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A Unifying Representer Theorem for Inverse Problems and Machine Learning

Publications associées (81)

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Total Variation Regularization of Shape Signals

Martin Kurt Storath

This paper introduces the concept of shape signals, i.e., series of shapes which have a natural temporal or spatial ordering, as well as a variational formulation for the regularization of these signals. The proposed formulation can be seen as the shape-va ...

IEEE2015

PURIFY: a new approach to radio-interferometric imaging

Yves Wiaux, Rafael Eduardo Carrillo Rangel, Jason Douglas McEwen

In a recent article series, the authors have promoted convex optimization algorithms for radio-interferometric imaging in the framework of compressed sensing, which leverages sparsity regularization priors for the associated inverse problem and defines a m ...

Wiley-Blackwell2014

An Equivalence between the Lasso and Support Vector Machines

Martin Jaggi

We investigate the relation of two fundamental tools in machine learning and signal processing, that is the support vector machine (SVM) for classification, and the Lasso technique used in regression. We show that the resulting optimization problems are eq ...

Chapman and Hall/CRC2014

Estimating the ice thickness of shallow glaciers from surface topography and mass-balance data with a shape optimization algorithm

Marco Picasso, Laurent Michel, Heinz Blatter, Martin Funk

A shape optimization algorithm is presented that estimates the ice thickness distribution within a three-dimensional, shallow glacier, given a transient surface geometry and a mass-balance distribution. The approach is based on the minimization of the surf ...

Pergamon-Elsevier Science Ltd2014

Enhancing statistical performance of data-driven controller tuning via L2-regularization

Alireza Karimi

Noniterative data-driven techniques are design methods that allow optimal feedback control laws to be derived from input-output (I/O) data only, without the need of a model of the process. A drawback of these methods is that, in their standard formulation, ...

Pergamon-Elsevier Science Ltd2014

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

On L2-Regularization for Virtual Reference Feedback Tuning

Alireza Karimi

The Virtual Reference Feedback Tuning (VRFT) approach is a design method that allow optimal feedback control laws to be derived from input-output (I/O) data only, without need of a model of the process. A drawback of this methods is that, in its standard f ...

2013

Manifold Sparse Beamforming

Volkan Cevher, Afsaneh Asaei, Baran Gözcü

We consider the minimum variance distortionless response (MVDR) beamforming problems where the array covariance matrix is rank deficient. The conventional approach handles such rank-deficiencies via diagonal loading on the covariance matrix. In this settin ...

2013

Manifold Sparse Beamforming

Volkan Cevher, Afsaneh Asaei, Baran Gözcü

IEEE2013