Publications related to The Marr Wavelet Pyramid

Fractional Laplacian Pyramids

Michaël Unser, Ricard Delgado Gonzalo, Pouya Dehghani Tafti

We provide an extension of the L-2-spline pyramid (Unser et al., 1993) using polyharmonic splines. We analytically prove that the corresponding error pyramid behaves exactly as a multi-scale Laplace operator. We use the multiresolution properties of polyha ...

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

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

Pyramid-Based Texture Synthesis Using Local Orientation and Multidimensional Histogram Matching

Michaël Unser, Dimitri Nestor Alice Van De Ville, Matthieu Guerquin-Kern

One very influential method for texture synthesis is based on the steerable pyramid by alternately imposing marginal statistics on the image and the pyramid's subbands. In this work, we investigate two extensions to this framework. First, we exploit the st ...

SPIE2009

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

Michaël Unser, Dimitri Nestor Alice Van De Ville

We introduce a new semi-orthogonal complex wavelet basis of L-2(R-2). The basis functions are associated to the complex gradient-Laplace operator, which plays a central role in image processing. We define analytically a single-generator wavelet that is shi ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2008

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

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

A fast iterative thresholding algorithm for wavelet-regularized deconvolution - art. no. 67010D

Michaël Unser, Cédric René Jean Vonesch

We present an iterative deconvolution algorithm that minimizes a functional with a non-quadratic wavelet-domain regularization term. Our approach is to introduce subband-dependent parameters into the bound optimization framework of Daubechies et al.; it is ...

Spie-Int Soc Optical Engineering, Po Box 10, Bellingham, Wa 98227-0010 Usa2007

The SURE-LET Approach to Image Denoising

Thierry Blu, Florian Luisier

We propose a new approach to image denoising, based on the image-domain minimization of an estimate of the mean squared error—Stein's unbiased risk estimate (SURE). Unlike most existing denoising algorithms, using the SURE makes it needless to hypothesize ...

Institute of Electrical and Electronics Engineers2007

From Differential Equations to the Construction of New Wavelet-Like Bases

Michaël Unser, Ildar Khalidov

In this paper, an approach is introduced based on differential operators to construct wavelet-like basis functions. Given a differential operator L with rational transfer function, elementary building blocks are obtained that are shifted replicates of the ...

IEEE2006

The Marr Wavelet Pyramid

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Fractional Laplacian Pyramids

Operator-like wavelets with application to functional magnetic resonance imaging

Pyramid-Based Texture Synthesis Using Local Orientation and Multidimensional Histogram Matching

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

The Marr Wavelet Pyramid

The Monogenic Riesz-Laplace Wavelet Transform

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

A fast iterative thresholding algorithm for wavelet-regularized deconvolution - art. no. 67010D

The SURE-LET Approach to Image Denoising

From Differential Equations to the Construction of New Wavelet-Like Bases

Operator-like wavelets with application to functional magnetic resonance imaging

The SURE-LET Approach to Image Denoising

Fractional Laplacian Pyramids

A fast iterative thresholding algorithm for wavelet-regularized deconvolution - art. no. 67010D

The Monogenic Riesz-Laplace Wavelet Transform

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

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

The Marr Wavelet Pyramid

Pyramid-Based Texture Synthesis Using Local Orientation and Multidimensional Histogram Matching

From Differential Equations to the Construction of New Wavelet-Like Bases