Publications related to Compressed Sensing of Simultaneous Low-Rank and Joint-Sparse Matrices

Structure from sound with incomplete data

Martin Vetterli, Ivan Dokmanic, Gilles Baechler, Miranda Krekovic

In this paper, we consider the problem of jointly localizing a microphone array and identifying the direction of arrival of acoustic events. Under the assumption that the sources are in the far field, this problem can be formulated as a constrained low-ran ...

2018

Acoustic DoA Estimation by One Unsophisticated Sensor

Martin Vetterli, Ivan Dokmanic, Dalia Salem Hassan Fahmy El Badawy

We show how introducing known scattering can be used in direction of arrival estimation by a single sensor. We first present an analysis of the geometry of the underlying measurement space and show how it enables localizing white sources. Then, we extend t ...

Springer Verlag2017

Sparsity-Based Data Reconstruction Models for Biomedical Imaging

Emrah Bostan

We propose new regularization models to solve inverse problems encountered in biomedical imaging applications. In formulating mathematical schemes, we base our approach on the sparse signal processing principles that have emerged as a central paradigm in t ...

EPFL2016

Estimation Error of the Constrained Lasso

Volkan Cevher, Yen-Huan Li, Ya-Ping Hsieh, Nissim Zerbib

This paper presents a non-asymptotic upper bound for the estimation error of the constrained lasso, under the high-dimensional (

n \ll p

) setting. In contrast to existing results, the error bound in this paper is sharp, is valid when the parameter to be e ...

2016

Compressive PCA for Low-Rank Matrices on Graphs

Pierre Vandergheynst, Gilles Puy, Nathanaël Perraudin, Nauman Shahid

We introduce a novel framework for an approxi- mate recovery of data matrices which are low-rank on graphs, from sampled measurements. The rows and columns of such matrices belong to the span of the first few eigenvectors of the graphs constructed between ...

Ieee-Inst Electrical Electronics Engineers Inc2016

Signal structure: from manifolds to molecules and structured sparsity

Sofia Karygianni

Effective representation methods and proper signal priors are crucial in most signal processing applications. In this thesis we focus on different structured models and we design appropriate schemes that allow the discovery of low dimensional latent struct ...

EPFL2015

Robust Principal Component Analysis on Graphs

Pierre Vandergheynst, Michael Bronstein, Xavier Bresson, Nauman Shahid, Vasilis Kalofolias

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA solves the first iss ...

2015

A Modulated Closed Form solution for Quantitative Susceptibility Mapping - A thorough evaluation and comparison to iterative methods based on edge prior knowledge

Rolf Gruetter, Yves Wiaux, José Pedro Rebelo Ferreira Marques, Diana Khabipova

The aim of this study is to perform a thorough comparison of quantitative susceptibility mapping (QSM) techniques and their dependence on the assumptions made. The compared methodologies were: two iterative single orientation methodologies minimizing the l ...

Elsevier2015

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

Jump-Sparse and Sparse Recovery Using Potts Functionals

Martin Kurt Storath

We recover jump-sparse and sparse signals from blurred incomplete data corrupted by (possibly non-Gaussian) noise using inverse Potts energy functionals. We obtain analytical results (existence of minimizers, complexity) on inverse Potts functionals and pr ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Compressed Sensing of Simultaneous Low-Rank and Joint-Sparse Matrices

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Structure from sound with incomplete data

Acoustic DoA Estimation by One Unsophisticated Sensor

Sparsity-Based Data Reconstruction Models for Biomedical Imaging

Estimation Error of the Constrained Lasso

Compressive PCA for Low-Rank Matrices on Graphs

Signal structure: from manifolds to molecules and structured sparsity

Robust Principal Component Analysis on Graphs

A Modulated Closed Form solution for Quantitative Susceptibility Mapping - A thorough evaluation and comparison to iterative methods based on edge prior knowledge

PURIFY: a new approach to radio-interferometric imaging

Jump-Sparse and Sparse Recovery Using Potts Functionals

Signal structure: from manifolds to molecules and structured sparsity

PURIFY: a new approach to radio-interferometric imaging

Structure from sound with incomplete data

Acoustic DoA Estimation by One Unsophisticated Sensor

Sparsity-Based Data Reconstruction Models for Biomedical Imaging

Jump-Sparse and Sparse Recovery Using Potts Functionals

Compressive PCA for Low-Rank Matrices on Graphs

A Modulated Closed Form solution for Quantitative Susceptibility Mapping - A thorough evaluation and comparison to iterative methods based on edge prior knowledge

Robust Principal Component Analysis on Graphs

Estimation Error of the Constrained Lasso