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Steerable Pyramids and Tight Wavelet Frames in L_2(R^d)

Related publications (38)

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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

Complex B-Splines

Michaël Unser, Thierry Blu

We propose a complex generalization of Schoenberg's cardinal splines. To this end, we go back to the Fourier domain definition of the B-splines and extend it to complex-valued degrees. We show that the resulting complex B-splines are piecewise modulated po ...

Elsevier2006

An Orthogonal Family of Quincunx Wavelets with Continuously Adjustable Order

Michaël Unser, Dimitri Nestor Alice Van De Ville

We present a new family of two-dimensional and three-dimensional orthogonal wavelets which uses quincunx sampling. The orthogonal refinement filters have a simple analytical expression in the Fourier domain as a function of the order λ, which may be nonint ...

IEEE2005

Isotropic Polyharmonic B-Splines: Scaling Functions and Wavelets

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

In this paper, we use polyharmonic B-splines to build multidimensional wavelet bases. These functions are nonseparable, multidimensional basis functions that are localized versions of radial basis functions. We show that Rabut's elementary polyharmonic B-s ...

IEEE2005

Generalized Daubechies Wavelets

Michaël Unser, Thierry Blu, Cédric René Jean Vonesch

We present a generalization of the Daubechies wavelet family. The context is that of a non-stationary multiresolution analysis—i.e., a sequence of embedded approximation spaces generated by scaling functions that are not necessarily dilates of one another. ...

IEEE2005

Isotropic-Polyharmonic B-Splines and Wavelets

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

We propose the use of polyharmonic B-splines to build non-separable two-dimensional wavelet bases. The central idea is to base our design on the isotropic polyharmonic B-splines, a new type of polyharmonic B-splines that do converge to a Gaussian as the or ...

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

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

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

Fractal additive synthesis

Pietro Polotti

Musical and audio signals in general form a major part of the large amount of data exchange taking place in our information-based society. Transmission of high quality audio signals through narrow-band channels, such as the Internet, requires refined metho ...

EPFL2003