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Convex optimization in sums of Banach spaces

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A fixed point theorem for L1 spaces

Nicolas Monod

We prove a fixed point theorem for a family of Banach spaces, notably for L^1. Applications include the optimal answer to the "derivation problem" for group algebras which originated in the 1960s. ...

Springer-Verlag2012

Approaches to Conditional Risk

Damir Filipovic

We present and compare two different approaches to conditional risk measures. One approach draws from convex analysis in vector spaces and presents risk measures as functions on Lp spaces, while the other approach utilizes module-based convex analysis wher ...

2012

Matrix ALPS: Accelerated Low Rank and Sparse Matrix Reconstruction

Volkan Cevher, Anastasios Kyrillidis

We propose Matrix ALPS for recovering a sparse plus low-rank decomposition of a matrix given its corrupted and incomplete linear measurements. Our approach is a first-order projected gradient method over non-convex sets, and it exploits a well-known memory ...

IEEE2012

Asymptotic linearity and Hadamard differentiability

Charles Stuart

For a mapping between Banach spaces, two weaker variants of the usual notion of asymptotic linearity are defined and explored. It is shown that, under inversion through the unit sphere, they correspond to Hadamard and weak Hadamard differentiability at the ...

2012

Optimal image alignment with random projections of manifolds: algorithm and geometric analysis

Pascal Frossard, Daniel Kressner, Effrosyni Kokiopoulou

This paper addresses the problem of image alignment based on random measurements. Image alignment consists of estimating the relative transformation between a query image and a reference image. We consider the specific problem where the query image is prov ...

2011

A Fast Wavelet-Based Reconstruction Method for Magnetic Resonance Imaging

Michaël Unser, Matthieu Guerquin-Kern

In this work, we exploit the fact that wavelets can represent magnetic resonance images well, with relatively few coefficients. We use this property to improve magnetic resonance imaging (MRI) reconstructions from undersampled data with arbitrary k-space t ...

Institute of Electrical and Electronics Engineers2011

Sparsity-Driven Reconstruction for FDOT With Anatomical Priors

Michaël Unser, Jean-Charles Baritaux, Kai Hassler, Sebanti Sanyal, Martina Bucher

In this paper we propose a method based on (2, 1)-mixed-norm penalization for incorporating a structural prior in FDOT image reconstruction. The effect of (2, 1)-mixed-norm penalization is twofold: first, a sparsifying effect which isolates few anatomical ...

IEEE2011

Robust Controller Design by Convex Optimization based on Finite Frequency Samples of Spectral Models

Alireza Karimi, Roland Longchamp, Gorka Galdos Sanz de Galdeano

Some frequency-domain controller design problems are solved using a finite number of frequency samples. Consequently, the performance and stability conditions are not guaranteed for the frequencies between the frequency samples. In this paper, all possible ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

Moyennabilité et courbure

Martin Anderegg

As Avez showed (in 1970), the fundamental group of a compact Riemannian manifold of nonpositive sectional curvature has exponential growth if and only if it is not flat. After several generalizations from Gromov, Zimmer, Anderson, Burger and Shroeder, the ...

EPFL2010

Fast hard thresholding with Nesterov's gradient method

Volkan Cevher, Sina Jafarpour

We provide an algorithmic framework for structured sparse recovery which unifies combinatorial optimization with the non-smooth convex optimization framework by Nesterov [1, 2]. Our algorithm, dubbed Nesterov iterative hard-thresholding (NIHT), is similar ...

2010