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Variational reconstruction of scalar and vector images from non-uniform samples

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A Functional Perspective on Information Measures

Amedeo Roberto Esposito

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

EPFL2022

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

Convex optimization in sums of Banach spaces

Michaël Unser, Shayan Aziznejad

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

Shortest-support multi-spline bases for generalized sampling

Michaël Unser, Alexis Marie Frederic Goujon, Shayan Aziznejad, Alireza Naderi

Generalized sampling consists in the recovery of a function f, from the samples of the responses of a collection of linear shift-invariant systems to the input f . The reconstructed function is typically a member of a finitely generated integer-shift invar ...

2021

Adaptive Approximation of Shapes

We consider scalar-valued shape functionals on sets of shapes which are small perturbations of a reference shape. The shapes are described by parameterizations and their closeness is induced by a Hilbert space structure on the parameter domain. We justify ...

TAYLOR & FRANCIS INC2021

A projected super-penalty method for the C1-coupling of multi-patch isogeometric Kirchhoff plates

Annalisa Buffa, Luca Coradello

This work focuses on the development of a super-penalty strategy based on the L2-projection of suitable coupling terms to achieve C1-continuity between non-conforming multi-patch isogeometric Kirchhoff plates. In particular, the choice of penalty parameter ...

2021

Dictionary Learning for Two-Dimensional Kendall Shapes

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann, Anna You-Lai Song

We propose a novel sparse dictionary learning method for planar shapes in the sense of Kendall, namely configurations of landmarks in the plane considered up to similitudes. Our shape dictionary method provides a good trade-off between algorithmic simplici ...

SIAM PUBLICATIONS2020

Continuous-Domain Signal Reconstruction Using L-p-Norm Regularization

Michaël Unser, Pakshal Narendra Bohra

We focus on the generalized-interpolation problem. There, one reconstructs continuous-domain signals that honor discrete data constraints. This problem is infinite-dimensional and ill-posed. We make it well-posed by imposing that the solution balances data ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

A Unifying Representer Theorem for Inverse Problems and Machine Learning

Michaël Unser

Regularization addresses the ill-posedness of the training problem in machine learning or the reconstruction of a signal from a limited number of measurements. The method is applicable whenever the problem is formulated as an optimization task. The standar ...

2020

On Gaussian Process based Koopman Operator

Colin Neil Jones

Enabling analysis of non-linear systems in linear form, the Koopman operator has been shown to be a powerful tool for system identification and controller design. However, current data-driven methods cannot provide quantification of model uncertainty given ...

2020