Publications related to Multiresolution analysis

Fast Explicit Nonlinear Model Predictive Control Via Multiresolution Function Approximation with Guaranteed Stability Nonlinear Control Systems

In this paper an algorithm for nonlinear explicit model predictive control is introduced based on multiresolution function approximation that returns a low complexity approximate receding horizon control law built on a hierarchy of second order interpolets ...

2010

Adaptive Multiresolution Methods for the Simulation of Waves in Excitable Media

Ricardo Esteban Ruiz Baier

We present fully adaptive multiresolution methods for a class of spatially two-dimensional reaction-diffusion systems which describe excitable media and often give rise to the formation of spiral waves. A novel model ingredient is a strongly degenerate dif ...

Springer Verlag2010

Analytical Footprints: Compact Representation of Elementary Singularities in Wavelet Bases

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

We introduce a family of elementary singularities that are point-Holder alpha-regular. These singularities are self-similar and are the Green functions of fractional derivative operators; i.e., by suitable fractional differentiation, one retrieves a Dirac ...

Institute of Electrical and Electronics Engineers2010

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

Michaël Unser, Chandra Sekhar Seelamantula

This paper deals with the problem of time-resolved fluorescence diffuse optical tomography. We propose a new reconstruction scheme based on a multi-resolution approximation of the time-resolved signals. The underlying basis functions are exponential B-spli ...

IEEE2009

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

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

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

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

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

Multiresolution analysis

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Fast Explicit Nonlinear Model Predictive Control Via Multiresolution Function Approximation with Guaranteed Stability Nonlinear Control Systems

Adaptive Multiresolution Methods for the Simulation of Waves in Excitable Media

Analytical Footprints: Compact Representation of Elementary Singularities in Wavelet Bases

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

A Fast Multilevel Algorithm for Wavelet-Regularized Image Restoration

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Operator-like wavelets with application to functional magnetic resonance imaging

Shift-Invariant Spaces from Rotation-Covariant Functions

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

Fast Computation of Polyharmonic B-Spline Autocorrelation Filters

Fast Explicit Nonlinear Model Predictive Control Via Multiresolution Function Approximation with Guaranteed Stability Nonlinear Control Systems

Adaptive Multiresolution Methods for the Simulation of Waves in Excitable Media

Analytical Footprints: Compact Representation of Elementary Singularities in Wavelet Bases

Shift-Invariant Spaces from Rotation-Covariant Functions

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

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

A Fast Multilevel Algorithm for Wavelet-Regularized Image Restoration

Operator-like wavelets with application to functional magnetic resonance imaging

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

Fast Computation of Polyharmonic B-Spline Autocorrelation Filters