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Job: PhD position: Sparse representations for seismic wave fields restoration and quantitative analysis
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Caroline Chaux (

PostPosted: Wed Sep 28, 2011 1:50 pm    
Subject: Job: PhD position: Sparse representations for seismic wave fields restoration and quantitative analysis
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Job: PhD thesis proposal 2011-2014

Title: Sparse representations for seismic wave fields restoration and quantitative analysis

Seismic data have provoked a large amount of signal processing research (including, deconvolution or early wavelet developments) due to the complexity of various wave field interferences. Interestingly, they inherit a combination of signal- and image-like features that make them suitable to a variety of 1-D or more directional transforms, better adapted to the wave fronts' behaviours. Yet, they still challenge traditional processing methods, with different wave types mixed together like surface or tube waves and multiples.

Recently, intrinsically 2-D techniques, arising from the image processing field such as structure tensors, 2-D directional complex wavelets or curvelets, have raised some interest for filtering or migration applications. Additional experience suggests that geophysical data processing might strongly benefit from the development of adapted multidimensional frames (a generalization of vector bases), with a certain amount of redundancy and reasonable space-frequency localization, to yield local directional transforms. Those frames are candidates to faithfully approximate large data volumes with a relatively small number of coefficients, i.e. provide a sparse representation of the data, to ease their subsequent processing in highly disturbed environment (strong noise, for instance).

We aim at developing a series of tools, inspired from recent image processing discoveries, to address increasingly difficult contexts, from random noise filtering to varying kernel deconvolution, through coherent wave field separation, based on their local characteristics. In addition to standard time-frequency attributes, a special attention will be paid to the complex trace (a.k.a. the analytical signal), [Gabor1946] which gives access to the notion of instantaneous phase.

The ability to accurately estimate the phase in a multi-scale fashion and the development of phase preserving data restoration algorithms will be at the heart of the proposed thesis, with a devotion to seismic signals. The candidate will work within the signal processing team, in close contact to geophysicists and an industrial partner.
Since this topic as already emerged as important in the image processing community, the candidate work will benefit from a blossoming research atmosphere, with different potential applications outside the geophysical world.

Université Paris-Est : Jean-Christophe Pesquet
IFP Energies nouvelles : Laurent Duval, Patrice Ricarte

Applicants are advised to send along with their resume a brief report of preliminary research tracks related to the proposed subject:


Adaptive multiple subtraction with wavelet-based complex unary Wiener filters,
Sergi Ventosa, Hérald Rabeson, Patrice Ricarte, Laurent Duval
Submitted 2011

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity
Laurent Jacques, Laurent Duval, Caroline Chaux and Gabriel Peyré
Signal Processing, December 2011, Special issue on Advances in Multirate Filter Bank Structures and Multiscale Representations

Optimization of Synthesis Oversampled Complex Filter Banks
Jérôme Gauthier, Laurent Duval and Jean-Christophe Pesquet
IEEE Transactions on Signal Processing, October 2009

A Nonlinear Stein Based Estimator for Multichannel Image Denoising
Caroline Chaux, Laurent Duval, Amel Benazza-Benyahia and Jean-Christophe Pesquet
IEEE Transactions on Signal Processing, August 2008

Noise covariance properties in Dual-Tree Wavelet Decompositions
Caroline Chaux, Jean-Christophe Pesquet, Laurent Duval
IEEE Transactions on Information Theory, December 2007
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