Matrix probing: A randomized preconditioner for the wave-equation Hessian

Laurent Demanet, Pierre David Létourneau, Nicolas Boumal, Henri Calandra, Jiawei Chiu, Stanley Snelson

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


This paper considers the problem of approximating the inverse of the wave-equation Hessian, also called normal operator, in seismology and other types of wave-based imaging. An expansion scheme for the pseudodifferential symbol of the inverse Hessian is set up. The coefficients in this expansion are found via least-squares fitting from a certain number of applications of the normal operator on adequate randomized trial functions built in curvelet space. It is found that the number of parameters that can be fitted increases with the amount of information present in the trial functions, with high probability. Once an approximate inverse Hessian is available, application to an image of the model can be done in very low complexity. Numerical experiments show that randomized operator fitting offers a compelling preconditioner for the linearized seismic inversion problem.

Original languageEnglish (US)
Pages (from-to)155-168
Number of pages14
JournalApplied and Computational Harmonic Analysis
Issue number2
StatePublished - Mar 2012

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


  • Curvelets
  • Discrete symbol calculus
  • Randomized algorithms
  • Seismic imaging


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