Publications related to Directionlets: Anisotropic Multidirectional representation with separable filtering

Optimally Localized Wavelets and Smoothing Kernels

It is well-known that the Gaussian functions and, more generally, their modulations-translations (the Gabor functions) have the unique property of being optimally localized in space and frequency in the sense of Heisenberg's uncertainty principle. In this ...

EPFL2011

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

On the Shiftability of Dual-Tree Complex Wavelet Transforms

Michaël Unser, Kunal Narayan Chaudhury

The dual-tree complex wavelet transform (DT-ℂWT) is known to exhibit better shift-invariance than the conventional discrete wavelet transform. We propose an amplitude-phase representation of the DT-ℂWT which, among other things, offers a direct explanation ...

IEEE2010

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

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

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

Invariances, Laplacian-Like Wavelet Bases, and the Whitening of Fractal Processes

Michaël Unser, Dimitri Nestor Alice Van De Ville, Pouya Dehghani Tafti

In this contribution, we study the notion of affine invariance (specifically, invariance to the shifting, scaling, and rotation of the coordinate system) as a starting point for the development of mathematical tools and approaches useful in the characteriz ...

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

A Fast Thresholded Landweber Algorithm for Wavelet-Regularized Multidimensional Deconvolution

Michaël Unser, Cédric René Jean Vonesch

We present a fast variational deconvolution algorithm that minimizes a quadratic data term subject to a regularization on the

\ell ^{ 1 }

-norm of the wavelet coefficients of the solution. Previously available methods have essentially consisted in alte ...

IEEE2008

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

Directionlets: Anisotropic Multidirectional representation with separable filtering

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Optimally Localized Wavelets and Smoothing Kernels

Sparse Image Representation by Directionlets

On the Shiftability of Dual-Tree Complex Wavelet Transforms

Gabor Wavelet Analysis and the Fractional Hilbert Transform

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

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Invariances, Laplacian-Like Wavelet Bases, and the Whitening of Fractal Processes

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

A Fast Thresholded Landweber Algorithm for Wavelet-Regularized Multidimensional Deconvolution

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

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

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Invariances, Laplacian-Like Wavelet Bases, and the Whitening of Fractal Processes

On the Shiftability of Dual-Tree Complex Wavelet Transforms

Optimally Localized Wavelets and Smoothing Kernels

Sparse Image Representation by Directionlets

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

Gabor Wavelet Analysis and the Fractional Hilbert Transform

A Fast Thresholded Landweber Algorithm for Wavelet-Regularized Multidimensional Deconvolution

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