Publications related to Wavelet Footprints: Theory, Algorithms and Applications

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

Wavelets on the 2-Hyperboloid

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

We build wavelets on the 2-Hyperboloid. First, we define dilations on the hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to

SO_0(1,2)

, we define a family of hyperbolic wavelets. The continuous wavelet transform (CW ...

2004

Guest Editorial: Wavelets in Medical Imaging

Michaël Unser

I. Introduction Wavelets are the result of collective efforts that recognized common threads between ideas and concepts that had been independently developed and investigated by distinct research communities. They provide a unifying framework for decompos ...

2003

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

Wavelet footprints and frames for signal processing and communication

Pier Luigi Dragotti

Linear transforms and expansions are fundamental mathematical tools of signal processing. In particular, the wavelet transform has played an important role in several signal processing tasks, compression being a prime example. A signal can be represented i ...

EPFL2002

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

Wavelets, approximation, and compression

Martin Vetterli

Over the last decade or so, wavelets have had a growing impact on signal processing theory and practice, both because of the unifying role and their successes in applications. Filter banks, which lie at the heart of wavelet-based algorithms, have become st ...

2001

ESMAC-SIAMOC 2001 Joint Congress: Body Postures and Walking Period Estimation Using a Kinematic Sensor: Application for Long Term Monitoring of Physical Activity in Elderly Subjects

Kamiar Aminian, Philippe Robert, Anisoara Ionescu, Bijan Najafi

Introduction: A reliable measurement of the physical activity in everyday life should allow a better assessment of the utility and the relevance of a number of medical treatments. Continuous 24-h recordings of posture and motion can be generally useful in ...

2001

Approximation and Compression of Piecewise Smooth Functions

Martin Vetterli, Paolo Prandoni

Wavelet or sub–band coding has been quite successful in compression applications, and this success can be attributed in part to the good approximation properties of wavelets. In this paper, we revisit rate–distortion (RD) bounds for the wavelet approximati ...

1999

Comparison of Wavelets from the Point of View of Their Approximation Error

Michaël Unser, Thierry Blu

We present new quantitative results for the characterization of the

L _{ 2 }

-error of wavelet-like expansions as a function of the scale a. This yields an extension as well as a simplification of the asymptotic error formulas that have been published ...

SPIE1998

Wavelet Footprints: Theory, Algorithms and Applications

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Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Wavelets on the 2-Hyperboloid

Guest Editorial: Wavelets in Medical Imaging

Wavelet Theory Demystified

Wavelet footprints and frames for signal processing and communication

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

Wavelets, approximation, and compression

ESMAC-SIAMOC 2001 Joint Congress: Body Postures and Walking Period Estimation Using a Kinematic Sensor: Application for Long Term Monitoring of Physical Activity in Elderly Subjects

Approximation and Compression of Piecewise Smooth Functions

Comparison of Wavelets from the Point of View of Their Approximation Error

Wavelet footprints and frames for signal processing and communication

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

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

Wavelets on the 2-Hyperboloid

Guest Editorial: Wavelets in Medical Imaging

Wavelet Theory Demystified

Approximation and Compression of Piecewise Smooth Functions

Wavelets, approximation, and compression

Comparison of Wavelets from the Point of View of Their Approximation Error

ESMAC-SIAMOC 2001 Joint Congress: Body Postures and Walking Period Estimation Using a Kinematic Sensor: Application for Long Term Monitoring of Physical Activity in Elderly Subjects