Publications related to Discrete wavelet transform

The continuous wavelet transform on conic sections

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

We review the known construction of the continuous wavelet transform (CWT) on the two-sphere. Next we describe the construction of a CWT on the upper sheet of a two- sheeted hyperboloid, emphasizing the similarities between the two cases. Finally we give s ...

2008

The continous wavelet transform on conic sections

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

We review the coherent state or group-theoretical construction of the continuous wavelet transform (CWT) on the two-sphere. Next we describe the construction of a CWT on the upper sheet of a two-sheeted hyperboloid, emphasizing the similarities between the ...

2008

The Marr Wavelet Pyramid

Michaël Unser, Dimitri Nestor Alice Van De Ville

We introduce a new semi-orthogonal complex wavelet basis of

L _{ 2 }

(\mathbb{R} ^{ 2 }

). The basis functions are associated to the complex gradient-Laplace operator, which plays a central role in image processing. We define analytically a single- ...

IEEE2008

Shift-Invariant Spaces from Rotation-Covariant Functions

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

We consider shift-invariant multiresolution spaces generated by rotation-covariant functions ρ in

\mathbb{R}^{ 2 }

. To construct corresponding scaling and wavelet functions, ρ has to be localized with an appropriate multiplier, such that the localized ...

Elsevier2008

A Fast Thresholded Landweber Algorithm for General Wavelet Bases: Application to 3D Deconvolution Microscopy

Michaël Unser, Cédric René Jean Vonesch

Wavelet-domain

ℓ _{ 1 }

-regularization is a promising approach to deconvolution. The corresponding variational problem can be solved using a “thresholded Landweber” (TL) algorithm. While this iterative procedure is simple to implement, it is known to ...

IEEE2008

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 graph. We define a notion of scaling using the graph analogue of the Fourier domain, namely the space of eigenfunctions forming the sp ...

2008

Fast Computation of Polyharmonic B-Spline Autocorrelation Filters

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

A fast computational method is given for the Fourier transform of the polyharmonic B-spline autocorrelation sequence in d dimensions. The approximation error is exponentially decaying with the number of terms taken into account. The algorithm improves spee ...

Institute of Electrical and Electronics Engineers2008

A Fast Thresholded Landweber Algorithm for Wavelet-Regularized Multidimensional Deconvolution

Michaël Unser, Cédric René Jean Vonesch

We present a fast variational deconvolution algorithm that minimizes a quadratic data term subject to a regularization on the

\ell ^{ 1 }

-norm of the wavelet coefficients of the solution. Previously available methods have essentially consisted in alte ...

IEEE2008

Bitstream format for spatio-temporal wave field coder

Martin Vetterli, Francisco Pereira Correia Pinto

We present a non-parametric method for compressing multichannel audio data for reproduction through Wave Field Synthesis. The method consists of applying a two-dimensional filterbank to the input mul- tichannel signal, in both time and channel dimensions, ...

2008

Innovation modelling and wavelet analysis of fractal processes in bio-imaging

Michaël Unser, Dimitri Nestor Alice Van De Ville, Pouya Dehghani Tafti

Growth and form in biology are often associated with some level of fractality. Fractal characteristics have also been noted in a number of imaging modalities. These observations make fractal modelling relevant in the context of bio-imaging. ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2008

Discrete wavelet transform

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The continuous wavelet transform on conic sections

The continous wavelet transform on conic sections

The Marr Wavelet Pyramid

Shift-Invariant Spaces from Rotation-Covariant Functions

A Fast Thresholded Landweber Algorithm for General Wavelet Bases: Application to 3D Deconvolution Microscopy

Wavelets on Graphs via Spectral Graph Theory

Fast Computation of Polyharmonic B-Spline Autocorrelation Filters

A Fast Thresholded Landweber Algorithm for Wavelet-Regularized Multidimensional Deconvolution

Bitstream format for spatio-temporal wave field coder

Innovation modelling and wavelet analysis of fractal processes in bio-imaging

The continuous wavelet transform on conic sections

A Fast Thresholded Landweber Algorithm for General Wavelet Bases: Application to 3D Deconvolution Microscopy

Fast Computation of Polyharmonic B-Spline Autocorrelation Filters

The Marr Wavelet Pyramid

A Fast Thresholded Landweber Algorithm for Wavelet-Regularized Multidimensional Deconvolution

Wavelets on Graphs via Spectral Graph Theory

Bitstream format for spatio-temporal wave field coder

Innovation modelling and wavelet analysis of fractal processes in bio-imaging

Shift-Invariant Spaces from Rotation-Covariant Functions

The continous wavelet transform on conic sections