Publications related to Harmonic Singular Integrals and Steerable Wavelets in $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions-the B-spline factorization theorem. In particular, starting from well-localized sc ...

IEEE2009

The use of wavelet transform for an automated initialization in GPS/MEMS-IMU integration

Jan Skaloud, Adrian Wägli, Heidi Fournier

The main objective of this research is in automating the initialization phase of the MEMS-IMZ/GPS data integration. The motivation for this study is the special case where the before mentioned sensors are worn on a body (e.g. of an athlete) and where the u ...

2009

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 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

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

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

An Orthogonal Family of Quincunx Wavelets with Continuously Adjustable Order

Michaël Unser, Dimitri Nestor Alice Van De Ville

We present a new family of two-dimensional and three-dimensional orthogonal wavelets which uses quincunx sampling. The orthogonal refinement filters have a simple analytical expression in the Fourier domain as a function of the order λ, which may be nonint ...

IEEE2005

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

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

The approximate behavior of wavelets as differential operators is often considered as one of their most fundamental properties. In this paper, we investigate how we can further improve on the wavelet's behavior as differentiator. In particular, we propose ...

SPIE2005

Harmonic Singular Integrals and Steerable Wavelets in $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

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Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

The use of wavelet transform for an automated initialization in GPS/MEMS-IMU integration

The continuous wavelet transform on conic sections

The continous wavelet transform on conic sections

The Monogenic Riesz-Laplace Wavelet Transform

Wavelets on the two-sphere and other conic sections

Fast directional correlation on the sphere with steerable filters

Low-Rate Reduced Complexity Image Compression using Directionlets

An Orthogonal Family of Quincunx Wavelets with Continuously Adjustable Order

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

The continous wavelet transform on conic sections

The Monogenic Riesz-Laplace Wavelet Transform

The use of wavelet transform for an automated initialization in GPS/MEMS-IMU integration

Low-Rate Reduced Complexity Image Compression using Directionlets

The continuous wavelet transform on conic sections

Fast directional correlation on the sphere with steerable filters

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Wavelets on the two-sphere and other conic sections

An Orthogonal Family of Quincunx Wavelets with Continuously Adjustable Order