10 citations · 13 across the 10 of their papers we have counts for
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TV-based Spline Reconstruction with Fourier Measurements: Uniqueness and Convergence of Grid-Based Methods
Thomas Debarre, Quentin Denoyelle, Julien Fageot
We study the problem of recovering piecewise-polynomial periodic functions from their low-frequency information. This means that we only have access to possibly corrupted versions…
On the Uniqueness of Solutions for the Basis Pursuit in the Continuum
Thomas Debarre, Quentin Denoyelle, Julien Fageot
This paper studies the continuous-domain inverse problem of recovering Radon measures on the one-dimensional torus from low-frequency Fourier coefficients, where Kc is the cutoff f…
TV-based Reconstruction of Periodic Functions
Julien Fageot, Matthieu Simeoni
We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is for…
Sparsest Piecewise-Linear Regression of One-Dimensional Data
Thomas Debarre, Quentin Denoyelle, Michael Unser +1
We study the problem of one-dimensional regression of data points with total-variation (TV) regularization (in the sense of measures) on the second derivative, which is known to pr…
Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems
Anaïs Badoual, Julien Fageot, Michael Unser
This paper deals with the resolution of inverse problems in a periodic setting or, in other terms, the reconstruction of periodic continuous-domain signals from their noisy measure…