Publications related to Optimally Localized Wavelets and Smoothing Kernels

Dynamic PET Reconstruction Using Wavelet Regularization with Adapted Basis Functions

Michaël Unser, Dimitri Nestor Alice Van De Ville, Ildar Khalidov

Tomographic reconstruction from positron emission tomography (PET) data is an ill-posed problem that requires regularization. An attractive approach is to impose an

\ell_{ 1 }

-regularization constraint, which favors sparse solutions in the wavelet dom ...

Institute of Electrical and Electronics Engineers2008

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 converge ...

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

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 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

Fast Wavelet based Ultrasound Image Segmentation for Liver Vessels Extraction

Charles Baur, Benoît Dagon

A method for extracting in real-time the position and size of liver vessels from 2D ultrasound images is described. It proceeds in two steps. Starting with a rough localization of the vessels using the scale-space theory, seed points are defined. Then, ves ...

2008

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

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

The “Marr wavelet pyramid” is a wavelet decomposition that implements a multiscale version of the complex gradient-Laplace operator. It is closely linked to a multiresolution analysis of

L _{ 2 }

(\mathbb{R} ^{ 2 }

) and it has a fast filterbank im ...

EURASIP2008

SURE-LET Multichannel Image Denoising: Interscale Orthonormal Wavelet Thresholding

Thierry Blu, Florian Luisier

We propose a vector/matrix extension of our denoising algorithm initially developed for grayscale images, in order to efficiently process multichannel (e.g., color) images. This work follows our recently published SURE-LET approach where the denoising algo ...

Institute of Electrical and Electronics Engineers2008

Image Modeling and Denoising With Orientation-Adapted Gaussian Scale Mixtures

We develop a statistical model to describe the spatially varying behavior of local neighborhoods of coefficients in a multi- scale image representation. Neighborhoods are modeled as samples of a multivariate Gaussian density that are modulated and rotated ...

2008

Construction of Hilbert transform pairs of wavelet bases and optimal time-frequency localization

Michaël Unser, Kunal Narayan Chaudhury

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 ...

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

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

Michaël Unser, Kunal Narayan Chaudhury

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

Optimally Localized Wavelets and Smoothing Kernels

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Dynamic PET Reconstruction Using Wavelet Regularization with Adapted Basis Functions

A fast thresholded landweber algorithm for general wavelet bases: Application to 3D deconvolution microscopy

Shift-Invariant Spaces from Rotation-Covariant Functions

A Fast Thresholded Landweber Algorithm for Wavelet-Regularized Multidimensional Deconvolution

Fast Wavelet based Ultrasound Image Segmentation for Liver Vessels Extraction

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

SURE-LET Multichannel Image Denoising: Interscale Orthonormal Wavelet Thresholding

Image Modeling and Denoising With Orientation-Adapted Gaussian Scale Mixtures

Construction of Hilbert transform pairs of wavelet bases and optimal time-frequency localization

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

A Fast Thresholded Landweber Algorithm for Wavelet-Regularized Multidimensional Deconvolution

Image Modeling and Denoising With Orientation-Adapted Gaussian Scale Mixtures

Shift-Invariant Spaces from Rotation-Covariant Functions

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

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

Dynamic PET Reconstruction Using Wavelet Regularization with Adapted Basis Functions

A fast thresholded landweber algorithm for general wavelet bases: Application to 3D deconvolution microscopy

Fast Wavelet based Ultrasound Image Segmentation for Liver Vessels Extraction

Construction of Hilbert transform pairs of wavelet bases and optimal time-frequency localization

SURE-LET Multichannel Image Denoising: Interscale Orthonormal Wavelet Thresholding