Publications related to Filter Bank Fusion frames

Sparse Image Representation by Directionlets

Martin Vetterli, Vladan Velisavljevic, Pier Luigi Dragotti

Despite the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency and sparsity of its representation are limited by the spatial symmetry and separability of its basis functions built in the horizontal and vertic ...

Elsevier2010

Gabor Wavelet Analysis and the Fractional Hilbert Transform

Michaël Unser, Kunal Narayan Chaudhury

We propose an amplitude-phase representation of the dual-tree complex wavelet transform (DT-ℂWT) which provides an intuitive interpretation of the associated complex wavelet coefficients. The representation, in particular, is based on the shifting action o ...

SPIE2009

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville, Daniel Sage

The monogenic signal is the natural 2-D counterpart of the 1-D analytic signal. We propose to transpose the concept to the wavelet domain by considering a complexified version of the Riesz transform which has the remarkable property of mapping a real-value ...

Institute of Electrical and Electronics Engineers2009

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

Michaël Unser, Kunal Narayan Chaudhury

We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions-the B-spline factorization theorem. In particular, starting from well-localized sc ...

IEEE2009

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Michaël Unser, Dimitri Nestor Alice Van De Ville

A distinction is usually made between wavelet bases and wavelet frames. The former are associated with a one-to-one representation of signals, which is somewhat constrained but most efficient computationally. The latter are over-complete, but they offer ad ...

Institute of Electrical and Electronics Engineers2008

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

Michaël Unser, Dimitri Nestor Alice Van De Ville

Our aim in this paper is to tighten the link between wavelets, some classical image-processing operators, and David Marr's theory of early vision. The cornerstone of our approach is a new complex wavelet basis that behaves like a smoothed version of the Gr ...

Institute of Electrical and Electronics Engineers2008

The Monogenic Riesz-Laplace Wavelet Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville, Katarina Balac

We introduce a family of real and complex wavelet bases of

L _{ 2 }

(\mathbb{R} ^{ 2 }

) that are directly linked to the Laplace and Riesz operators. The crucial point is that the family is closed with respect to the Riesz transform which maps a re ...

EURASIP2008

Shift-Invariant Spaces from Rotation-Covariant Functions

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

We consider shift-invariant multiresolution spaces generated by rotation-covariant functions ρ in

\mathbb{R}^{ 2 }

. To construct corresponding scaling and wavelet functions, ρ has to be localized with an appropriate multiplier, such that the localized ...

Elsevier2008

Filter Bank Design based on Minimization of Individual Aliasing Terms for Minimum Mutual Information Subband Adaptive Beamforming

Philip Neil Garner, Weifeng Li

This paper presents new filter bank design methods for sub- band adaptive beamforming. In this work, we design analysis and synthesis prototypes for modulated filter banks so as to minimize each aliasing term individually. We then drive the total response ...

2008

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

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Sparse Image Representation by Directionlets

Gabor Wavelet Analysis and the Fractional Hilbert Transform

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

The Monogenic Riesz-Laplace Wavelet Transform

Shift-Invariant Spaces from Rotation-Covariant Functions

Filter Bank Design based on Minimization of Individual Aliasing Terms for Minimum Mutual Information Subband Adaptive Beamforming

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

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

The Monogenic Riesz-Laplace Wavelet Transform

Sparse Image Representation by Directionlets

Gabor Wavelet Analysis and the Fractional Hilbert Transform

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

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

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

Filter Bank Design based on Minimization of Individual Aliasing Terms for Minimum Mutual Information Subband Adaptive Beamforming

Shift-Invariant Spaces from Rotation-Covariant Functions