Publications related to Wavelets: on the virtues and applications of the mathematical microscope

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

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

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

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

Orthogonal Hilbert transform filter banks and wavelets

Martin Vetterli, Thierry Blu

Complex wavelet transforms offer the opportunity to perform directional and coherent processing based on the local magnitude and phase of signals and images. Although denoising, segmentation, and image enhancement are significantly improved using complex w ...

IEEE2003

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

Wavelets on the 2-Sphere: A Group-Theoretical Approach

Pierre Vandergheynst

We present a purely group-theoretical derivation of the continuous wavelet transform (CWT) on the 2-sphere S2, based on the construction of general coherent states associated to square integrable group representations. The parameter space X of our CWT is t ...

1999

Wavelets: approximation and compression--a review

Martin Vetterli

In this paper, we briefly review the connection between subband coding, wavelet approximation and general compression problems. Wavelet or subband coding is successful in compression applications partly because of the good approximation properties of wavel ...

SPIE1999

Construction of Fractional Spline Wavelet Bases

Michaël Unser, Thierry Blu

We extend Schoenberg's B-splines to all fractional degrees α > -1/2. These splines are constructed using linear combinations of the integer shifts of the power functions

x _{ + } ^{ \alpha }

(one-sided) or

|x| _{ * } ^{ \alpha }

(symmetric); in eac ...

SPIE1999

Wavelets: on the virtues and applications of the mathematical microscope

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Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

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

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

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Wavelets on the 2-Hyperboloid

Orthogonal Hilbert transform filter banks and wavelets

Guest Editorial: Wavelets in Medical Imaging

Wavelets on the 2-Sphere: A Group-Theoretical Approach

Wavelets: approximation and compression--a review

Construction of Fractional Spline Wavelet Bases

Orthogonal Hilbert transform filter banks and wavelets

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

Wavelets on the 2-Hyperboloid

Wavelets on the 2-Sphere: A Group-Theoretical Approach

Guest Editorial: Wavelets in Medical Imaging

Wavelets: approximation and compression--a review

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

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Construction of Fractional Spline Wavelet Bases