Publications related to Saddle-to-Saddle Dynamics in Diagonal Linear Networks

Sparse Dictionaries for Continuous-Domain Inverse Problems

Michaël Unser, Shayan Aziznejad, Thomas Jean Debarre

We study 1D continuous-domain inverse problems for multicomponent signals. The prior assumption on these signals is that each component is sparse in a different dictionary specified by a regularization operators. We introduce a hybrid regularization functi ...

2019

CoCoA: A General Framework for Communication-Efficient Distributed Optimization

Martin Jaggi, Chenxin Ma

The scale of modern datasets necessitates the development of efficient distributed optimization methods for machine learning. We present a general-purpose framework for distributed computing environments, CoCoA, that has an efficient communication scheme a ...

MICROTOME PUBL2018

Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces

Volkan Cevher, Junhong Lin

In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms, including ridge regressi ...

2018

A Least-Squares/Relaxation Method for the Numerical Solution of the Three-Dimensional Elliptic Monge-Ampere Equation

Alexandre Caboussat, Dimitrios Gourzoulidis

In this article, we address the numerical solution of the Dirichlet problem for the three-dimensional elliptic Monge-Ampere equation using a least-squares/relaxation approach. The relaxation algorithm allows the decoupling of the differential operators fro ...

SPRINGER/PLENUM PUBLISHERS2018

General Proximal Gradient Method: A Case for Non-Euclidean Norms

Volkan Cevher, Ya-Ping Hsieh, Marwa El Halabi, Cong Bang Vu, Van Quang Nguyen

In this paper, we consider composite convex minimization problems. We advocate the merit of considering Generalized Proximal gradient Methods (GPM) where the norm employed is not Euclidean. To that end, we show the tractability of the general proximity ope ...

2017

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

Optimization Of Compound Regularization Parameters Based On Stein'S Unbiased Risk Estimate

Xin Liu, Hanjie Pan, Feng Xue, Jiaqi Liu

Recently, the type of compound regularizers has become a popular choice for signal reconstruction. The estimation quality is generally sensitive to the values of multiple regularization parameters. In this work, based on BDF algorithm, we develop a data-dr ...

Ieee2017

Smoothing technique for nonsmooth composite minimization with linear operator

Volkan Cevher, Van Quang Nguyen

We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap technique. In addition t ...

2017

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

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Michaël Unser, Julien René Pierre Fageot, Harshit Gupta

We present a theoretical analysis and comparison of the effect of

ℓ _{ 1 }

versus

ℓ _{ 2 }

regularization for the resolution of ill-posed linear inverse and/or compressed sensing problems. Our formulation covers the most general setting where the s ...

IEEE2016

Saddle-to-Saddle Dynamics in Diagonal Linear Networks

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Sparse Dictionaries for Continuous-Domain Inverse Problems

CoCoA: A General Framework for Communication-Efficient Distributed Optimization

Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces

A Least-Squares/Relaxation Method for the Numerical Solution of the Three-Dimensional Elliptic Monge-Ampere Equation

General Proximal Gradient Method: A Case for Non-Euclidean Norms

Acoustic DoA Estimation by One Unsophisticated Sensor

Optimization Of Compound Regularization Parameters Based On Stein'S Unbiased Risk Estimate

Smoothing technique for nonsmooth composite minimization with linear operator

Sparsity-Based Data Reconstruction Models for Biomedical Imaging

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Optimization Of Compound Regularization Parameters Based On Stein'S Unbiased Risk Estimate

General Proximal Gradient Method: A Case for Non-Euclidean Norms

A Least-Squares/Relaxation Method for the Numerical Solution of the Three-Dimensional Elliptic Monge-Ampere Equation

Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Acoustic DoA Estimation by One Unsophisticated Sensor

Sparsity-Based Data Reconstruction Models for Biomedical Imaging

Sparse Dictionaries for Continuous-Domain Inverse Problems

Smoothing technique for nonsmooth composite minimization with linear operator

CoCoA: A General Framework for Communication-Efficient Distributed Optimization