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

Multiscale analysis of high resolution digital elevation models using the wavelet transform

At the end of the nineties the emergence of high resolution (1 m) digital elevation models (DEMs) settled the context of high precision geomorphological analysis. These new elevation models permitted to reveal structures that remained heretofore undetectab ...

EPFL2010

Analytical Footprints: Compact Representation of Elementary Singularities in Wavelet Bases

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

We introduce a family of elementary singularities that are point-Holder alpha-regular. These singularities are self-similar and are the Green functions of fractional derivative operators; i.e., by suitable fractional differentiation, one retrieves a Dirac ...

Institute of Electrical and Electronics Engineers2010

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

Operator-like wavelets with application to functional magnetic resonance imaging

Ildar Khalidov

We introduce a new class of wavelets that behave like a given differential operator L. Our construction is inspired by the derivative-like behavior of classical wavelets. Within our framework, the wavelet coefficients of a signal y are the samples of a smo ...

EPFL2009

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

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

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

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 Marr Wavelet Pyramid and Multiscale Directional Image Analysis

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

The “Marr wavelet pyramid” is a wavelet decomposition that implements a multiscale version of the complex gradient-Laplace operator. It is closely linked to a multiresolution analysis of

L _{ 2 }

(\mathbb{R} ^{ 2 }

) and it has a fast filterbank im ...

EURASIP2008

Shift-Invariant Spaces from Rotation-Covariant Functions

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Multiscale analysis of high resolution digital elevation models using the wavelet transform

Analytical Footprints: Compact Representation of Elementary Singularities in Wavelet Bases

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Operator-like wavelets with application to functional magnetic resonance imaging

Gabor Wavelet Analysis and the Fractional Hilbert 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

The Monogenic Riesz-Laplace Wavelet Transform

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

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

Multiscale analysis of high resolution digital elevation models using the wavelet transform

Analytical Footprints: Compact Representation of Elementary Singularities in Wavelet Bases

Operator-like wavelets with application to functional magnetic resonance imaging

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

The Monogenic Riesz-Laplace Wavelet Transform

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

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

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

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

Gabor Wavelet Analysis and the Fractional Hilbert Transform