Publications de Karin Schnass | EPFL Graph Search

Classification via Incoherent Subspaces

In this article we present a signal model for classification based on a collection of low dimensional subspaces embedded into the high dimensional signal space. We develop an alternate projection algorithm to find such a collection and finally test the cla ...

2011

Dictionary Identification - Sparse Matrix-Factorisation via $\ell_1$-Minimisation

Karin Schnass, Rémi Gribonval

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

\ell_1

-minimisation. The problem can also be seen as factorising a

\ddim \times \nsig

matrix $Y=(y_1 \ldots y_\nsig), , y_n\in \R^\ ...

Institute of Electrical and Electronics Engineers2010

A union of incoherent spaces model for classification

Pierre Vandergheynst, Karin Schnass

We present a new and computationally efficient scheme for classifying signals into a fixed number of known classes. We model classes as subspaces in which the corresponding data is well represented by a dictionary of features. In order to ensure low miscla ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

Sparsity & [and] dictionaries - algorithms & [and] design

Karin Schnass

With the flood of information available today the question how to deal with high dimensional data/signals, which are cumbersome to handle, to calculate with and to store, is highly important. One approach to reducing this flood is to find sparse signal rep ...

EPFL2009

Basis Identification from Random Sparse Samples

Karin Schnass, Rémi Gribonval

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

\ell_1

minimisation. The problem is to identify a dictionary

\dico

from a set of training samples

\Y

knowing that

\Y = \dico \X

...

2009

Dictionary preconditioning for greedy algorithms

Pierre Vandergheynst, Karin Schnass

This article presents an alteration of greedy algorithms like thresholding or (Orthogonal) Matching Pursuit which improves their performance in finding sparse signal representations in redundant dictionaries. These algorithms can be split into a sensing an ...

2008

Dictionary Identifiability from Few Training Samples

Karin Schnass, Rémi Gribonval

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

Dictionary Learning Based Dimensionality Reduction for Classification

Pierre Vandergheynst, Karin Schnass

In this article we present a signal model for classification based on a low dimensional dictionary embedded into the high dimensional signal space. We develop an alternate projection algorithm to find the embedding and the dictionary and finally test the c ...

2008

Some Recovery Conditions for Basis Learning by L1-Minimization

Karin Schnass, Rémi Gribonval

Many recent works have shown that if a given signal admits a sufficiently sparse representation in a given dictionary, then this representation is recovered by several standard optimization algorithms, in particular the convex

\ell^1

minimization approac ...

2008

Atoms of all channels, unite! Average case analysis of multi-channel sparse recovery using greedy algorithms

Pierre Vandergheynst, Karin Schnass, Rémi Gribonval

This paper provides new results on computing simultaneous sparse approximations of multichannel signals over redundant dictionaries using two greedy algorithms. The first one, p-thresholding, selects the S atoms that have the largest

p

-correlation while ...

2008

Compressed sensing and redundant dictionaries

Pierre Vandergheynst, Karin Schnass

This article extends the concept of it compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a deterministic ...

2008

Average case analysis of multichannel thresholding

Pierre Vandergheynst, Karin Schnass, Rémi Gribonval

This paper introduces p-thresholding, an algorithm to compute simultaneous sparse approximations of multichannel signals over redundant dictionaries. We work out both worst case and average case recovery analyses of this algorithm and show that the latter ...

2007

Multichannel thresholding with sensing dictionaries

Pierre Vandergheynst, Karin Schnass, Rémi Gribonval

This paper shows introduces the use sensing dictionaries for p-thresholding, an algorithm to compute simultaneous sparse approximations of multichannel signals over redundant dictionaries. We do both a worst case and average case recovery analyses of this ...

2007

Average case analysis of multichannel sparse approximations using p- thresholding

Pierre Vandergheynst, Karin Schnass, Rémi Gribonval

This paper introduces

p

-thresholding, an algorithm to compute simultaneous sparse approximations of multichannel signals over redundant dictionaries. We work out both worst case and average case recovery analyses of this algorithm and show that the latte ...

2007

Average Performance Analysis for Thresholding

Pierre Vandergheynst, Karin Schnass

In this article is shown that with high probability the thresholding algorithm can recover signals that are sparse in a redundant dictionary as long as the {\it 2-Babel function} is growing slowly. This implies that it can succeed for sparsity levels up to ...

IEEE Institute of Electrical and Electronics Engineers2007

Distributed sensing of noisy signals by thresholding of redundant expansions

Pascal Frossard, Pierre Vandergheynst, Karin Schnass

This paper addresses the problem of sensing or recovering a signal s, captured by distributed low-complexity sensors. Each sensor observes a noisy version of the signal of interest, and independently forms an approximant of its observation. This approximan ...

2006