We introduce a family of adaptive estimators on graphs, based on penalizing the l 1 norm of
discrete graph differences. This generalizes the idea of trend filtering (Kim et al., 2009; …

A very fast noniterative algorithm is proposed for denoising or smoothing one-dimensional
discrete signals, by solving the total variation regularized least-squares problem or the …

We introduce novel image regularization penalties to overcome the practical problems
associated with the classical total variation (TV) scheme. Motivated by novel …

This article presents a fast and robust algorithm for trend filtering, a recently developed
nonparametric regression tool. It has been shown that, for estimating functions whose …

Splines come in a variety of flavors that can be characterized in terms of some differential
operator L. The simplest piecewise-constant model corresponds to the derivative operator …

Removing noise from piecewise constant (PWC) signals is a challenging signal processing
problem arising in many practical contexts. For example, in exploration geosciences, noisy …

We consider efficient implementations of the generalized lasso dual path algorithm given by
Tibshirani and Taylor in. We first describe a generic approach that covers any penalty matrix …

In this work, we investigate image registration in a variational framework and focus on
regularization generality and solver efficiency. We first propose a variational model …

Suppose we observe a random vector X from some distribution in a known family with
unknown parameters. We ask the following question: when is it possible to split X into two …

In the 1-dimensional multiple changepoint detection problem, we derive a new fast error rate
for the fused lasso estimator, under the assumption that the mean vector has a sparse …