Publications related to The Monogenic Riesz-Laplace Wavelet Transform

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

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

The approximate behavior of wavelets as differential operators is often considered as one of their most fundamental properties. In this paper, we investigate how we can further improve on the wavelet's behavior as differentiator. In particular, we propose ...

SPIE2005

Generalized L-Spline Wavelet Bases

Michaël Unser, Thierry Blu, Ildar Khalidov

We build wavelet-like functions based on a parametrized family of pseudo-differential operators

L _{ v }

that satisfy some admissibility and scalability conditions. The shifts of the generalized B-splines, which are localized versions of the Green func ...

SPIE2005

Exponential-Spline Wavelet Bases

Michaël Unser, Ildar Khalidov

We build a multiresolution analysis based on shift-invariant exponential B-spline spaces. We construct the basis functions for these spaces and for their orthogonal complements. This yields a new family of wavelet-like basis functions of

L _{ 2 }

, wit ...

IEEE2005

Wavelet Transform Analysis of Truncated Fringe Patterns in 3-D Surface Profilometry

Sai Siva Gorthi

Wavelet transform analysis of projected fringe pattern for phase recovery in 3-D shape measurement of objects is investigated. The present communication specifically outlines and evaluates the errors that creep in to the reconstructed profiles when fringe ...

2005

Correspondence principle between spherical and Euclidean wavelets

Pierre Vandergheynst, Yves Wiaux, Laurent Jacques

Wavelets on the sphere are reintroduced and further developed independently of the original group theoretic formalism, in an equivalent, but more straightforward approach. These developments are motivated by the interest of the scale-space analysis of the ...

2005

Generalized Biorthogonal Daubechies Wavelets

Michaël Unser, Thierry Blu, Cédric René Jean Vonesch

We propose a generalization of the Cohen-Daubechies-Feauveau (CDF) and 9⁄7 biorthogonal wavelet families. This is done within the framework of non-stationary multiresolution analysis, which involves a sequence of embedded approximation spaces generated by ...

SPIE2005

Stair climbing detection during daily physical activity using a miniature gyroscope

Kamiar Aminian, Anisoara Ionescu, Bijan Najafi, Brian Coley

A new method of monitoring physical activity that is able to detect walking upstairs using a miniature gyroscope attached to the shank is presented. Wavelet transformation, in conjunction with a simple kinematics model, was used to detect toe-off, heel-str ...

2005

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

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

Microscopy imaging often suffers from limited depth-of-focus. However, the specimen can be “optically sectioned” by moving the object along the optical axis; different areas appear in focus in different images. Extended depth-of-focus is a fusion algorithm ...

IEEE2004

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Pierre Vandergheynst, Oscar Divorra Escoda

In this work, we study the effect of inserting spatially local temporal adaptivity to motion compensated frame adaptive transforms for video coding. Motion compensation aligns the temporal wavelet decomposition along motion trajectories. However, valid tra ...

2004

Complex Wavelets for Extended Depth-of-Field: A New Method for the Fusion of Multichannel Microscopy Images

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

Microscopy imaging often suffers from limited depth-of-field. However, the specimen can be “optically sectioned” by moving the object along the optical axis. Then different areas appear in focus in different images. Extended depth-of-field is a fusion algo ...

Wiley-Liss2004

The Monogenic Riesz-Laplace Wavelet Transform

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Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Generalized L-Spline Wavelet Bases

Exponential-Spline Wavelet Bases

Wavelet Transform Analysis of Truncated Fringe Patterns in 3-D Surface Profilometry

Correspondence principle between spherical and Euclidean wavelets

Generalized Biorthogonal Daubechies Wavelets

Stair climbing detection during daily physical activity using a miniature gyroscope

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Complex Wavelets for Extended Depth-of-Field: A New Method for the Fusion of Multichannel Microscopy Images

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Generalized L-Spline Wavelet Bases

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

Wavelet Transform Analysis of Truncated Fringe Patterns in 3-D Surface Profilometry

Exponential-Spline Wavelet Bases

Generalized Biorthogonal Daubechies Wavelets

Complex Wavelets for Extended Depth-of-Field: A New Method for the Fusion of Multichannel Microscopy Images

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Correspondence principle between spherical and Euclidean wavelets

Stair climbing detection during daily physical activity using a miniature gyroscope