Publications related to Optimal Representations of Sparse Stochastic Processes with Applications in Image Processing

A Unifying Parametric Framework for 2D Steerable Wavelet Transforms

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

Decay Properties of Riesz Transforms and Steerable Wavelets

Michaël Unser, John Paul Ward, Kunal Narayan Chaudhury

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

Graph Matching for Adaptation in Remote Sensing

Devis Tuia

We present an adaptation algorithm focused on the description of the data changes under different acquisition conditions. When considering a source and a destination domain, the adaptation is carried out by transforming one data set to the other using an a ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Optimally Localized Wavelets and Smoothing Kernels

Kunal Narayan Chaudhury

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

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

The SURE-LET approach to image denoising

Florian Luisier

Denoising is an essential step prior to any higher-level image-processing tasks such as segmentation or object tracking, because the undesirable corruption by noise is inherent to any physical acquisition device. When the measurements are performed by phot ...

EPFL2010

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

Michaël Kalbermatten

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

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

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

Michaël Unser, Dimitri Nestor Alice Van De Ville

Based on the class of complex gradient-Laplace operators, we show the design of a non-separable two-dimensional wavelet basis from a single and analytically defined generator wavelet function. The wavelet decomposition is implemented by an efficient FFT-ba ...

SPIE2009

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

Optimal Representations of Sparse Stochastic Processes with Applications in Image Processing

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A Unifying Parametric Framework for 2D Steerable Wavelet Transforms

Decay Properties of Riesz Transforms and Steerable Wavelets

Graph Matching for Adaptation in Remote Sensing

Optimally Localized Wavelets and Smoothing Kernels

Wavelet Steerability and the Higher-Order Riesz Transform

The SURE-LET approach to image denoising

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

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

The Monogenic Riesz-Laplace Wavelet Transform

Wavelet Steerability and the Higher-Order Riesz Transform

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Optimally Localized Wavelets and Smoothing Kernels

The SURE-LET approach to image denoising

Decay Properties of Riesz Transforms and Steerable Wavelets

Graph Matching for Adaptation in Remote Sensing

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

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

The Monogenic Riesz-Laplace Wavelet Transform

A Unifying Parametric Framework for 2D Steerable Wavelet Transforms