41 citations · 45 across the 7 of their papers we have counts for
7 papers
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…
Coupled Splines for Sparse Curve Fitting
Icíar Lloréns Jover, Thomas Debarre, Shayan Aziznejad +1
We formulate as an inverse problem the construction of sparse parametric continuous curve models that fit a sequence of contour points. Our prior is incorporated as a regularizatio…
Sparsest Univariate Learning Models Under Lipschitz Constraint
Shayan Aziznejad, Thomas Debarre, Michael Unser
Beside the minimization of the prediction error, two of the most desirable properties of a regression scheme are stability and interpretability. Driven by these principles, we prop…
Continuous-Domain Formulation of Inverse Problems for Composite Sparse-Plus-Smooth Signals
Thomas Debarre, Shayan Aziznejad, Michael Unser
We present a novel framework for the reconstruction of 1D composite signals assumed to be a mixture of two additive components, one sparse and the other smooth, given a finite numb…
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…
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…
Pocket Guide to Solve Inverse Problems with GlobalBioIm
Emmanuel Soubies, Ferréol Soulez, Michael T. McCann +5
GlobalBioIm is an open-source MATLAB library for solving inverse problems. The library capitalizes on the strong commonalities between forward models to standardize the resolution…