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A Dual-Tree Rational-Dilation Complex Wavelet Transform

Related publications (52)

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Signal Processing in Space and Time

Francisco Pereira Correia Pinto

Sound waves propagate through space and time by transference of energy between the particles in the medium, which vibrate according to the oscillation patterns of the waves. These vibrations can be captured by a microphone and translated into a digital sig ...

EPFL2010

Wavelet Steerability and the Higher-Order Riesz Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville

Our main goal in this paper is to set the foundations of a general continuous-domain framework for designing steerable, reversible signal transformations (a.k.a. frames) in multiple dimensions (d ≥ 2). To that end, we introduce a self-reversible, Nth-order ...

Institute of Electrical and Electronics Engineers2010

Sensing and Recovery under Sparsity Constraints

Ali Hormati

Popular transforms, like the discrete cosine transform or the wavelet transform, owe their success to the fact that they promote sparsity. These transforms are capable of extracting the structure of a large class of signals and representing them by a few t ...

EPFL2010

Public space in Beijing

Béatrice Ferrari

This is a short exploration of public space in Beijing (and elsewhere). But how do we define public space and does it exist as such in Beijing? In this short presentation, instead of simply focusing on physical spaces, I will try to capture some of the ele ...

2010

The empirical mode decomposition: a must-have tool in speckle interferometry?

Pierre Jacquot, Sébastien Equis

In a wider and wider range of research and engineering activities, there is a growing interest for full-field techniques, featuring nanometric sensitivities, and able to be addressed to dynamic behaviors characterization. Speckle interferometry (SI) techni ...

Optical Society of America2009

On Sampling Lattices with Similarity Scaling Relationships

Dimitri Nestor Alice Van De Ville, Thierry Blu

We provide a method for constructing regular sampling lattices in arbitrary dimensions together with an integer dilation matrix. Subsampling using this dilation matrix leads to a similarity-transformed version of the lattice with a chosen density reduction ...

LATP2009

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

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

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