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Discrete-Time Wavelet Extrema Representation - Design and Consistent Reconstruction

Related publications (39)

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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

Framing pyramids

Martin Vetterli, Minh Do

In 1983, Burt and Adelson introduced the Laplacian pyramid (LP) as a multiresolution representation for images. We study the LP using the frame theory, and this reveals that the usual reconstruction is suboptimal. We show that the LP with orthogonal filter ...

2003

Statistical wavelet analysis of functional images of the brain

Functional magnetic resonance imaging (fMRI) is a recent, non-invasive technique that allows the measurement of brain metabolism while a subject is performing specific motor or cognitive tasks. The practical difficulty is that the signal changes are very s ...

EPFL2002

Fourier and wavelet transform analysis, a tool for visualising regular patterns in DNA

Pierre Vandergheynst

A correlation function that compares each base in a DNA sequence to its various neighbours and which is subsequently processed by Fourier and wavelet transforms has been developed. The procedure has been applied to sequences from the human chromosome 22, t ...

2000

Wavelet Projections for Volume Rendering

Michaël Unser, Martin Vetterli

We extended Gross's method of volume wavelet rendering by computing splats via an orthogonal projection operator. The method decomposes the volume data into a wavelet pyramid representation in the spline domain. The splats of the basis functions are approx ...

EUROGRAPHICS1999

Directional Wavelets Revisited: Cauchy Wavelets and Symmetry Detection in Patterns

Pierre Vandergheynst

The analysis of oriented features in images requires two-dimensional directional wavelets. Among these, we study in detail the class of Cauchy wavelets, which are strictly supported in a (narrow) convex cone in spatial frequency space. They have excellent ...

1999

Using Iterated Rational Filter Banks Within the ARSIS Concept for Producing 10 m Landsat Multispectral Images

Thierry Blu

The ARSIS concept is designed to increase the spatial resolution of an image without modification of its spectral contents, by merging structures extracted from a higher resolution image of the same scene, but in a different spectral band. It makes use of ...

International Journal of Remote Sensing1998

Wavelets and Filter Banks: Theory and Design

Martin Vetterli

The wavelet transform is compared with the more classical short-time Fourier transform approach to signal analysis. Then the relations between wavelets, filter banks, and multiresolution signal processing are explored. A brief review is given of perfect re ...

1992