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Sparse image approximation with application to flexible image coding

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The Marr Wavelet Pyramid

Michaël Unser, Dimitri Nestor Alice Van De Ville

We introduce a new semi-orthogonal complex wavelet basis of L-2(R-2). The basis functions are associated to the complex gradient-Laplace operator, which plays a central role in image processing. We define analytically a single-generator wavelet that is shi ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2008

Algorithms and methods for sparse approximation in structured dictionaries

Lorenzo Peotta

In the last decade we observed an increasing interaction between data compression and sparse signals approximations. Sparse approximations are desirable because they compact the energy of the signals in few elements and correspond to a structural simplific ...

EPFL2007

Coarse scene geometry estimation from sparse approximations of multi-view omnidirectional images

Pascal Frossard, Ivana Tosic

This paper presents a framework for coarse scene geometry estimation, based on sparse representations of omnidirectional images with geometrical basis functions. We introduce a correlation model that relates sparse components in different views with local ...

2007

Algorithmic aspects of sparse approximations

Philippe Jost

Typical tasks in signal processing may be done in simpler ways or more efficiently if the signals to analyze are represented in a proper way. This thesis deals with some algorithmic problems related to signal approximation, more precisely, in the novel fie ...

EPFL2007

On the modelling of multi-modal data using redundant dictionaries

Gianluca Monaci

Real-world phenomena involve complex interactions between multiple signal modalities. As a consequence, humans are used to integrate at each instant perceptions from all their senses in order to enrich their understanding of the surrounding world. This par ...

EPFL2007

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

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 ...

2007

Multichannel thresholding with sensing dictionaries

Pierre Vandergheynst, Rémi Gribonval, Karin Schnass

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

On finding nearest neighbors in a set of compressible signals

Pierre Vandergheynst, Philippe Jost

Numerous applications demand that we manipulate large sets of very high-dimensional signals. A simple yet common example is the problem of finding those signals in a database that are closest to a query. In this paper, we tackle this problem by restricting ...

2007

Matching Pursuit with Block Incoherent Dictionaries

Pierre Vandergheynst, Lorenzo Peotta

There has been an intense activity recently in the field of sparse approximations with redundant dictionaries, largely motivated by the practical performances of algorithms such as Matching Pursuit and Basis Pursuit. However, most of the theoretical result ...

2007