Publications related to Dual norm

Non-normal forms

In this thesis, we propose to formally derive amplitude equations governing the weakly nonlinear evolution of non-normal dynamical systems, when they respond to harmonic or stochastic forcing, or to an initial condition. This approach reconciles the non-mo ...

EPFL2024

Transportation-based functional ANOVA and PCA for covariance operators

Victor Panaretos, Yoav Zemel, Valentina Masarotto

We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Vari ...

Inst Mathematical Statistics-Ims2024

Fairness and Explainability in Clustering Problems

Xinrui Jia

In this thesis we present and analyze approximation algorithms for three different clustering problems. The formulations of these problems are motivated by fairness and explainability considerations, two issues that have recently received attention in the ...

EPFL2023

Procrustes Metrics and Optimal Transport for Covariance Operators

Valentina Masarotto

Covariance operators play a fundamental role in functional data analysis, providing the canonical means to analyse functional variation via the celebrated Karhunen-Loève expansion. These operators may themselves be subject to variation, for instance in con ...

EPFL2019

Dissipative Boundary Conditions for Nonlinear 1-D Hyperbolic Systems: Sharp Conditions Through an Approach via Time-Delay Systems

Hoài-Minh Nguyên

We analyze dissipative boundary conditions for nonlinear hyperbolic systems in one space dimension. We show that a known sufficient condition for exponential stability with respect to the H-2-norm is not sufficient for the exponential stability with respec ...

Society for Industrial and Applied Mathematics2015

Convex computation of the region of attraction of polynomial control systems

Milan Korda

We address the long-standing problem of computing the region of attraction (ROA) of a target set (typically a neighborhood of an equilibrium point) of a controlled nonlinear system with polynomial dynamics and semialgebraic state and input constraints. We ...

Institute of Electrical and Electronics Engineers2014

Low Loss MEMS-Reconfigurable 1-Bit Reflectarray Cell With Dual-Linear Polarization

Julien Perruisseau-Carrier, Tomislav Debogovic

We present a X-band 1-bit reconfigurable reflectarray (RRA) cell capable of independent reflection phase control of each linear component of a dual-polarized wave. It presents the lowest loss ever reported in an operational RRA cell at microwave frequencie ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Convex computation of the region of attraction of polynomial control systems

Milan Korda

We address the long-standing problem of computing the region of attraction (ROA) of a target set (typically a neighborhood of an equilibrium point) of a controlled nonlinear system with polynomial dynamics and semialgebraic state and input constraints. We ...

2013

Poisson Image Reconstruction With Hessian Schatten-Norm Regularization

Michaël Unser, Stamatios Lefkimmiatis

Poisson inverse problems arise in many modern imaging applications, including biomedical and astronomical ones. The main challenge is to obtain an estimate of the underlying image from a set of measurements degraded by a linear operator and further corrupt ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Hessian Schatten-Norm Regularization for Linear Inverse Problems

Michaël Unser, John Paul Ward, Stamatios Lefkimmiatis

We introduce a novel family of invariant, convex, and non-quadratic functionals that we employ to derive regularized solutions of ill-posed linear inverse imaging problems. The proposed regularizers involve the Schatten norms of the Hessian matrix, which a ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Convex Generalizations of Total Variation Based on the Structure Tensor with Applications to Inverse Problems

Michaël Unser, Stamatios Lefkimmiatis

We introduce a generic convex energy functional that is suitable for both grayscale and vector-valued images. Our functional is based on the eigenvalues of the structure tensor, therefore it penalizes image variation at every point by taking into account t ...

Springer2013

Electric field within lightning protection volume in presence of a descending leader

Farhad Rachidi-Haeri

Electric field distributions within lightning protection volume of a single lightning rod are studied for the case of a vertical downward leader. The boundaries of volumes with the electrical strength exceeding its critical value for ionization in air are ...

Elsevier2012

Regularized Interpolation for Noisy Images

Michaël Unser, Philippe Thévenaz, Sathish Ramani

Interpolation is the means by which a continuously defined model is fit to discrete data samples. When the data samples are exempt of noise, it seems desirable to build the model by fitting them exactly. In medical imaging, where quality is of paramount im ...

Institute of Electrical and Electronics Engineers2010