Publications related to (S)GD over Diagonal Linear Networks: Implicit Regularisation, Large Stepsizes and Edge of Stability

Wavelet Shrinkage With Consistent Cycle Spinning Generalizes Total Variation Denoising

Michaël Unser, Emrah Bostan, Ulugbek Kamilov

We introduce a new wavelet-based method for the implementation of Total-Variation-type denoising. The data term is least-squares, while the regularization term is gradient-based. The particularity of our method is to exploit a link between the discrete gra ...

IEEE2012

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

Pierre Vandergheynst, Mohammad Golbabaee

In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is generic enough to ...

Institute of Electrical and Electronics Engineers2012

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

Pierre Vandergheynst, Mohammad Golbabaee

In this paper we consider recovery of a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model which can efficiently restricts the degrees of freedom of data and, at the same time, is generic so that f ...

2012

Combinatorial Selection and Least Absolute Shrinkage via the CLASH Algorithm

Volkan Cevher, Anastasios Kyrillidis

The least absolute shrinkage and selection operator (LASSO) for linear regression exploits the geometric interplay of the

\ell_2

-data error objective and the

\ell_1

-norm constraint to arbitrarily select sparse models. Guiding this uninformed selection ...

IEEE2012

Hessian-Based Regularization For 3-D Microscopy Image Restoration

Michaël Unser, Aurélien Bourquard, Stamatios Lefkimmiatis

We investigate a non quadratic regularizer that is based on the Hessian operator for dealing with the restoration of 3-D images in a variational framework. We show that the regularizer under study is a valid extension of the total-variation (TV) functional ...

Ieee2012

Hessian-Based Regularization for 3-D Microscopy Image Restoration

Michaël Unser, Aurélien Bourquard, Stamatios Lefkimmiatis

We investigate a non quadratic regularizer that is based on the Hessian operator for dealing with the restoration of 3-D images in a variational framework. We show that the regularizer under study is a valid extension of the total-variation (TV) functiona ...

IEEE2012

Fast Geodesic Active Fields for Image Registration based on Splitting and Augmented Lagrangian Approaches

Jean-Philippe Thiran, Xavier Bresson, Dominique Zosso

In this paper we present an efficient numerical scheme for the recently introduced Geodesic Active Fields (GAF) framework for geometric image registration. This framework considers the registration task as a weighted minimal surface problem. Hence, data-te ...

2011

Compressive sensing meets game theory

Volkan Cevher, Sina Jafarpour

We introduce the Multiplicative Update Selector and Estimator (MUSE) algorithm for sparse approximation in under-determined linear regression problems. Given ƒ = Φα* + μ, the MUSE provably and efficiently finds a k-sparse vector α̂ such that ∥Φα̂ − ƒ∥∞ ≤ ∥ ...

IEEE2011

Joint reconstruction of correlated images from compressed linear measurements

Pascal Frossard, Vijayaraghavan Thirumalai

This paper proposes a joint reconstruction algorithm for compressed correlated images that are given under the form of linear measurements. We first propose a geometry based model in order to describe the correlation between visual information in pairs of ...

2010

Nonideal sampling and regularized interpolation of noisy data

Sathish Ramani

Conventional sampling (Shannon's sampling formulation and its approximation-theoretic counterparts) and interpolation theories provide effective solutions to the problem of reconstructing a signal from its samples, but they are primarily restricted to the ...

EPFL2009

(S)GD over Diagonal Linear Networks: Implicit Regularisation, Large Stepsizes and Edge of Stability

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Wavelet Shrinkage With Consistent Cycle Spinning Generalizes Total Variation Denoising

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

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

Combinatorial Selection and Least Absolute Shrinkage via the CLASH Algorithm

Hessian-Based Regularization For 3-D Microscopy Image Restoration

Hessian-Based Regularization for 3-D Microscopy Image Restoration

Fast Geodesic Active Fields for Image Registration based on Splitting and Augmented Lagrangian Approaches

Compressive sensing meets game theory

Joint reconstruction of correlated images from compressed linear measurements

Nonideal sampling and regularized interpolation of noisy data

Nonideal sampling and regularized interpolation of noisy data

Hessian-Based Regularization for 3-D Microscopy Image Restoration

Fast Geodesic Active Fields for Image Registration based on Splitting and Augmented Lagrangian Approaches

Compressive sensing meets game theory

Joint reconstruction of correlated images from compressed linear measurements

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

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

Wavelet Shrinkage With Consistent Cycle Spinning Generalizes Total Variation Denoising

Combinatorial Selection and Least Absolute Shrinkage via the CLASH Algorithm

Hessian-Based Regularization For 3-D Microscopy Image Restoration