one. In this work we introduce a more flexible way of sparse regularization by varying exponents. We introduce the corresponding functional analytic framework, that leaves the setting of normed spaces but works with so-called F-norms. One curious result is that there are F-norms which generate the $ell^1$ space, but they are strictly convex, while the $ell^1$-norm is just convex." @default.
• W2336136902 created "2016-06-24" @default.
• W2336136902 creator A5012941200 @default.
• W2336136902 creator A5069699303 @default.
• W2336136902 date "2016-12-05" @default.
• W2336136902 modified "2023-10-16" @default.
• W2336136902 title "Flexible sparse regularization" @default.
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• W2336136902 doi "https://doi.org/10.1088/0266-5611/33/1/014002" @default.
• W2336136902 hasPublicationYear "2016" @default.
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