Publications related to Time Resolved Fluorescence Diffuse Optical Tomography Using Multi-Resolution Exponential B-Splines

Sensing and Recovery under Sparsity Constraints

Popular transforms, like the discrete cosine transform or the wavelet transform, owe their success to the fact that they promote sparsity. These transforms are capable of extracting the structure of a large class of signals and representing them by a few t ...

EPFL2010

Sparse Image Representation by Directionlets

Martin Vetterli, Vladan Velisavljevic, Pier Luigi Dragotti

Despite the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency and sparsity of its representation are limited by the spatial symmetry and separability of its basis functions built in the horizontal and vertic ...

Elsevier2010

A Fast Multilevel Algorithm for Wavelet-Regularized Image Restoration

Michaël Unser, Cédric René Jean Vonesch

We present a multilevel extension of the popular "thresholded Landweber" algorithm for wavelet-regularized image restoration that yields an order of magnitude speed improvement over the standard fixed-scale implementation. The method is generic and targete ...

IEEE2009

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

Invariances, Laplacian-Like Wavelet Bases, and the Whitening of Fractal Processes

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

In this contribution, we study the notion of affine invariance (specifically, invariance to the shifting, scaling, and rotation of the coordinate system) as a starting point for the development of mathematical tools and approaches useful in the characteriz ...

IEEE2009

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

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

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

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

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

Time Resolved Fluorescence Diffuse Optical Tomography Using Multi-Resolution Exponential B-Splines

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Sensing and Recovery under Sparsity Constraints

Sparse Image Representation by Directionlets

A Fast Multilevel Algorithm for Wavelet-Regularized Image Restoration

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Invariances, Laplacian-Like Wavelet Bases, and the Whitening of Fractal Processes

Operator-like wavelets with application to functional magnetic resonance imaging

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

Dynamic PET Reconstruction Using Wavelet Regularization with Adapted Basis Functions

Generalized Daubechies Wavelet Families

Fast directional correlation on the sphere with steerable filters

A Fast Multilevel Algorithm for Wavelet-Regularized Image Restoration

Sensing and Recovery under Sparsity Constraints

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Sparse Image Representation by Directionlets

Operator-like wavelets with application to functional magnetic resonance imaging

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

Dynamic PET Reconstruction Using Wavelet Regularization with Adapted Basis Functions

Invariances, Laplacian-Like Wavelet Bases, and the Whitening of Fractal Processes

Generalized Daubechies Wavelet Families

Fast directional correlation on the sphere with steerable filters