Publications related to Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

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

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

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Michaël Unser, Dimitri Nestor Alice Van De Ville

A distinction is usually made between wavelet bases and wavelet frames. The former are associated with a one-to-one representation of signals, which is somewhat constrained but most efficient computationally. The latter are over-complete, but they offer ad ...

Institute of Electrical and Electronics Engineers2008

The Monogenic Riesz-Laplace Wavelet Transform

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

We introduce a family of real and complex wavelet bases of

L _{ 2 }

(\mathbb{R} ^{ 2 }

) that are directly linked to the Laplace and Riesz operators. The crucial point is that the family is closed with respect to the Riesz transform which maps a re ...

EURASIP2008

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 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

A New Family of Rotation-Covariant Wavelets on the Hexagonal Lattice

Dimitri Nestor Alice Van De Ville

We present multiresolution spaces of complex rotation-covariant functions, deployed on the 2-D hexagonal lattice. The designed wavelets, which are complex-valued, provide an important phase information for image analysis, which is missing in the discrete w ...

SPIE2007

Construction of wavelet bases that mimic the behaviour of some given operator - art. no. 67010S

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

Probably, the most important property of wavelets for signal processing is their multiscale derivative-like behavior when applied to functions. In order to extend the class of problems that can profit of wavelet-based techniques, we propose to build new fa ...

Spie-Int Soc Optical Engineering, Po Box 10, Bellingham, Wa 98227-0010 Usa2007

Construction of Wavelet Bases That Mimic the Behaviour of Some Given Operator

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

Probably the most important property of wavelets for signal processing is their multiscale derivative-like behavior when applied to functions. In order to extend the class of problems that can profit of wavelet-based techniques, we propose to build new fam ...

SPIE2007

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

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

The Marr Wavelet Pyramid

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

The Monogenic Riesz-Laplace Wavelet Transform

Shift-Invariant Spaces from Rotation-Covariant Functions

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

Fast Wavelet based Ultrasound Image Segmentation for Liver Vessels Extraction

A New Family of Rotation-Covariant Wavelets on the Hexagonal Lattice

Construction of wavelet bases that mimic the behaviour of some given operator - art. no. 67010S

Construction of Wavelet Bases That Mimic the Behaviour of Some Given Operator

The Monogenic Riesz-Laplace Wavelet Transform

Shift-Invariant Spaces from Rotation-Covariant Functions

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

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Construction of Wavelet Bases That Mimic the Behaviour of Some Given Operator

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

The Marr Wavelet Pyramid

A New Family of Rotation-Covariant Wavelets on the Hexagonal Lattice

Construction of wavelet bases that mimic the behaviour of some given operator - art. no. 67010S

Fast Wavelet based Ultrasound Image Segmentation for Liver Vessels Extraction