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Complexity L0L^0L0-penalized M-Estimation: Consistency in More Dimensions

23 January 2013
L. Demaret
F. Friedrich
V. Liebscher
G. Winkler
ArXiv (abs)PDFHTML
Abstract

We study the asymptotics in L2L^2L2 for complexity penalized least squares regression for the discrete approximation of finite-dimensional signals on continuous domains - e.g. images - by piecewise smooth functions. We introduce a fairly general setting which comprises most of the presently popular partitions of signal- or image- domains like interval-, wedgelet- or related partitions, as well as Delaunay triangulations. Then we prove consistency and derive convergence rates. Finally, we illustrate by way of relevant examples that the abstract results are useful for many applications.

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