Publications related to Optimizing Wavelets for the Analysis of fMRI Data

Construction of Hilbert Transform Pairs of Wavelet Bases and Optimal Time-Frequency Localization

We propose a novel method of constructing exact Hilbert transform (HT) pairs of wavelet bases using fractional B-splines and state necessary and sufficient conditions for generating such wavelet pairs. In particular, we demonstrate how HT pairs of biorthog ...

IEEE2008

Innovation modelling and wavelet analysis of fractal processes in bio-imaging

Michaël Unser, Dimitri Nestor Alice Van De Ville, Pouya Dehghani Tafti

Growth and form in biology are often associated with some level of fractality. Fractal characteristics have also been noted in a number of imaging modalities. These observations make fractal modelling relevant in the context of bio-imaging. ...

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

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

WSPM: Wavelet-Based Statistical Parametric Mapping

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

Recently, we have introduced an integrated framework that combines wavelet-based processing with statistical testing in the spatial domain. In this paper, we propose two important enhancements of the framework. First, we revisit the underlying paradigm; i. ...

Elsevier2007

Activelets and sparsity: A new way to detect brain activation from fMRI data - art. no. 67010Y

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

FMRI time course processing is traditionally performed using linear regression followed by statistical hypothesis testing. While this analysis method is robust against noise, it relies strongly on the signal model. In this paper, we propose a non-parametri ...

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

Activelets and Sparsity: A New Way to Detect Brain Activation from fMRI Data

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

FMRI time course processing is traditionally performed using linear regression followed by statistical hypothesis testing. While this analysis method is robust against noise, it relies strongly on the signal model. In this paper, we propose a non-parametri ...

SPIE2007

Continuous Wavelet Transform on the Hyperboloid

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

In this paper we build a Continuous Wavelet Transform (CWT) on the upper sheet of the 2-hyperboloid

H_+^2

. First, we define a class of suitable dilations on the hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to $SO ...

2007

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

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

Wavelet based statistical analysis for optical imaging in mouse olfactory bulb

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

Optical imaging is a powerful technique to map brain function in animals. In this study, we consider in vivo optical imaging of the murine olfactory bulb, using an intrinsic Signal and a genetically expressed activity reporter fluorescent protein (synaptop ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2007

Optimizing Wavelets for the Analysis of fMRI Data

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Construction of Hilbert Transform Pairs of Wavelet Bases and Optimal Time-Frequency Localization

Innovation modelling and wavelet analysis of fractal processes in bio-imaging

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

WSPM: Wavelet-Based Statistical Parametric Mapping

Activelets and sparsity: A new way to detect brain activation from fMRI data - art. no. 67010Y

Activelets and Sparsity: A New Way to Detect Brain Activation from fMRI Data

Continuous Wavelet Transform on the Hyperboloid

Generalized Daubechies Wavelet Families

Wavelets on the two-sphere and other conic sections

Wavelet based statistical analysis for optical imaging in mouse olfactory bulb

Wavelets on the two-sphere and other conic sections

Continuous Wavelet Transform on the Hyperboloid

WSPM: Wavelet-Based Statistical Parametric Mapping

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

Wavelet based statistical analysis for optical imaging in mouse olfactory bulb

Activelets and sparsity: A new way to detect brain activation from fMRI data - art. no. 67010Y

Construction of Hilbert Transform Pairs of Wavelet Bases and Optimal Time-Frequency Localization

Innovation modelling and wavelet analysis of fractal processes in bio-imaging

Activelets and Sparsity: A New Way to Detect Brain Activation from fMRI Data

Generalized Daubechies Wavelet Families