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Wavelets on the sphere : Implementation and approximations

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Fractal additive synthesis

Pietro Polotti

Musical and audio signals in general form a major part of the large amount of data exchange taking place in our information-based society. Transmission of high quality audio signals through narrow-band channels, such as the Internet, requires refined metho ...

EPFL2003

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

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

Statistical Parametric Mapping (SPM) is a widely deployed tool for detecting and analyzing brain activity from fMRI data. One of SPM's main features is smoothing the data by a Gaussian filter to increase the SNR. The subsequent statistical inference is bas ...

SPIE2003

Body movement monitoring device

Kamiar Aminian, Pascal Morel, Bijan Najafi, Jean Gramiger

The invention relates to a device and a method for measuring gait parameters. It is based on autonomous sensing units for estimation of spatio-temporal parameters during walking and uses a wavelet transform to compute the values of gait parameters from the ...

2003

Ambulatory system for human motion analysis using a kinematic sensor: Monitoring of daily physical activity in the elderly

Kamiar Aminian, Philippe Robert, Anisoara Ionescu, Bijan Najafi

A new method of physical activity monitoring is presented, which is able to detect body postures (sitting, standing, and lying) and periods of walking in elderly persons using only one kinematic sensor attached to the chest. The wavelet transform, in conju ...

2003

Directional dyadic wavelet transforms: design and algorithms

Pierre Vandergheynst

We propose a simple and efficient technique for designing translation invariant dyadic wavelet transforms (DWTs) in two dimensions. Our technique relies on an extension of the work of Duval-Destin et al. (1993) where dyadic decompositions are constructed s ...

2002

Continuous Wavelet Transform with Arbitrary Scales and O(N) Complexity

Michaël Unser

Summary The continuous wavelet transform (CWT) is a common signal-processing tool for the analysis of nonstationary signals. We propose here a new B-spline-based method that allows the CWT computation at any scale. A nice property of the algorithm is that ...

Elsevier2002

Wavelets, Fractals, and Radial Basis Functions

Michaël Unser, Thierry Blu

Wavelets and radial basis functions (RBFs) lead to two distinct ways of representing signals in terms of shifted basis functions. RBFs, unlike wavelets, are nonlocal and do not involve any scaling, which makes them applicable to nonuniform grids. Despite t ...

IEEE2002

Discrete Ridgelet Transforms for Image Representation

Martin Vetterli, Minh Do

The ridgelet transform (Candes and Donoho, 1999) was introduced as a new multiscale representation for functions on continuous spaces that are smooth away from discontinuities along lines. In this paper, we present several discrete versions of the ridgelet ...

2001

Fast Continuous Wavelet Transform Based on B-Splines

Michaël Unser

The Continuous Wavelet Transform (CWT) is an effective way to analyze nonstationary signals and to localize and characterize singularities. Fast algorithms have already been developed to compute the CWT at integer time points and dyadic or integer scales. ...

SPIE2001

Optimizing Wavelets for the Analysis of fMRI Data

Michaël Unser, Thierry Blu

Ruttimann et al. have proposed to use the wavelet transform for the detection and localization of activation patterns in functional magnetic resonance imaging (fMRI). Their main idea was to apply a statistical test in the wavelet domain to detect the coeff ...

SPIE2000