PhD studentship: Sparse representations for seismic wave fields restoration and quantitative analysis

Laurent Duval sent me the following announcement for a PhD studentship

Dear colleagues
Please find attached a PhD proposal at IFPEN on "Sparse representations for seismic wave fields restoration and quantitative analysis". Do not hesitate to forward it to worthy candidates, for a start no later than beginning of 2012 (optimally end of 2011). The thesis advisor will be Jean-Christophe Pesquet.
Thank you in advance.

Here is the abstract of the proposal:

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.

For more information, check Laurent's entry at: http://www.laurent-duval.eu/lcd-2011-2014-phd-thesis-sparsity-geosciences.html

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