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Adaptive Rates for Total Variation Image Denoising
We study the theoretical properties of image denoising via total variation penalized least-squares.
Prediction bounds for higher order total variation regularized least squares
We establish adaptive results for trend filtering: least squares estimation with a penalty on the total variation of $(k-1)^{\rm th}$ order differences.
Oracle inequalities for square root analysis estimators with application to total variation penalties
Through the direct study of the analysis estimator we derive oracle inequalities with fast and slow rates by adapting the arguments involving projections by Dalalyan, Hebiri and Lederer (2017).
On the total variation regularized estimator over a class of tree graphs
We generalize to tree graphs obtained by connecting path graphs an oracle result obtained for the Fused Lasso over the path graph.
