Publications related to Wavelet-Regularized Reconstruction for Rapid MRI

Near-Optimal Bayesian Localization via Incoherence and Sparsity

This paper exploits recent developments in sparse approximation and compressive sensing to efficiently perform localization in a sensor network. We introduce a Bayesian framework for the localization problem and provide sparse approximations to its optimal ...

2009

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

WSPM: Wavelet-Based Statistical Parametric Mapping

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

Recently, we have introduced an integrated framework that combines wavelet-based processing with statistical testing in the spatial domain. In this paper, we propose two important enhancements of the framework. First, we revisit the underlying paradigm; i. ...

Elsevier2007

Generalized Daubechies Wavelet Families

Michaël Unser, Thierry Blu, Cédric René Jean Vonesch

We present a generalization of the orthonormal Daubechies wavelets and of their related biorthogonal flavors (Cohen-Daubechies-Feauveau, 9⁄7). Our fundamental constraint is that the scaling functions should reproduce a predefined set of exponential polynom ...

IEEE2007

Low-Rate Reduced Complexity Image Compression using Directionlets

Martin Vetterli, Vladan Velisavljevic, Pier Luigi Dragotti

The standard separable two-dimensional (2-D) wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to capture efficiently one-dimensional (1-D) disco ...

2006

Fast directional correlation on the sphere with steerable filters

Pierre Vandergheynst, Yves Wiaux, Laurent Jacques

A fast algorithm is developed for the directional correlation of scalar band-limited signals and band-limited steerable filters on the sphere. The asymptotic complexity associated to it through simple quadrature is of order O(L^5), where 2L stands for the ...

2006

Steerable wavelet analysis of CMB structures alignment

Pierre Vandergheynst, Yves Wiaux

This paper reviews the application of a novel methodology for analysing the isotropy of the universe by probing the alignment of local structures in the CMB. The strength of the proposed methodology relies on the steerable wavelet filtering of the CMB sign ...

2006

Toward sparse and geometry adapted video approximations

Oscar Divorra Escoda

Video signals are sequences of natural images, where images are often modeled as piecewise-smooth signals. Hence, video can be seen as a 3D piecewise-smooth signal made of piecewise-smooth regions that move through time. Based on the piecewise-smooth model ...

EPFL2005

Directionlets

Vladan Velisavljevic

Efficient representation of geometrical information in images is very important in many image processing areas, including compression, denoising and feature extraction. However, the design of transforms that can capture these geometrical features and repre ...

EPFL2005

Wavelet-Based fMRI Statistical Analysis and Spatial Interpretation: A Unifying Approach

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

Wavelet-based statistical analysis methods for fMRI are able to detect brain activity without smoothing the data. Typically, the statistical inference is performed in the wavelet domain by testing the t-values of each wavelet coefficient; subsequently, an ...

IEEE2004

Wavelet-Regularized Reconstruction for Rapid MRI

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Near-Optimal Bayesian Localization via Incoherence and Sparsity

Dynamic PET Reconstruction Using Wavelet Regularization with Adapted Basis Functions

WSPM: Wavelet-Based Statistical Parametric Mapping

Generalized Daubechies Wavelet Families

Low-Rate Reduced Complexity Image Compression using Directionlets

Fast directional correlation on the sphere with steerable filters

Steerable wavelet analysis of CMB structures alignment

Toward sparse and geometry adapted video approximations

Directionlets

Wavelet-Based fMRI Statistical Analysis and Spatial Interpretation: A Unifying Approach

Dynamic PET Reconstruction Using Wavelet Regularization with Adapted Basis Functions

Near-Optimal Bayesian Localization via Incoherence and Sparsity

Fast directional correlation on the sphere with steerable filters

Directionlets

Wavelet-Based fMRI Statistical Analysis and Spatial Interpretation: A Unifying Approach

WSPM: Wavelet-Based Statistical Parametric Mapping

Steerable wavelet analysis of CMB structures alignment

Low-Rate Reduced Complexity Image Compression using Directionlets

Toward sparse and geometry adapted video approximations

Generalized Daubechies Wavelet Families