Murtagh, Fionn, Contreras, Pedro, Starck, Jean-Luc
By a "covering" we mean a Gaussian mixture model fit to observed data. Approximations of the Bayes factor can be availed of to judge model fit to the data within a given Gaussian mixture model....
Wavelets, Ridgelets, and Curvelets for Poisson Noise Removal (2009)
Bo Zhang, Jalal M. Fadili, Jean-luc Starck
Abstract—In order to denoise Poisson count data, we introduce a variance stabilizing transform (VST) applied on a filtered discrete Poisson process, yielding a near Gaussian process with asymptotic...
Astronomical Data Analysis and Sparsity: from Wavelets to Compressed Sensing (2009)
Starck, Jean-Luc, Bobin, Jerome
Wavelets have been used extensively for several years now in astronomy for many purposes, ranging from data filtering and deconvolution, to star and galaxy detection or cosmic ray removal. More...
Dictionary learning with spatio-spectral sparsity constraints (2009)
Moudden, Yassir, Bobin, Jérome, Starck, Jean-Luc, Fadili, Jalal
Devising efficient sparse decomposition algorithms in large redundant dictionaries has attracted much attention recently. However, choosing the right dictionary for a given data set remains an issue....
Dictionary learning with spatio-spectral sparsity constraints (2009)
Moudden, Yassir, Bobin, Jérome, Starck, Jean-Luc, Fadili, Jalal
Devising efficient sparse decomposition algorithms in large redundant dictionaries has attracted much attention recently. However, choosing the right dictionary for a given data set remains an issue....
Image Deconvolution by Stein Block Thresholding (2009)
Chesneau, Christophe, Fadili, Jalal, Starck, Jean-Luc
In this paper, we propose a fast image deconvolution algorithm that combines adaptive block thresholding and Vaguelet-Wavelet Decomposition. The approach consists in first denoising the observed...
Image Deconvolution by Stein Block Thresholding (2009)
Chesneau, Christophe, Fadili, Jalal, Starck, Jean-Luc
In this paper, we propose a fast image deconvolution algorithm that combines adaptive block thresholding and Vaguelet-Wavelet Decomposition. The approach consists in first denoising the observed...
Fionn Murtagh, Pedro Contreras, Jean-Luc Starck
By a “covering” we mean a Gaussian mixture model fit to observed data. Approximations of the Bayes factor can be availed of to judge model fit to the data within a given Gaussian mixture model....
Inpainting with 3D sparse transforms (2009)
WOISELLE, Arnaud, STARCK, Jean-Luc, FADILI, Jalal
Nous présentons deux nouvelles transformées parcimonieuses en 3D, qui sont les deux extensions 3D des curvelets 2D première génération. Ces transformées ont des atomes qui ressemblent à des...
Jean-luc Starck, Fionn Murtagh, Albert Bijaoui
Preface vii 1 The wavelet transform 1 1.1 Multiscale methods........................ 1 1.1.1 Some perspectives on the wavelet transform...... 2
Stein Block Thresholding For Image Denoising (2008)
Chesneau, Christophe, Fadili, Jalal, Starck, Jean-Luc
In this paper, we investigate the minimax properties of Stein block thresholding in any dimension $d$ with a particular emphasis on $d=2$. Towards this goal, we consider a frame coefficient space...
Full-Sky Weak Lensing Simulation with 70 Billion Particles (2008)
Teyssier, Romain, Pires, Sandrine, Prunet, Simon, Aubert, Dominique, Pichon, Christophe, Amara, Adam, ...
We have performed a 70 billion dark-matter particles N-body simulation in a 2 $h^{-1}$ Gpc periodic box, using the concordance, cosmological model as favored by the latest WMAP3 results. We have...
Murtagh, Fionn, Starck , Jean-Luc
We show the potential for classifying images of mixtures of aggregate, based themselves on varying, albeit well-defined, sizes and shapes, in order to provide a far more effective approach compared...
b Service d’Astrophysique Centre d’Etudes de Saclay (2008)
Fionn Murtagh, Jean-luc Starck, Ormes Des Mérisiers
While a dominant (additive, stationary) Gaussian noise component in image data will ensure that wavelet coefficients are of Gaussian distribution, long tailed distributions (symptomatic, for example,...
Wavelet-Based Combined Signal Filtering and Prediction (2008)
Olivier Renaud, Jean-luc Starck, Fionn Murtagh
Abstract — We survey a number of applications of the wavelet transform in time series prediction. We show how multiresolution prediction can capture short-range and long-term dependencies with only...
Murtagh, Fionn, Starck, Jean-Luc
We show the potential for classifying images of mixtures of aggregate, based themselves on varying, albeit well-defined, sizes and shapes, in order to provide a far more effective approach compared...
Moudden, Sparsity and morphological diversity in blind source separation (2008)
Jérôme Bobin, Jean-luc Starck, Jalal Fadili, Yassir Moudden
Abstract—Over the last few years, the development of multichannel sensors motivated interest in methods for the coherent processing of multivariate data. Some specific issues have already been...
Wavelet-Based Combined Signal Filtering and Prediction (2008)
Olivier Renaud, Jean-luc Starck, Fionn Murtagh
Abstract — We survey a number of applications of the wavelet transform in time series prediction. We show how multiresolution prediction can capture short-range and long-term dependencies with only...
Stein Block Thresholding For Image Denoising (2008)
Chesneau, Christophe, Fadili, Jalal, Starck, Jean-Luc
In this paper, we investigate the minimax properties of Stein block thresholding in any dimension $d$ with a particular emphasis on $d=2$. Towards this goal, we consider a frame coefficient space...
Stein Block Thresholding For Image Denoising (2008)
Chesneau, Christophe, Fadili, Jalal, Starck, Jean-Luc
In this paper, we investigate the minimax properties of Stein block thresholding in any dimension $d$ with a particular emphasis on $d=2$. Towards this goal, we consider a frame coefficient space...
Jean-luc Starck, Emmanuel J. C, David L. Donoho
We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform [3] and the curvelet transform [7, 6]. Our implementations oer exact reconstruction,...
Deconvolution by the Multiscale Maximum Entropy Method (2007)
. In 1994, to overcome the difficulties encountered by the Maximum Entropy Method (MEM) to restore images containing both high and low frequencies, Bontekoe et al. introduced the Pyramid Maximum...
Noise Detection and Filtering using Multiresolution Transform Methods (2007)
R. Albrecht, R. N. Hook, H. A. Bushouse, Fionn Murtagh, Jean-luc Starck
. A new and powerful methodology for treating noise and clutter in astronomical images is described. This is based on the use of the redundant a trous wavelet transform, and the multiresolution...
September Mitchell, Mitchell Morehart, Fionn Murtagh, Jean-luc Starck
A foundation is set forth for use of the wavelet transform as a spatial analysis tool for modelling the geographic representation of economic and financial measures used in agriculture. This provides...
Kalman-type Filtering using the Wavelet Transform (2007)
Olivier Renaud, Jean-luc Starck, Fionn Murtagh
We survey a number of applications of the wavelet transform in time series prediction. We pay particular attention to the modeling and prediction of time series when future data is unknown. We show...
Image Restoration with Denoising Using Multi-Resolution (2007)
R. J. Hanisch, R. L. White, Jean-luc Starck, Fionn Murtagh, Albert Bijaoui
Abstract. This paper shows how an effective noise suppression strategy can be incorporated into algorithms for the solution of the inverse problem. The residual in the fit of the restored image, at...
Looking at Noise, Information, and Scale (2007)
Jean-luc Starck, Fionn Murtagh
The information content of an image is a key aspect of any processing task, and there are two ways to define information: we can recognize the different objects in the image, which is fundamental for...
Dark matter maps reveal cosmic scaffolding (2007)
Massey, Richard, Rhodes, Jason, Ellis, Richard, Scoville, Nick, Leauthaud, Alexie, Finoguenov, Alexis, ...
Ordinary baryonic particles (such as protons and neutrons) account for only one-sixth of the total matter in the Universe. The remainder is a mysterious "dark matter" component, which does not...
Dark matter maps reveal cosmic scaffolding (2007)
Massey, Richard, Rhodes, Jason, Ellis, Richard, Scoville, Nick, Leauthaud, Alexie, Finoguenov, Alexis, ...
Ordinary baryonic particles (such as protons and neutrons) account for only one-sixth of the total matter in the Universe. The remainder is a mysterious "dark matter" component, which does not...
Dark matter maps reveal cosmic scaffolding (2007)
Massey, Richard, Rhodes, Jason, Ellis, Richard, Scoville, Nick, Leauthaud, Alexie, Finoguenov, Alexis, ...
Apprentissage de dictionnaires parcimonieux adaptés pour la séparation d'images (2007)
PEYRE, Gabriel, FADILI, Jalal, STARCK, Jean-Luc
Cet article propose une nouvelle méthode pour séparer une image en une superposition linéaire de composantes morphologiques ayant des structures caractéristiques. Pour chaque composante, un...
Wavelets, Ridgelets and Curvelets for Poisson Noise Removal (2007)
Bo Zhang, Jalal M. Fadili, Jean-luc Starck
In order to denoise Poisson count data, we introduce a variance stabilizing transform (VST) applied on a filtered discrete Poisson process, yielding a near Gaussian process with asymptotic constant...
Morphological component analysis: An adaptive thresholding strategy (2007)
Jérôme Bobin, Jean-luc Starck, Jalal M. Fadili, Yassir Moudden, David L. Donoho
Abstract—In a recent paper, a method called morphological component analysis (MCA) has been proposed to separate the texture from the natural part in images. MCA relies on an iterative thresholding...
Multi-scale morphology of the galaxy distribution (2006)
Saar, Enn, Martinez, Vicent J., Starck, Jean-Luc, Donoho, David L.
Many statistical methods have been proposed in the last years for analyzing the spatial distribution of galaxies. Very few of them, however, can handle properly the border effects of complex...
Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit (2006)
David L. Donoho, Yaakov Tsaig, Iddo Drori, Jean-luc Starck
Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NP-hard in general. We show here that for systems with ‘typical’/‘random ’ Φ, a good approximation to...
Wavelets, ridgelets and curvelets on the sphere (2005)
Starck, Jean-Luc, Moudden, Yassir, Abrial, Pierrick, Nguyen, Mai
We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet...
Weak Lensing Mass Reconstruction using Wavelets (2005)
Starck, Jean-Luc, Pires, Sandrine, Refregier, Alexandre
This paper presents a new method for the reconstruction of weak lensing mass maps. It uses the multiscale entropy concept, which is based on wavelets, and the False Discovery Rate which allows us to...
CARDOSO, Jean-Francois, ABRIAL, Pierrick, MOUDDEN, Yassir, STARCK, Jean-Luc, DELABROUILLE, Jacques
Cet article décrit des statistiques de corrélation localisées en fréquence et position sur la sphère et leur application pour la séparation de composantes dans les observations multi-spectrales...
The XMM-LSS survey : Survey design and first results* (2004)
Pierre, Marguerite, Valtchanov, Ivan, Altieri, Bruno, Andreon, Stefano, Bolzonella, Micol, Bremer, Malcolm, ...
Gray and color image contrast enhancement by the curvelet transform (2003)
Starck, Jean-Luc, Murtagh, Fionn, Candès, Emmanuel J., Donoho, David L.
We present a new method for contrast enhancement based on the curvelet transform. The curvelet transform represents edges better than wavelets, and is therefore well-suited for multiscale edge...
Gray and Color Image Contrast Enhancement by the Curvelet Transform (2003)
Jean-luc Starck, Fionn Murtagh, Emmanuel J. Cands, Emmanuel J. C, David L. Donoho
We present in this paper a new method for contrast enhancement based on the curvelet transform. The curvelet transform represents edges better than wavelets, and is therefore well-suited for...
The curvelet transform for image denoising (2002)
Starck, Jean-Luc, Candès, Emmanuel J., Donoho, David L.
We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform and the curvelet transform. Our implementations offer exact reconstruction,...
The curvelet transform for image denoising (2002)
Jean-luc Starck, Emmanuel J. C, David L. Donoho
We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform [3] and the curvelet transform [7, 6]. Our implementations offer exact...
Bayesian Inference for Color Image Quantization via Model-Based Clustering Trees (2001)
Fionn Murtagh, Adrian E. Raftery, Jean-luc Starck
We consider the problem of color image quantization, or clustering of the color space. We propose a new methodology for doing this, called model-based clustering trees. This is grounded in...
Bayesian Inference for Color Image Quantization via Model-Based Clustering Trees (2001)
Fionn Murtagh, Adrian E. Raftery, Jean-luc Starck
\Ve consider the problem of color image quantization, or clustering of the color space. vVe propose a new methodology for doing this, called model-based clustering trees. This is grounded in...
Overcoming the Curse of Dimensionality in Clustering by means of the Wavelet Transform (2000)
Fionn Murtagh, Jean-luc Starck, Michael W. Berry
We use a redundant wavelet transform analysis to detect clusters in high-dimensional data spaces. We overcome Bellman's \curse of dimensionality" in such problems by (i) using some...
Overcoming the Curse of Dimensionality in Clustering by Means of the Wavelet Transform (2000)
Murtagh, Fionn, Starck, Jean-Luc, Berry, Michael W.
We use a redundant wavelet transform analysis to detect clusters in high-dimensional data spaces. We overcome Bellman's `curse of dimensionality' in such problems by (i) using some...
Wavelets and Multiscale Transforms in Massive Data Sets (1999)
Fionn Murtagh, Jean-Luc Starck
With the requirements of scientific and medical image database support in mind, we describe a range of useful technologies for storage, transmission and display. These new technologies are all based...
Structure Detection in Low Intensity X-Ray Images (1997)
Starck, Jean-Luc, Pierre, Marguerite
In the context of assessing and characterizing structures in X-ray images, we compare different approaches. Most often the intensity level is very low and necessitates a special treatment of Poisson...
X-ray structures in galaxy cluster cores (1997)
Pierre, Marguerite, Starck, Jean-Luc
Using a set of ROSAT HRI deep pointings, we investigate the presence of small-scale structures in the central regions of clusters of galaxies. Our sample comprises 23 objects up to z=0.32, 13 of them...
Pattern Clustering based on Noise Modeling in Wavelet Space (1997)
Fionn Murtagh, Jean-luc Starck
We describe an effective approach to object or feature detection in point patterns via noise modeling. This is based on use of a redundant or non-pyramidal wavelet transform. Noise modeling is based...
Multiresolution Support Applied to Image Filtering and Restoration (1995)
European Southern Observatory, Jean-luc Starck, Jean-luc Starck, Fionn Murtagh, Fionn Murtagh, Albert Bijaoui, ...
The notion of a multiresolution support is introduced. This is a sequence of boolean images, related to significant pixels at each of a number of resolution levels. The multiresolution support is...
Image Restoration with Noise Suppression Using a Multiresolution Support (1995)
Fionn Murtagh, Jean-luc Starck, Albert Bijaoui
. In Starck & Murtagh, 1994 (SM94), it was shown how noise suppression could be built into widely-used image restoration methods, such as the Richardson-Lucy method. Arising from this work, two...
Multiresolution in Astronomical Image Processing: A General Framework (1995)
Fionn Murtagh, Jean-luc Starck, Albert Bijaoui
Multiresolution transforms, including a wavelet transform, are applied to image visualization, image restoration, filtering and compression, and object detection. Variance stabilization is used, when...
STARCK, Jean-Luc, BIJAOUI, Albert
Cet article montre comment une stratégie de suppression du bruit peut-être introduite dans les algorithmes de déconvolution itératifs. Pour ce faire, un algorithme de transformée en ondelettes a...
Restauration d'images en multiresolution (1991)
STARCK, Jean-Luc, BIJAOUI, Albert
La transformée en ondelettes est un outil qui nous permet d'obtenir de l'information à la fois en temps et en fréquence. Avec une ondelette isotrope et un algorithme basé sur la FFT, on obtient...