Publications related to Wavelet analysis of the Besov regularity of Levy white noise

Gabor Wavelet Analysis and the Fractional Hilbert Transform

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

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

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

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

Michaël Unser, Kunal Narayan Chaudhury

We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions-the B-spline factorization theorem. In particular, starting from well-localized sc ...

IEEE2009

The Fractional Hilbert Transform and Dual-Tree Gabor-Like Wavelet Analysis

Michaël Unser, Kunal Narayan Chaudhury

We provide an amplitude-phase representation of the dual-tree complex wavelet transform by extending the fixed quadrature relationship of the dual-tree wavelets to arbitrary phase-shifts using the fractional Hilbert transform (fHT). The fHT is a generaliza ...

IEEE2009

Towards a femtosecond laser micro-machined optofluidic device for distinguishing algae species

Yves Bellouard

We demonstrate a small device with a microfluidic channel and an integrated waveguide that functions a compact rudimentary tool for the detection, real-time monitoring, and potentially classification of algae. In order to reduce parasitic noise the micro-d ...

2009

The Fractional Hilbert Transform And Dual-Tree Gabor-Like Wavelet Analysis

Michaël Unser, Kunal Narayan Chaudhury

We provide an amplitude-phase representation of the dual-tree complex wavelet transform by extending the fixed quadrature relationship of the dual-tree wavelets to arbitrary phase-shifts using the fractional Hilbert transform. (fHT). The fHT is a generaliz ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2009

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

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Michaël Unser, Dimitri Nestor Alice Van De Ville

A distinction is usually made between wavelet bases and wavelet frames. The former are associated with a one-to-one representation of signals, which is somewhat constrained but most efficient computationally. The latter are over-complete, but they offer ad ...

Institute of Electrical and Electronics Engineers2008

Wavelet analysis of the Besov regularity of Levy white noise

Graph Chatbot

Chat with Graph Search

Gabor Wavelet Analysis and the Fractional Hilbert Transform

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

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

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

The Fractional Hilbert Transform and Dual-Tree Gabor-Like Wavelet Analysis

Towards a femtosecond laser micro-machined optofluidic device for distinguishing algae species

The Fractional Hilbert Transform And Dual-Tree Gabor-Like Wavelet Analysis

Self-Similar Random Vector Fields and Their Wavelet Analysis

The Monogenic Riesz-Laplace Wavelet Transform

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

Self-Similar Random Vector Fields and Their Wavelet Analysis

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

Towards a femtosecond laser micro-machined optofluidic device for distinguishing algae species

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Gabor Wavelet Analysis and the Fractional Hilbert Transform

The Fractional Hilbert Transform and Dual-Tree Gabor-Like Wavelet Analysis

The Fractional Hilbert Transform And Dual-Tree Gabor-Like Wavelet Analysis

The Monogenic Riesz-Laplace Wavelet Transform