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Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Related publications (162)

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Fractional Wavelets, Derivatives, and Besov Spaces

Michaël Unser, Thierry Blu

We show that a multi-dimensional scaling function of order γ (possibly fractional) can always be represented as the convolution of a polyharmonic B-spline of order γ and a distribution with a bounded Fourier transform which has neither order nor smoothness ...

SPIE2003

Wavelet Theory Demystified

Michaël Unser, Thierry Blu

In this paper, we revisit wavelet theory starting from the representation of a scaling function as the convolution of a B-spline (the regular part of it) and a distribution (the irregular or residual part). This formulation leads to some new insights on wa ...

IEEE2003

Body movement monitoring device

Kamiar Aminian, Pascal Morel, Bijan Najafi, Jean Gramiger

The invention relates to a device and a method for measuring gait parameters. It is based on autonomous sensing units for estimation of spatio-temporal parameters during walking and uses a wavelet transform to compute the values of gait parameters from the ...

2003

Fresnelets: New Multiresolution Wavelet Bases for Digital Holography

Michaël Unser, Thierry Blu

We propose a construction of new wavelet-like bases that are well suited for the reconstruction and processing of optically generated Fresnel holograms recorded on CCD-arrays. The starting point is a wavelet basis of

L _{ 2 }

to which we apply a unitar ...

IEEE2003

Wavelet Footprints: Theory, Algorithms and Applications

Martin Vetterli, Pier Luigi Dragotti

In recent years, wavelet-based algorithms have been successful in different signal processing tasks. The wavelet trans- form is a powerful tool because it manages to represent both tran- sient and stationary behaviors of a signal with few transform coeffi- ...

2003

Locally Temporal Adaptive Transform Scheme for Sub-band Video Coding

Pierre Vandergheynst, Oscar Divorra Escoda

The work presented in this paper extends the concept of sub-band video coding based on a 3D wavelet transform to a more adaptive approach. A formal comparison is presented between the performances inferred by the use of the 3D wavelet transform and the use ...

IEEE2003

Ambulatory system for human motion analysis using a kinematic sensor: Monitoring of daily physical activity in the elderly

Kamiar Aminian, Philippe Robert, Anisoara Ionescu, Bijan Najafi

A new method of physical activity monitoring is presented, which is able to detect body postures (sitting, standing, and lying) and periods of walking in elderly persons using only one kinematic sensor attached to the chest. The wavelet transform, in conju ...

2003

Framing pyramids

Martin Vetterli, Minh Do

In 1983, Burt and Adelson introduced the Laplacian pyramid (LP) as a multiresolution representation for images. We study the LP using the frame theory, and this reveals that the usual reconstruction is suboptimal. We show that the LP with orthogonal filter ...

2003

Wavelets on the sphere : Implementation and approximations

Pierre Vandergheynst, Laurent Jacques

We continue the analysis of the continuous wavelet transform on the 2-sphere, introduced in a previous paper. After a brief review of the transform, we define and discuss the notion of directional spherical wavelet, i.e., wavelets on the sphere that are se ...

2002

Continuous Wavelet Transform with Arbitrary Scales and O(N) Complexity

Michaël Unser

Summary The continuous wavelet transform (CWT) is a common signal-processing tool for the analysis of nonstationary signals. We propose here a new B-spline-based method that allows the CWT computation at any scale. A nice property of the algorithm is that ...

Elsevier2002

Fresnelets: New Multiresolution Wavelet Bases for Digital Holography

Michaël Unser, Thierry Blu

L _{ 2 }

to which we apply a unitar ...

IEEE2003