Publications related to Some Recovery Conditions for Basis Learning by L1-Minimization

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

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

A Note on Natural Risk Statistics

Damir Filipovic, Gregor Svindland

Recently Heyde, Kou and Peng (2007) proposed the notion of a natural risk statistic associated with a finite sample that relaxes the subadditivity assumption in the classical coherent risk statistics. In this note we use convex analysis to provide alternat ...

Elsevier2008

Dictionary Identifiability from Few Training Samples

Rémi Gribonval, Karin Schnass

This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via

ell^1

minimisation, or more precisely the problem of identifying a dictionary

dico

from a set of training samples

Y

knowing that $ ...

2008

Collaboration in a Video Game : Impacts of Location Awareness

Pierre Dillenbourg, Nicolas Nova

This paper presents an experimental research that focuses on collaboration in a multi-player game. The aim of the project is to study the cognitive impacts of awareness tools, i.e. artifacts that allow users of a collaborative system to be aware of what is ...

2007

Dimensionality Reduction with Adaptive Approximation

Pascal Frossard, Effrosyni Kokiopoulou

In this paper, we propose the use of (adaptive) nonlinear approximation for dimensionality reduction. In particular, we propose a dimensionality reduction method for learning a parts based representation of signals using redundant dictionaries. A redundant ...

2007

Nonlinear approximation with redundant multi-component dictionaries

Lorenzo Granai

The problem of efficiently representing and approximating digital data is an open challenge and it is of paramount importance for many applications. This dissertation focuses on the approximation of natural signals as an organized combination of mutually c ...

EPFL2006

Analysis of Multimodal Signals Using Redundant Representations [Winner of IBM Student Paper Award]

Pierre Vandergheynst, Gianluca Monaci, Oscar Divorra Escoda

In this work we explore the potentialities of a framework for the representation of audio-visual signals using decompositions on overcomplete dictionaries. Redundant decompositions may describe audio-visual sequences in a concise fashion, preserving good r ...

2005

Learning structured dictionaries for image representation

Pierre Vandergheynst, Gianluca Monaci

The dictionary approach to signal and image processing has been massively investigated in the last two decades, proving very attractive for a wide range of applications. The effectiveness of dictionary-based methods, however, is strongly influenced by the ...

IEEE2004

Learning Structured Dictionaries for Image Representation

Pierre Vandergheynst, Gianluca Monaci

The dictionary approach to signal and image processing has been massively investigated in the last two decades, proving very attractive for a wide range of applications. The effectiveness of dictionary-based methods, however, is strongly influenced by the ...

2004

The lexico-smallest representation of convex polyhedra

Stefano Picozzi

Every convex polyhedron in the Euclidean space

R^d

admits both H- and V-representation. For both formats, a representation is canonical if it is minimal and unique up to some elementary operations. In this paper, we extend the usual definition of canonic ...

2003

Some Recovery Conditions for Basis Learning by L1-Minimization

Graph Chatbot

Chat with Graph Search

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

A Note on Natural Risk Statistics

Dictionary Identifiability from Few Training Samples

Collaboration in a Video Game : Impacts of Location Awareness

Dimensionality Reduction with Adaptive Approximation

Nonlinear approximation with redundant multi-component dictionaries

Analysis of Multimodal Signals Using Redundant Representations [Winner of IBM Student Paper Award]

Learning structured dictionaries for image representation

Learning Structured Dictionaries for Image Representation

The lexico-smallest representation of convex polyhedra

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

Dictionary Identifiability from Few Training Samples

Dimensionality Reduction with Adaptive Approximation

Learning structured dictionaries for image representation

Learning Structured Dictionaries for Image Representation

Nonlinear approximation with redundant multi-component dictionaries

Analysis of Multimodal Signals Using Redundant Representations [Winner of IBM Student Paper Award]

The lexico-smallest representation of convex polyhedra

Collaboration in a Video Game : Impacts of Location Awareness

A Note on Natural Risk Statistics