Publications related to Correspondence principle between spherical and Euclidean wavelets

The continuous wavelet transform on conic sections

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

We review the known construction of the continuous wavelet transform (CWT) on the two-sphere. Next we describe the construction of a CWT on the upper sheet of a two- sheeted hyperboloid, emphasizing the similarities between the two cases. Finally we give s ...

2008

The continous wavelet transform on conic sections

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

We review the coherent state or group-theoretical construction of the continuous wavelet transform (CWT) on the two-sphere. Next we describe the construction of a CWT on the upper sheet of a two-sheeted hyperboloid, emphasizing the similarities between the ...

2008

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

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

Sparsity-based Source Separation with Scale-Discretized Steerable Wavelets

Pierre Vandergheynst, Yves Wiaux

In this talk, we discuss the issue of source separation in a signal on the sphere or on the plane, relying on the sparsity of one signal component in a scale-discretized steerable wavelet basis. The steerability of wavelets allows to probe in detail the lo ...

2008

Wavelets on the two-sphere and other conic sections

Pierre Vandergheynst

We review the construction of the continuous wavelet transform (CWT) on the two-sphere by two methods, the group-theoretical approach and the geometrical method based on conformal invariance. Then we discuss the discretization of the spherical CWT, obtaini ...

2007

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

Alignment and signed-intensity anomalies in WMAP data

Pierre Vandergheynst, Yves Wiaux

Significant alignment and signed-intensity anomalies of local features of the cosmic microwave background (CMB) are detected on the three-year WMAP data, through a decomposition of the signal with steerable wavelets on the sphere. In addition to identifyin ...

2007

Fast directional correlation on the sphere with steerable filters

Pierre Vandergheynst, Yves Wiaux, Laurent Jacques

A fast algorithm is developed for the directional correlation of scalar band-limited signals and band-limited steerable filters on the sphere. The asymptotic complexity associated to it through simple quadrature is of order O(L^5), where 2L stands for the ...

2006

Low-Rate Reduced Complexity Image Compression using Directionlets

Martin Vetterli, Vladan Velisavljevic, Pier Luigi Dragotti

The standard separable two-dimensional (2-D) wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to capture efficiently one-dimensional (1-D) disco ...

2006

Correspondence principle between spherical and Euclidean wavelets

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The continuous wavelet transform on conic sections

The continous wavelet transform on conic sections

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

The Monogenic Riesz-Laplace Wavelet Transform

Sparsity-based Source Separation with Scale-Discretized Steerable Wavelets

Wavelets on the two-sphere and other conic sections

Cosmological applications of a wavelet analysis on the sphere

Alignment and signed-intensity anomalies in WMAP data

Fast directional correlation on the sphere with steerable filters

Low-Rate Reduced Complexity Image Compression using Directionlets

Sparsity-based Source Separation with Scale-Discretized Steerable Wavelets

The Monogenic Riesz-Laplace Wavelet Transform

Cosmological applications of a wavelet analysis on the sphere

Wavelets on the two-sphere and other conic sections

Alignment and signed-intensity anomalies in WMAP data

Low-Rate Reduced Complexity Image Compression using Directionlets

The continuous wavelet transform on conic sections

The continous wavelet transform on conic sections

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

Fast directional correlation on the sphere with steerable filters