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.

- Tristan van Leeuwen and Felix J. Herrmann, “Fast waveform inversion without source encoding”, Geophysical Prospecting, vol. 61, p. 10-19, 2013. Abstract
- Aleksandr Y. Aravkin, Michael P. Friedlander, Felix J. Herrmann, and Tristan van Leeuwen, “Robust inversion, dimensionality reduction, and randomized sampling”, Mathematical Programming, vol. 134, p. 101-125, 2012. Abstract
- Felix J. Herrmann, Andrew J. Calvert, Ian Hanlon, Mostafa Javanmehri, Rajiv Kumar, Tristan van Leeuwen, Xiang Li, Brendan Smithyman, Eric Takam Takougang, and Haneet Wason, “Frugal full-waveform inversion: from theory to a practical algorithm”, The Leading Edge, vol. 32, p. 1082-1092, 2013. Abstract
- Tristan van Leeuwen and Felix J. Herrmann, “3D frequency-domain seismic inversion with controlled sloppiness”, SIAM Journal on Scientific Computing, vol. 36, p. S192-S217, 2014. Abstract

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

- Felix J. Herrmann and Xiang Li, “Efficient least-squares imaging with sparsity promotion and compressive sensing”, Geophysical Prospecting, vol. 60, p. 696-712, 2012. Abstract
oneapplication 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.

- Felix J. Herrmann, Michael P. Friedlander, and Ozgur Yilmaz, “Fighting the curse of dimensionality: compressive sensing in exploration seismology”, Signal Processing Magazine, IEEE, vol. 29, p. 88-100, 2012. Abstract.

Kind regards,

Felix J. Herrmann

UBC—Seismic Laboratory for Imaging and Modelling

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