Publications related to Generalized Biorthogonal Daubechies 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

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

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 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

Dynamic PET Reconstruction Using Wavelet Regularization with Adapted Basis Functions

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

Tomographic reconstruction from positron emission tomography (PET) data is an ill-posed problem that requires regularization. An attractive approach is to impose an

\ell_{ 1 }

-regularization constraint, which favors sparse solutions in the wavelet dom ...

Institute of Electrical and Electronics Engineers2008

The Marr Wavelet Pyramid

Michaël Unser, Dimitri Nestor Alice Van De Ville

We introduce a new semi-orthogonal complex wavelet basis of

L _{ 2 }

(\mathbb{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- ...

IEEE2008

Nonlinear dynamics of cardiovascular aging

The application of methods drawn from nonlinear and stochastic dynamics to the analysis of cardiovascular time series are applied with particular interests in the identification of changes associated with aging. Scale invariant and scale dependent approach ...

Lancaster University2007

A New Family of Rotation-Covariant Wavelets on the Hexagonal Lattice

Dimitri Nestor Alice Van De Ville

We present multiresolution spaces of complex rotation-covariant functions, deployed on the 2-D hexagonal lattice. The designed wavelets, which are complex-valued, provide an important phase information for image analysis, which is missing in the discrete w ...

SPIE2007

Generalized Daubechies Wavelet Families

Michaël Unser, Thierry Blu, Cédric René Jean Vonesch

We present a generalization of the orthonormal Daubechies wavelets and of their related biorthogonal flavors (Cohen-Daubechies-Feauveau, 9⁄7). Our fundamental constraint is that the scaling functions should reproduce a predefined set of exponential polynom ...

IEEE2007

Generalized Biorthogonal Daubechies Wavelets

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Optimally Localized Wavelets and Smoothing Kernels

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

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

The Monogenic Riesz-Laplace Wavelet Transform

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

Dynamic PET Reconstruction Using Wavelet Regularization with Adapted Basis Functions

The Marr Wavelet Pyramid

Nonlinear dynamics of cardiovascular aging

A New Family of Rotation-Covariant Wavelets on the Hexagonal Lattice

Generalized Daubechies Wavelet Families

Optimally Localized Wavelets and Smoothing Kernels

Generalized Daubechies Wavelet Families

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Nonlinear dynamics of cardiovascular aging

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

The Marr Wavelet Pyramid

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

The Monogenic Riesz-Laplace Wavelet Transform

Dynamic PET Reconstruction Using Wavelet Regularization with Adapted Basis Functions

A New Family of Rotation-Covariant Wavelets on the Hexagonal Lattice