Publications related to Shift-Invariant Spaces from Rotation-Covariant Functions

CMOS realization of two-dimensional mixed analog-digital Hamming distance discriminator circuits for real-time imaging applications

Alexandre Schmid, Yusuf Leblebici, Stéphane Badel

The architecture of an integrated Hamming artificial neural network, and its use as a versatile signal/image processing circuit is presented. The circuit operation relies oil the charge-based processing of sum-of-products terms, complemented with digital p ...

2008

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

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

Some linear and nonlinear problems involving differential forms

Saugata Bandyopadhyay

In this thesis, we study some linear and nonlinear problems involving differential forms. We begin by studying the problem of pullbacks which asks the following question: for two given differential forms, if one is the pullback of the other via a diffeomor ...

EPFL2007

From Differential Equations to the Construction of New Wavelet-Like Bases

Michaël Unser, Ildar Khalidov

In this paper, an approach is introduced based on differential operators to construct wavelet-like basis functions. Given a differential operator L with rational transfer function, elementary building blocks are obtained that are shifted replicates of the ...

IEEE2006

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

Continuous Wavelet Transform Ridge Extraction for Spectral Interferometry Imaging

Michaël Unser, Theo Lasser

The combination of wavelength multiplexing and spectral interferometry allows for the encoding of multidimensional information and its transmission over a mono-dimensional channel; for example, measurements of a surface's topography acquired through a mono ...

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

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

Shift-Invariant Spaces from Rotation-Covariant Functions

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CMOS realization of two-dimensional mixed analog-digital Hamming distance discriminator circuits for real-time imaging applications

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

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

Some linear and nonlinear problems involving differential forms

From Differential Equations to the Construction of New Wavelet-Like Bases

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Continuous Wavelet Transform Ridge Extraction for Spectral Interferometry Imaging

Generalized L-Spline Wavelet Bases

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

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

CMOS realization of two-dimensional mixed analog-digital Hamming distance discriminator circuits for real-time imaging applications

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Some linear and nonlinear problems involving differential forms

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

Continuous Wavelet Transform Ridge Extraction for Spectral Interferometry Imaging

Generalized L-Spline Wavelet Bases

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

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

From Differential Equations to the Construction of New Wavelet-Like Bases