407 citations · 681 across the 14 of their papers we have counts for
17 papers
Tensor denoising with trend filtering
Francesco Ortelli, Sara van de Geer
We extend the notion of trend filtering to tensors by considering the -order Vitali variation, a discretized version of the integral of the absolute value of the $k^{\r…
Logistic regression with total variation regularization
Sara van de Geer
We study logistic regression with total variation penalty on the canonical parameter and show that the resulting estimator satisfies a sharp oracle inequality: the excess risk of t…
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…