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Dictionary Learning Based Dimensionality Reduction for Classification

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Trends in Bioimaging and Signal Processing

Michaël Unser

This is the second in a series of three columns summarizing the "Trends" expert sessions organized by the Signal Processing Society Technical Committees during ICASSP 2011 in Prague, Czech Republic. Readers have an opportunity to access these Trends sessio ...

IEEE2011

A Signal Processing Approach to Generalized 1-D Total Variation

Dimitri Nestor Alice Van De Ville, Fikret Isik Karahanoglu, Ilker Bayram

Total variation (TV) is a powerful method that brings great benefit for edge-preserving regularization. Despite being widely employed in image processing, it has restricted applicability for 1-D signal processing since piecewise-constant signals form a rat ...

Institute of Electrical and Electronics Engineers2011

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

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

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. 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

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

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. The problem is to identify a dictionary

\dico

from a set of training samples

\Y

knowing that

\Y = \dico \X

...

2009

Signal Processing for Communications

Martin Vetterli, Paolo Prandoni

With a novel, less classical approach to the subject, the authors have written a book with the conviction that signal processing should be taught to be fun. The threatment is therefore less focused on the mathematics and more on the conceptual aspects, the ...

EPFL Press, CRC2008

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

A simple test to check the optimality of a sparse signal approximation

Pierre Vandergheynst, Rémi Gribonval

Approximating a signal or an image with a sparse linear expansion from an overcomplete dictionary of atoms is an extremely useful tool to solve many signal processing problems. Finding the sparsest approximation of a signal from an arbitrary dictionary is ...

2006

Learning redundant dictionaries with translation invariance property: the MoTIF algorithm

Pierre Vandergheynst, Rémi Gribonval, Philippe Jost

Sparse approximation using redundant dictionaries is an efficient tool for many applications in the field of signal processing. The performances largely depend on the adaptation of the dictionary to the signal to decompose. As the statistical dependencies ...

IEEE2005