Concept

Gabor atom

Publications associées (13)

Optimal Window and Lattice in Gabor Transform. Application to Audio Analysis

This article deals with the use of optimal lattice and optimal window in Discrete Gabor Transform computation. In the case of a generalized Gaussian window, extending earlier contributions, we introduce an additional local window adaptation technique for n ...

Ieee2016

An optimally concentrated Gabor transform for localized time-frequency components

Benjamin Ricaud

Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing. Many time-freque ...

Springer2014

A Unifying Parametric Framework for 2D Steerable Wavelet Transforms

Michaël Unser

We introduce a complete parameterization of the family of two-dimensional steerable wavelets that are polar-separable in the Fourier domain under the constraint of self-reversibility. These wavelets are constructed by multiorder generalized Riesz transform ...

Siam Publications2013

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

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

Wavelets on graphs via spectral graph theory

Pierre Vandergheynst, Rémi Gribonval

We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely the spectral deco ...

Elsevier2011

On the Shiftability of Dual-Tree Complex Wavelet Transforms

Michaël Unser, Kunal Narayan Chaudhury

The dual-tree complex wavelet transform (DT-ℂWT) is known to exhibit better shift-invariance than the conventional discrete wavelet transform. We propose an amplitude-phase representation of the DT-ℂWT which, among other things, offers a direct explanation ...

IEEE2010

Gabor Wavelet Analysis and the Fractional Hilbert Transform

Michaël Unser, Kunal Narayan Chaudhury

We propose an amplitude-phase representation of the dual-tree complex wavelet transform (DT-ℂWT) which provides an intuitive interpretation of the associated complex wavelet coefficients. The representation, in particular, is based on the shifting action o ...

SPIE2009

A Fast Multilevel Algorithm for Wavelet-Regularized Image Restoration

Michaël Unser, Cédric René Jean Vonesch

We present a multilevel extension of the popular "thresholded Landweber" algorithm for wavelet-regularized image restoration that yields an order of magnitude speed improvement over the standard fixed-scale implementation. The method is generic and targete ...

IEEE2009

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville, Daniel Sage

The monogenic signal is the natural 2-D counterpart of the 1-D analytic signal. We propose to transpose the concept to the wavelet domain by considering a complexified version of the Riesz transform which has the remarkable property of mapping a real-value ...

Institute of Electrical and Electronics Engineers2009