Publications related to Wavelets and signal processing

Multiscale event detection in social media

Event detection has been one of the most important research topics in social media analysis. Most of the traditional approaches detect events based on fixed temporal and spatial resolutions, while in reality events of different scales usually occur simulta ...

Springer2015

A wavelet analysis for the X-ray absorption spectra of molecules

Majed Chergui, Ursula Röthlisberger, Ivano Tavernelli, Thomas James Penfold, Amal El Nahhas, Marco Eli Reinhard

We present a Wavelet transform analysis for the X-ray absorption spectra of molecules. In contrast to the traditionally used Fourier transform approach, this analysis yields a 2D correlation plot in both R- and k-space. As a consequence, it is possible to ...

American Institute of Physics2013

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

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

Accelerated Wavelet-Regularized Deconvolution For 3-D Fluorescence Microcopy

Michaël Unser, Matthieu Guerquin-Kern, Ilker Bayram, Raquel Terrés Cristofani

Modern deconvolution algorithms are often specified as minimization problems involving a non-quadratic regularization functional. When the latter is a wavelet-domain l(1)-norm that favors sparse solutions, the problem can be solved by a simple iterative sh ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

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

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

The use of wavelet transform for an automated initialization in GPS/MEMS-IMU integration

Jan Skaloud, Adrian Wägli, Heidi Fournier

The main objective of this research is in automating the initialization phase of the MEMS-IMZ/GPS data integration. The motivation for this study is the special case where the before mentioned sensors are worn on a body (e.g. of an athlete) and where the u ...

2009

Self-Similar Random Vector Fields and Their Wavelet Analysis

Michaël Unser, Pouya Dehghani Tafti

This paper is concerned with the mathematical characterization and wavelet analysis of self-similar random vector fields. The study consists of two main parts: the construction of random vector models on the basis of their invariance under coordinate trans ...

SPIE2009

The Monogenic Riesz-Laplace Wavelet Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville, Katarina Balac

We introduce a family of real and complex wavelet bases of

L _{ 2 }

(\mathbb{R} ^{ 2 }

) that are directly linked to the Laplace and Riesz operators. The crucial point is that the family is closed with respect to the Riesz transform which maps a re ...

EURASIP2008

Wavelets and signal processing

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Multiscale event detection in social media

A wavelet analysis for the X-ray absorption spectra of molecules

Optimally Localized Wavelets and Smoothing Kernels

On the Shiftability of Dual-Tree Complex Wavelet Transforms

Accelerated Wavelet-Regularized Deconvolution For 3-D Fluorescence Microcopy

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Gabor Wavelet Analysis and the Fractional Hilbert Transform

The use of wavelet transform for an automated initialization in GPS/MEMS-IMU integration

Self-Similar Random Vector Fields and Their Wavelet Analysis

The Monogenic Riesz-Laplace Wavelet Transform

Self-Similar Random Vector Fields and Their Wavelet Analysis

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Gabor Wavelet Analysis and the Fractional Hilbert Transform

Multiscale event detection in social media

The Monogenic Riesz-Laplace Wavelet Transform

Optimally Localized Wavelets and Smoothing Kernels

On the Shiftability of Dual-Tree Complex Wavelet Transforms

A wavelet analysis for the X-ray absorption spectra of molecules

Accelerated Wavelet-Regularized Deconvolution For 3-D Fluorescence Microcopy

The use of wavelet transform for an automated initialization in GPS/MEMS-IMU integration