Publications related to Generalized L-Spline Wavelet Bases

Analytical Footprints: Compact Representation of Elementary Singularities in Wavelet Bases

Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu

We introduce a family of elementary singularities that are point-Holder alpha-regular. These singularities are self-similar and are the Green functions of fractional derivative operators; i.e., by suitable fractional differentiation, one retrieves a Dirac ...

Institute of Electrical and Electronics Engineers2010

Wavelet Steerability and the Higher-Order Riesz Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville

Our main goal in this paper is to set the foundations of a general continuous-domain framework for designing steerable, reversible signal transformations (a.k.a. frames) in multiple dimensions (d ≥ 2). To that end, we introduce a self-reversible, Nth-order ...

Institute of Electrical and Electronics Engineers2010

Integrated use of time-frequency wavelet decompositions for fault location in distribution networks: Theory and experimental validation

Mario Paolone, Ali Abur

The paper presents a procedure for fault location in distribution networks, based on the use of the integrated time-frequency wavelet decompositions of the voltage transients associated with the fault-originated travelling waves. The proposed analysis of t ...

2010

Operator-like wavelets with application to functional magnetic resonance imaging

Ildar Khalidov

We introduce a new class of wavelets that behave like a given differential operator L. Our construction is inspired by the derivative-like behavior of classical wavelets. Within our framework, the wavelet coefficients of a signal y are the samples of a smo ...

EPFL2009

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

Integrated Use of Time-Frequency Wavelet Decompositions for Fault Location in Distribution Networks: Theory and Experimental Validation

Mario Paolone, Ali Abur

The paper presents a procedure for fault location in distribution networks, based on the use of the integrated time-frequency wavelet decompositions of the voltage transients associated with the fault-originated travelling waves. The proposed analysis of t ...

2009

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

Michaël Unser, Dimitri Nestor Alice Van De Ville

Based on the class of complex gradient-Laplace operators, we show the design of a non-separable two-dimensional wavelet basis from a single and analytically defined generator wavelet function. The wavelet decomposition is implemented by an efficient FFT-ba ...

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

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

Michaël Unser, Dimitri Nestor Alice Van De Ville

Our aim in this paper is to tighten the link between wavelets, some classical image-processing operators, and David Marr's theory of early vision. The cornerstone of our approach is a new complex wavelet basis that behaves like a smoothed version of the Gr ...

Institute of Electrical and Electronics Engineers2008

Generalized L-Spline Wavelet Bases

Graph Chatbot

Chat with Graph Search

Analytical Footprints: Compact Representation of Elementary Singularities in Wavelet Bases

Wavelet Steerability and the Higher-Order Riesz Transform

Integrated use of time-frequency wavelet decompositions for fault location in distribution networks: Theory and experimental validation

Operator-like wavelets with application to functional magnetic resonance imaging

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

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

Integrated Use of Time-Frequency Wavelet Decompositions for Fault Location in Distribution Networks: Theory and Experimental Validation

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

The Monogenic Riesz-Laplace Wavelet Transform

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

The Monogenic Riesz-Laplace Wavelet Transform

Analytical Footprints: Compact Representation of Elementary Singularities in Wavelet Bases

Wavelet Steerability and the Higher-Order Riesz Transform

Integrated use of time-frequency wavelet decompositions for fault location in distribution networks: Theory and experimental validation

Operator-like wavelets with application to functional magnetic resonance imaging

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

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

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

Integrated Use of Time-Frequency Wavelet Decompositions for Fault Location in Distribution Networks: Theory and Experimental Validation

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction