Publications related to Sparsity-based Source Separation with Scale-Discretized Steerable Wavelets

Optimally Localized Wavelets and Smoothing Kernels

It is well-known that the Gaussian functions and, more generally, their modulations-translations (the Gabor functions) have the unique property of being optimally localized in space and frequency in the sense of Heisenberg's uncertainty principle. In this ...

EPFL2011

Sensing and Recovery under Sparsity Constraints

Ali Hormati

Popular transforms, like the discrete cosine transform or the wavelet transform, owe their success to the fact that they promote sparsity. These transforms are capable of extracting the structure of a large class of signals and representing them by a few t ...

EPFL2010

Wavelet domain Bayesian denoising of string signal in the cosmic microwave background

Pierre Vandergheynst, Yves Wiaux

An algorithm is proposed for denoising the signal induced by cosmic strings in the cosmic microwave background (CMB). A Bayesian approach is taken, based on modeling the string signal in the wavelet domain with generalized Gaussian distributions. Good perf ...

2009

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville, Daniel Sage

The monogenic signal is the natural 2-D counterpart of the 1-D analytic signal. We propose to transpose the concept to the wavelet domain by considering a complexified version of the Riesz transform which has the remarkable property of mapping a real-value ...

Institute of Electrical and Electronics Engineers2009

Exact reconstruction with directional wavelets on the sphere

Pierre Vandergheynst, Yves Wiaux, Jason Douglas McEwen

A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of a previously developed wavelet formalism developed by Antoine & Vandergheynst and Wiaux et a ...

2008

Non-Gaussianity analysis on local morphological measures of WMAP data

Pierre Vandergheynst, Yves Wiaux

The decomposition of a signal on the sphere with the steerable wavelet constructed from the second Gaussian derivative gives access to the orientation, signed-intensity and elongation of the signal’s local features. In the present work, the non-Gaussianity ...

2008

The Monogenic Riesz-Laplace Wavelet Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville, Katarina Balac

We introduce a family of real and complex wavelet bases of

L _{ 2 }

(\mathbb{R} ^{ 2 }

) that are directly linked to the Laplace and Riesz operators. The crucial point is that the family is closed with respect to the Riesz transform which maps a re ...

EURASIP2008

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Michaël Unser, Dimitri Nestor Alice Van De Ville

A distinction is usually made between wavelet bases and wavelet frames. The former are associated with a one-to-one representation of signals, which is somewhat constrained but most efficient computationally. The latter are over-complete, but they offer ad ...

Institute of Electrical and Electronics Engineers2008

Cosmological applications of a wavelet analysis on the sphere

Yves Wiaux, Jason Douglas McEwen

The cosmic microwave background (CMB) is a relic radiation of the Big Bang and as such it contains a wealth of cosmological information. Statistical analyses of the CMB, in conjunction with other cosmological observables, represent some of the most powerfu ...

2007

Construction of wavelet bases that mimic the behaviour of some given operator - art. no. 67010S

Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu, Ildar Khalidov

Probably, the most important property of wavelets for signal processing is their multiscale derivative-like behavior when applied to functions. In order to extend the class of problems that can profit of wavelet-based techniques, we propose to build new fa ...

Spie-Int Soc Optical Engineering, Po Box 10, Bellingham, Wa 98227-0010 Usa2007

Sparsity-based Source Separation with Scale-Discretized Steerable Wavelets

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Optimally Localized Wavelets and Smoothing Kernels

Sensing and Recovery under Sparsity Constraints

Wavelet domain Bayesian denoising of string signal in the cosmic microwave background

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Exact reconstruction with directional wavelets on the sphere

Non-Gaussianity analysis on local morphological measures of WMAP data

The Monogenic Riesz-Laplace Wavelet Transform

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Cosmological applications of a wavelet analysis on the sphere

Construction of wavelet bases that mimic the behaviour of some given operator - art. no. 67010S

Optimally Localized Wavelets and Smoothing Kernels

Sensing and Recovery under Sparsity Constraints

The Monogenic Riesz-Laplace Wavelet Transform

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Cosmological applications of a wavelet analysis on the sphere

Non-Gaussianity analysis on local morphological measures of WMAP data

Exact reconstruction with directional wavelets on the sphere

Construction of wavelet bases that mimic the behaviour of some given operator - art. no. 67010S

Wavelet domain Bayesian denoising of string signal in the cosmic microwave background