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Splines Are Universal Solutions of Linear Inverse Problems with Generalized TV Regularization

Publications associées (41)

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Explicit representations for Banach subspaces of Lizorkin distributions

Michaël Unser, Sebastian Jonas Neumayer

The Lizorkin space is well suited to the study of operators like fractional Laplacians and the Radon transform. In this paper, we show that the space is unfortunately not complemented in the Schwartz space. In return, we show that it is dense in C0(Double- ...

WORLD SCIENTIFIC PUBL CO PTE LTD2023

Application of optimal spline subspaces for the removal of spurious outliers in isogeometric discretizations

Espen Sande

We show that isogeometric Galerkin discretizations of eigenvalue problems related to the Laplace operator subject to any standard type of homogeneous boundary conditions have no outliers in certain optimal spline subspaces. Roughly speaking, these optimal ...

ELSEVIER SCIENCE SA2022

We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a finite sum of compo ...

2021

Idempotents in the endomorphism algebra of a finite lattice

Jacques Thévenaz, Serge Bouc

We give a direct construction of a specific central idempotent in the endomorphism algebra of a finite lattice T. This idempotent is associated with all possible sublattices of T which are totally ordered. A generalization is considered in a conjectural fa ...

2021

Functional Inverse Problems on Spheres: Theory, Algorithms and Applications

Matthieu Martin Jean-André Simeoni

Many scientific inquiries in natural sciences involve approximating a spherical field -namely a scalar quantity defined over a continuum of directions- from generalised samples of the latter (e.g. directional samples, local averages, etc). Such an approxim ...

EPFL2020

Local Non-Rigid Structure-from-Motion from Diffeomorphic Mappings

Pascal Fua, Mathieu Salzmann, Shaifali Parashar

We propose a new formulation to non-rigid structure-from-motion that only requires the deforming surface to preserve its differential structure. This is a much weaker assumption than the traditional ones of isometry or conformality. We show that it is neve ...

IEEE2020

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We propose a new formulation to the non-rigid structure-from-motion problem that only requires the deforming surface to meaning that its differential structure is preserved. This is a much weaker assumption than the traditional ones of isometry or conforma ...

2020

B-Spline-Based Exact Discretization of Continuous-Domain Inverse Problems With Generalized TV Regularization

Michaël Unser, Julien René Pierre Fageot, Harshit Gupta, Thomas Jean Debarre

We study continuous-domain linear inverse problems with generalized total-variation (gTV) regularization, expressed in terms of a regularization operator L. It has recently been proved that such inverse problems have sparse spline solutions, with fewer jum ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

We study the kinematics of correlation functions of local and extended operators in a conformal field theory. We present a new method for constructing the tensor structures associated to primary operators in an arbitrary bosonic representation of the Loren ...

Springer2019

Sparse Spline Approximation on the Hypersphere by Generalised Total Variation Basis Pursuit

Matthieu Martin Jean-André Simeoni

Many scientific inquiries in natural sciences involve approximating a spherical field –namely a scalar quantity defined over a continuum of directions– from generalised samples of the latter. Typically, a convex optimisation problem is formulated in terms ...

2019