Publications related to Fractional Wavelets, Derivatives, and Besov Spaces

Construction of Hilbert Transform Pairs of Wavelet Bases and Optimal Time-Frequency Localization

We propose a novel method of constructing exact Hilbert transform (HT) pairs of wavelet bases using fractional B-splines and state necessary and sufficient conditions for generating such wavelet pairs. In particular, we demonstrate how HT pairs of biorthog ...

IEEE2008

A New Family of Rotation-Covariant Wavelets on the Hexagonal Lattice

Dimitri Nestor Alice Van De Ville

We present multiresolution spaces of complex rotation-covariant functions, deployed on the 2-D hexagonal lattice. The designed wavelets, which are complex-valued, provide an important phase information for image analysis, which is missing in the discrete w ...

SPIE2007

Self-Similarity: Part I—Splines and Operators

Michaël Unser, Thierry Blu

The central theme of this pair of papers (Parts I and II in this issue) is self-similarity, which is used as a bridge for connecting splines and fractals. The first part of the investigation is deterministic, and the context is that of L-splines; these are ...

IEEE2007

A fast iterative thresholding algorithm for wavelet-regularized deconvolution - art. no. 67010D

Michaël Unser, Cédric René Jean Vonesch

We present an iterative deconvolution algorithm that minimizes a functional with a non-quadratic wavelet-domain regularization term. Our approach is to introduce subband-dependent parameters into the bound optimization framework of Daubechies et al.; it is ...

Spie-Int Soc Optical Engineering, Po Box 10, Bellingham, Wa 98227-0010 Usa2007

Complex B-Splines

Michaël Unser, Thierry Blu

We propose a complex generalization of Schoenberg's cardinal splines. To this end, we go back to the Fourier domain definition of the B-splines and extend it to complex-valued degrees. We show that the resulting complex B-splines are piecewise modulated po ...

Elsevier2006

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

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

The approximate behavior of wavelets as differential operators is often considered as one of their most fundamental properties. In this paper, we investigate how we can further improve on the wavelet's behavior as differentiator. In particular, we propose ...

SPIE2005

Generalized L-Spline Wavelet Bases

Michaël Unser, Thierry Blu, Ildar Khalidov

We build wavelet-like functions based on a parametrized family of pseudo-differential operators

L _{ v }

that satisfy some admissibility and scalability conditions. The shifts of the generalized B-splines, which are localized versions of the Green func ...

SPIE2005

Generalized Daubechies Wavelets

Michaël Unser, Thierry Blu, Cédric René Jean Vonesch

We present a generalization of the Daubechies wavelet family. The context is that of a non-stationary multiresolution analysis—i.e., a sequence of embedded approximation spaces generated by scaling functions that are not necessarily dilates of one another. ...

IEEE2005

Time-lag in Derivative Convergence for Fixed Point Iterations

Daniel Kressner

In an earlier study it was proven and experimentally confirmed on a 2D Euler code that fixed point iterations can be differentiated to yield first and second order derivatives of implicit functions that are defined by state equations. It was also asserted ...

2005

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Pierre Vandergheynst, Oscar Divorra Escoda

In this work, we study the effect of inserting spatially local temporal adaptivity to motion compensated frame adaptive transforms for video coding. Motion compensation aligns the temporal wavelet decomposition along motion trajectories. However, valid tra ...

2004

Fractional Wavelets, Derivatives, and Besov Spaces

Graph Chatbot

Chat with Graph Search

Construction of Hilbert Transform Pairs of Wavelet Bases and Optimal Time-Frequency Localization

A New Family of Rotation-Covariant Wavelets on the Hexagonal Lattice

Self-Similarity: Part I—Splines and Operators

A fast iterative thresholding algorithm for wavelet-regularized deconvolution - art. no. 67010D

Complex B-Splines

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Generalized L-Spline Wavelet Bases

Generalized Daubechies Wavelets

Time-lag in Derivative Convergence for Fixed Point Iterations

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Construction of Hilbert Transform Pairs of Wavelet Bases and Optimal Time-Frequency Localization

A New Family of Rotation-Covariant Wavelets on the Hexagonal Lattice

Generalized L-Spline Wavelet Bases

Complex B-Splines

Self-Similarity: Part I—Splines and Operators

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

A fast iterative thresholding algorithm for wavelet-regularized deconvolution - art. no. 67010D

Generalized Daubechies Wavelets

Time-lag in Derivative Convergence for Fixed Point Iterations