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Concept

Riesz transform

Publications associées (10)

Optimized Steerable Wavelets for Texture Analysis of Lung Tissue In 3-D CT: Classification of Usual Interstitial Pneumonia

Michaël Unser, Adrien Raphaël Depeursinge, Pedram Pad

Our aim is to optimize wavelet-based feature extraction for differentiating between the classical versus atypical pattern of usual interstitial pneumonia (UIP) in volumetric CT. Our proposal is to act on the bandwidth of steerable wavelets while maintainin ...

IEEE2015

Decay Properties of Riesz Transforms and Steerable Wavelets

Michaël Unser, Kunal Narayan Chaudhury, John Paul Ward

The Riesz transform is a natural multidimensional extension of the Hilbert transform, and it has been the object of study for many years due to its nice mathematical properties. More recently, the Riesz transform and its variants have been used to construc ...

Siam Publications2013

A Unifying Parametric Framework for 2D Steerable Wavelet Transforms

Michaël Unser

We introduce a complete parameterization of the family of two-dimensional steerable wavelets that are polar-separable in the Fourier domain under the constraint of self-reversibility. These wavelets are constructed by multiorder generalized Riesz transform ...

Siam Publications2013

Local demodulation of holograms using the Riesz transform with application to microscopy

Michaël Unser, Christian Depeursinge, Nicolas Pavillon, Chandra Sekhar Seelamantula

We propose a Riesz transform approach to the demodulation of digital holograms. The Riesz transform is a higher-dimensional extension of the Hilbert transform and is steerable to a desired orientation. Accurate demodulation of the hologram requires a relia ...

Optical Society of America2012

3D Steerable Wavelets And Monogenic Analysis For Bioimaging

Michaël Unser

In this paper we introduce a 3D wavelet frame that has the key property of steerability. The proposed wavelet frame relies on the combination of a 3D isotropic wavelet transform with the 3D Riesz operator which brings steerability to the pyramid. The novel ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011

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

Higher-Order Riesz Transforms And Steerable Wavelet Frames

Michaël Unser, Dimitri Nestor Alice Van De Ville

We introduce an Nth-order extension of the Riesz transform in d dimensions. We prove that this generalized transform has the following remarkable properties: shift-invariance, scale-invariance, inner-product preservation, and steerability. The pleasing con ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2009

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

The Monogenic Riesz-Laplace Wavelet Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville

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

Exact reconstruction with directional wavelets on the sphere

Pierre Vandergheynst, Yves Wiaux, Jason Douglas McEwen, Olivier Blanc

A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of a previously developed wavelet formalism developed by Antoine & Vandergheynst and Wiaux et a ...

2008

Publications associées (10)

Optimized Steerable Wavelets for Texture Analysis of Lung Tissue In 3-D CT: Classification of Usual Interstitial Pneumonia

Michaël Unser, Adrien Raphaël Depeursinge, Pedram Pad

IEEE2015

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

Exact reconstruction with directional wavelets on the sphere

Pierre Vandergheynst, Yves Wiaux, Jason Douglas McEwen, Olivier Blanc

2008