Wednesday, December 17, 2014

More Oil and Compressive Sensing Connections

Felix Herrmann followed through to yesterday's "Another Donoho-Tao Moment ?" which itself was a followup to Sunday Morning Insight: The Stuff of Discovery and Hamming's time: Scientific Discovery Enabled by Compressive Sensing and related fields. Here what he has to say:

Hi Igor,
I agree with your assessment that the application of CS to seismic data acquisition may not qualify as a major scientific discovery but it will almost certainly lead to major scientific breakthroughs in crustal and mantle seismology as soon as my colleagues in those areas get wind of this innovation. Having said this it may be worth mentioning that randomized subsampling techniques are also having a major impact on carrying out large scale inversions in exploration seismology. For instance, a major seismic contractor company has been able to render full-waveform inversion (the seismic term for inverse problems involving PDE solves) into a commercially viable service by virtue of the fact that we were able to reduce the computational costs of these methods 5—7 fold using batching techniques. These references
were instrumental in motivating the oil & gas industry into adapting this batching technology into their business.
An area that is closer in spirit to Compressive Sensing is seismic imaging. Contrary to full-waveform inversion, seismic imaging entails the inversion of extremely large-scale tall systems of equations that can be made computationally viable using randomized sampling techniques in combination with sparsity promotion. While heuristic in nature, this technique
is able to approximately invert tall systems at the cost of roughly one pass through the data (read only one application of the full adjoint). It is very interesting to see that this heuristic technique has, at least at the conceptual level, connections with approximate message passing (see section 6.5 of “Graphical Models Concepts in Compressed Sensing”) and recent work on Kaczmarz: “A sparse Kaczmarz solver and a linearized Bregman method for online compressed sensing”.
While these developments may by themselves not qualify as major “scientific breakthroughs”, it is clear that these developments are having a major impact on the field of exploration seismology where inversions as opposed to applications of “single adjoints” are now possible that were until very recently computationally unfeasible. For further information on the application of Compressive Sensing to seismic data acquisition and wave-equation based inversion, I would like to point your readers to our website, mind map, and a recent overview article
Thanks again for your efforts promoting Compressive Sensing to the wider research community.
Kind regards,
Felix J. Herrmann
UBC—Seismic Laboratory for Imaging and Modelling
Thanks Felix !
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