Publications related to Non-local Functionals Related to the Total Variation and Connections with Image Processing

On linear and quadratic Lipschitz bounds for twice continuously differentiable functions

Dominique Bonvin, Grégory François, Gene Bunin

Lower and upper bounds for a given function are important in many mathematical and engineering contexts, where they often serve as a base for both analysis and application. In this short paper, we derive piecewise linear and quadratic bounds that are state ...

arXiv:1406.3991 [math.OC]2014

Convex Generalizations of Total Variation Based on the Structure Tensor with Applications to Inverse Problems

Michaël Unser, Stamatios Lefkimmiatis

We introduce a generic convex energy functional that is suitable for both grayscale and vector-valued images. Our functional is based on the eigenvalues of the structure tensor, therefore it penalizes image variation at every point by taking into account t ...

Springer2013

Joint image registration and reconstruction from compressed multi-view measurements

Pierre Vandergheynst, Gilles Puy

We present a method for joint reconstruction of a set of images representing a given scene from few multi-view measurements obtained by compressed sensing. We model the correlation between measurements using global geometric transformations represented by ...

Spie-Int Soc Optical Engineering2013

Joint image registration and reconstruction from compressed multi-view measurements

Pierre Vandergheynst, Gilles Puy

We present a method for joint reconstruction of a set of images representing a given scene from few multi-view measurements obtained by compressed sensing. We model the correlation between measurements using global geometric transformations represented by ...

Spie-Int Soc Optical Engineering2013

Joint reconstruction of misaligned images from incomplete measurements for cardiac MRI

Pierre Vandergheynst, Gilles Puy, Gabriele Vincenzo Bonanno

We present a novel method for robust reconstruction of the image of a moving object from incomplete linear measurements. We assume that only few measurements of this object can be acquired at different instants and model the correlation between measurement ...

2013

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

JOINT TRACE/TV NORM MINIMIZATION: A NEW EFFICIENT APPROACH FOR SPECTRAL COMPRESSIVE IMAGING

Pierre Vandergheynst, Mohammad Golbabaee

In this paper we propose a novel and efficient model for compressed sensing of hyperspectral images. A large-size hyperspectral image can be subsampled by retaining only 3% of its original size, yet robustly recovered using the new approach we present here ...

2012

FAST TV-L1 OPTICAL FLOW FOR INTERACTIVITY

Pierre Vandergheynst, Gilles Puy, Emmanuel D'Angelo, Johann Paratte

Vision is a natural tool for human-computer interaction, since it pro- vides visual feedback to the user and mimics some human behaviors. It requires however the fast and robust computation of motion primi- tives, which remains a difficult problem. In this ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011

An optimal first-order solver for the TV-$L_1$ optical flow problem

Pierre Vandergheynst, Gilles Puy, Emmanuel D'Angelo

In this study, we address the problem of computing efficiently a dense optical flow between two images under a total variation (TV) regularization and an

L_1

norm data fidelity constraint using a variational method. We build upon Nesterov's framework for ...

2010

The role of perspective functions in convexity, polyconvexity, rank-one convexity and separate convexity

Bernard Dacorogna

Any finite, separately convex, positively homogeneous function on

\mathbb{R}^2

is convex. This was first established by the first author ["Direct methods in calculus of variations", Springer-Verlag (1989)]. Here we give a new and concise proof of this re ...

2008

Non-local Functionals Related to the Total Variation and Connections with Image Processing

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On linear and quadratic Lipschitz bounds for twice continuously differentiable functions

Convex Generalizations of Total Variation Based on the Structure Tensor with Applications to Inverse Problems

Joint image registration and reconstruction from compressed multi-view measurements

Joint image registration and reconstruction from compressed multi-view measurements

Joint reconstruction of misaligned images from incomplete measurements for cardiac MRI

Matrix ALPS: Accelerated Low Rank and Sparse Matrix Reconstruction

JOINT TRACE/TV NORM MINIMIZATION: A NEW EFFICIENT APPROACH FOR SPECTRAL COMPRESSIVE IMAGING

FAST TV-L1 OPTICAL FLOW FOR INTERACTIVITY

An optimal first-order solver for the TV-$L_1$ optical flow problem

The role of perspective functions in convexity, polyconvexity, rank-one convexity and separate convexity

JOINT TRACE/TV NORM MINIMIZATION: A NEW EFFICIENT APPROACH FOR SPECTRAL COMPRESSIVE IMAGING

Matrix ALPS: Accelerated Low Rank and Sparse Matrix Reconstruction

Joint image registration and reconstruction from compressed multi-view measurements

An optimal first-order solver for the TV-$L_1$ optical flow problem

The role of perspective functions in convexity, polyconvexity, rank-one convexity and separate convexity

Convex Generalizations of Total Variation Based on the Structure Tensor with Applications to Inverse Problems

On linear and quadratic Lipschitz bounds for twice continuously differentiable functions

Joint image registration and reconstruction from compressed multi-view measurements

Joint reconstruction of misaligned images from incomplete measurements for cardiac MRI

FAST TV-L1 OPTICAL FLOW FOR INTERACTIVITY