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Adaptive Rates for Total Variation Image Denoising
Francesco Ortelli, Sara van de Geer
We study the theoretical properties of image denoising via total variation penalized least-squares. We define the total vatiation in terms of the two-dimensional total discrete der…
Prediction bounds for higher order total variation regularized least squares
Francesco Ortelli, Sara van de Geer
We establish adaptive results for trend filtering: least squares estimation with a penalty on the total variation of order differences. Our approach is based on co…
Oracle inequalities for square root analysis estimators with application to total variation penalties
Francesco Ortelli, Sara van de Geer
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 Le…
Synthesis and analysis in total variation regularization
Francesco Ortelli, Sara van de Geer
We generalize the bridge between analysis and synthesis estimators by Elad, Milanfar and Rubinstein (2007) to rank deficient cases. This is a starting point for the study of the co…