Publications related to Wavelets Versus Resels in the Context of fMRI: Establishing the Link with SPM

WSPM or How to Obtain Statistical Parametric Maps Using Shift-Invariant Wavelet Processing

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

Recently, we have proposed a new framework for detecting brain activity from fMRI data, which is based on the spatial discrete wavelet transform. The standard wavelet-based approach performs a statistical test in the wavelet domain, and therefore fails to ...

IEEE2006

Wavelet-Based Detection of Stimulus Responses in Time-Lapse Microscopy

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

Many experimental paradigms in biology aim at studying the response to coordinated stimuli. In dynamic imaging experiments, the observed data is often not straightforward to interpret and not directly measurable in a quantitative fashion. Consequently, the ...

IEEE2006

Generalized L-Spline Wavelet Bases

Michaël Unser, Thierry Blu, Ildar Khalidov

We build wavelet-like functions based on a parametrized family of pseudo-differential operators

L _{ v }

that satisfy some admissibility and scalability conditions. The shifts of the generalized B-splines, which are localized versions of the Green func ...

SPIE2005

Wavelet Transform Analysis of Truncated Fringe Patterns in 3-D Surface Profilometry

Sai Siva Gorthi

Wavelet transform analysis of projected fringe pattern for phase recovery in 3-D shape measurement of objects is investigated. The present communication specifically outlines and evaluates the errors that creep in to the reconstructed profiles when fringe ...

2005

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

Correspondence principle between spherical and Euclidean wavelets

Pierre Vandergheynst, Yves Wiaux, Laurent Jacques

Wavelets on the sphere are reintroduced and further developed independently of the original group theoretic formalism, in an equivalent, but more straightforward approach. These developments are motivated by the interest of the scale-space analysis of the ...

2005

Exponential-Spline Wavelet Bases

Michaël Unser, Ildar Khalidov

We build a multiresolution analysis based on shift-invariant exponential B-spline spaces. We construct the basis functions for these spaces and for their orthogonal complements. This yields a new family of wavelet-like basis functions of

L _{ 2 }

, wit ...

IEEE2005

Stereographic Wavelet Frames on the Sphere

Pierre Vandergheynst, Laurent Jacques, Iva Bogdanova Vandergheynst

In this paper we exploit the Continuous Wavelet Transform (CWT) on the two dimensional sphere, introduced previously by two of us, to build associated Discrete Wavelet Frames. We first explore half-continuous frames, i.e., frames where the position remains ...

2005

Generalized Biorthogonal Daubechies Wavelets

Michaël Unser, Thierry Blu, Cédric René Jean Vonesch

We propose a generalization of the Cohen-Daubechies-Feauveau (CDF) and 9⁄7 biorthogonal wavelet families. This is done within the framework of non-stationary multiresolution analysis, which involves a sequence of embedded approximation spaces generated by ...

SPIE2005

Construction and comparison of approximations for switching linear gaussian state space models

Bertrand Mesot

We introduce a new method for approximate inference in Hybrid Dynamical Graphical models, in particular, for switching dynamical networks. For the important special case of switching linear Gaussian state space models (switching Kalman Filters), our method ...

IDIAP2005

Wavelets Versus Resels in the Context of fMRI: Establishing the Link with SPM

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WSPM or How to Obtain Statistical Parametric Maps Using Shift-Invariant Wavelet Processing

Wavelet-Based Detection of Stimulus Responses in Time-Lapse Microscopy

Generalized L-Spline Wavelet Bases

Wavelet Transform Analysis of Truncated Fringe Patterns in 3-D Surface Profilometry

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Correspondence principle between spherical and Euclidean wavelets

Exponential-Spline Wavelet Bases

Stereographic Wavelet Frames on the Sphere

Generalized Biorthogonal Daubechies Wavelets

Construction and comparison of approximations for switching linear gaussian state space models

Generalized Biorthogonal Daubechies Wavelets

Correspondence principle between spherical and Euclidean wavelets

Exponential-Spline Wavelet Bases

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Wavelet Transform Analysis of Truncated Fringe Patterns in 3-D Surface Profilometry

Generalized L-Spline Wavelet Bases

Stereographic Wavelet Frames on the Sphere

Construction and comparison of approximations for switching linear gaussian state space models

Wavelet-Based Detection of Stimulus Responses in Time-Lapse Microscopy

WSPM or How to Obtain Statistical Parametric Maps Using Shift-Invariant Wavelet Processing