75 citations · 211 across the 27 of their papers we have counts for
7 papers · 1 filter
Variational Seasonal-Trend Decomposition with Sparse Continuous-Domain Regularization
Julien Fageot
We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly v…
Complex-Order Scale-Invariant Operators and Self-Similar Processes
Arash Amini, Julien Fageot, Michael Unser
Derivatives and integration operators are well-studied examples of linear operators that commute with scaling up to a fixed multiplicative factor; i.e., they are scale-invariant. F…
The Critical Smoothness of Generalized Functions
Julien Fageot, John Paul Ward
For each integrability parameter , the critical smoothness of a periodic generalized function , denoted by is the supremum over the smoothness paramet…
Native Banach spaces for splines and variational inverse problems
Michael Unser, Julien Fageot
We propose a systematic construction of native Banach spaces for general spline-admissible operators . In short, the native space for and the (dual) norm $\|\cdo…
Beyond Wiener's Lemma: Nuclear Convolution Algebras and the Inversion of Digital Filters
Julien Fageot, Michael Unser, John Paul Ward
A convolution algebra is a topological vector space that is closed under the convolution operation. It is said to be inverse-closed if each element of w…
Compactly-Supported Smooth Interpolators for Shape Modeling with Varying Resolution
Daniel Schmitter, Julien Fageot, Anaïs Badoual +2
In applications that involve interactive curve and surface modeling, the intuitive manipulation of shapes is crucial. For instance, user interaction is facilitated if a geometrical…
Splines are Universal Solutions of Linear Inverse Problems with Generalized-TV regularization
Michael Unser, Julien Fageot, John Paul Ward
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 operato…