The fact that the numerical complexity of wavefield simulation is proportional to the size of the discretized model and acquisition geometry, and not to the complexity of the simulated wavefield, is the main impediment within seismic imaging. By turning simulation into a compressive sensing problem---where simulated data is recovered from a relatively small number of independent simultaneous sources---we remove this impediment by showing that compressively sampling a simulation is equivalent to compressively sampling the sources, followed by solving a reduced system. As in compressive sensing, this allows for a reduction in sampling rate and hence in simulation costs. We demonstrate this principle for the time-harmonic Helmholtz solver. The solution is computed by inverting the reduced system, followed by a recovery of the full wavefield with a sparsity promoting program. Depending on the wavefield's sparsity, this approach can lead to significant cost reductions, in particular when combined with the implicit preconditioned Helmholtz solver, which is known to converge even for decreasing mesh sizes and increasing angular frequencies. These properties make our scheme a viable alternative to explicit time-domain finite-differences.
Jared Tanner just mentioned to me the organization of a meeting called SampTA '09 in Marseilles, France.
The purpose of SAMPTA's is to bring together mathematicians and engineers interested in sampling theory and its applications to related fields (such as signal and image processing, coding theory, control theory, complex analysis, harmonic analysis, differential equations) to exchange recent advances and to discuss open problems.
SAMPTA09 will be organized around plenary lectures, general sessions on sampling and applications, and special sessions on selected topics. Ample time will be left for discussions. The topics of the special sessions are the following:Compensation of channel mismatch errors in time-interleaved analog-to-digital converters, Compressed sensing, Mathematical aspects of compressed sensing, Frame theory and oversampling, Geometric multiscale analysis, Sampling and quantization, Sampling and communication, Sampling and painting, Sampling and industrial applications, Sampling using finite rate of innovation principles, Sparse approximation and high-dimensional geometry, and Super-resolution.
Submissions will be reviewed. Please notice the following important dates:
* January 15, 2009: Deadline for paper submission.
* February 15, 2009: Notification of paper acceptance.
* April 15, 2009: Deadline for final paper submission and registration
Martin Vetterli will give a talk at Columbia on October 22. The title of the talk is Sparse Sampling: Variations on a Theme by Shannon
The last two items are listed in the Compressive Sensing Calendar.