Concept

Discrete wavelet transform

Publications associées (527)

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A Laplacian pyramid scheme in graph signal processing

Mohammadjavad Faraji

In this report we extend the ideas behind classical multiscale signal processing techniques in order to analyze data residing on graphs. In particular, we extend the notions of filtering, downsampling, and upsampling to functions defined on graphs. We then ...

2011

Filter Bank Fusion frames

Amina Chebira

In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly designed, fusion fra ...

Institute of Electrical and Electronics Engineers2011

On the Hilbert Transform of Wavelets

Michaël Unser, Kunal Narayan Chaudhury

A wavelet is a localized function having a prescribed number of vanishing moments. In this correspondence, we provide precise arguments as to why the Hilbert transform of a wavelet is again a wavelet. In particular, we provide sharp estimates of the locali ...

IEEE2011

Optimally Localized Wavelets and Smoothing Kernels

Kunal Narayan Chaudhury

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

Time-scale joint representation of DNS and LES numerical data

Michel Deville, Emmanuel Leriche, Roland Bouffanais

A spectral analysis and a multiscale study are performed on the numerical data obtained from direct numerical simulation and large-eddy simulation of the turbulent flow in a cubical lid-driven cavity. The analyzed data or signals are picked at three specif ...

2011

Semi-Supervised Learning with Spectral Graph Wavelets

Pierre Vandergheynst, David Shuman, Mohammadjavad Faraji

We consider the transductive learning problem when the labels belong to a continuous space. Through the use of spectral graph wavelets, we explore the benefits of multiresolution analysis on a graph constructed from the labeled and unlabeled data. The spec ...

2011

Image Denoising in Mixed Poisson-Gaussian Noise

Michaël Unser, Thierry Blu, Florian Luisier

We propose a general methodology (PURE-LET) to design and optimize a wide class of transform-domain thresholding algorithms for denoising images corrupted by mixed Poisson-Gaussian noise. We express the denoising process as a linear expansion of thresholds ...

Institute of Electrical and Electronics Engineers2011

An automatic system to locate phase-to-ground faults in medium voltage cable networks based on the wavelet analysis of high-frequency signals

Mario Paolone

The paper presents a microcontroller-based automatic system that applies the continuous wavelet analysis to the measured fault-originated electromagnetic transients in order to locate phase-to-ground faults in power distribution networks composed by coaxia ...

2011

On the effect of image denoising on galaxy shape measurements

Frédéric Courbin, Georges Meylan, Marc Gentile, Guldariya Nurbaeva

Weak gravitational lensing is a very sensitive way of measuring cosmological parameters, including dark energy, and of testing current theories of gravitation. In practice, this requires exquisite measurement of the shapes of billions of galaxies over larg ...

2011

Wavelet Frames On Graphs Defined By Fmri Functional Connectivity

Dimitri Nestor Alice Van De Ville, Nora Leonardi

Multiscale representations such as the wavelet transform are useful for many signal processing tasks. Graphs are flexible models to represent complex networks and a spectral graph wavelet transform (SGWT) has recently been developed as a generalization of ...

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