Beating Nyquist by randomized sampling

Abstract

Seismic exploration is rooted in the paradigm of regular Nyquist sampling. Recent developments in the area of “compressive sensing” have shown that regular-Nyquist sampling may not be most favorable for signals that are compressible, e.g., by curvelets. In that case, appropriate randomization of the acquisition; such as by jittered1 sampling, creates favorable recovery conditions from data collected at a limited number of randomly placed sources and receivers. By virtue of the randomization, and the subsequent nonlinear recovery by transform-domain sparsity promotion, significant improvements can be made in the frequency content and quality of regularly sampled data volumes obtained from highly undersampled randomized measurements. In this new paradigm, the effective sampling rates are no longer dictated by Nyquist but by transformdomain sparsity. Consequently, twice as compressible signals can be recovered from only halve the randomized sample points. This removes a major impediment of acquisition where costs are proportional to sample rates and survey areas. During this talk, we will discuss multidimensional and continuous2 (opposed to gridded) extensions of randomized jitter sampling. These will include investigations of Poisson disk sampling3 and Farthest Point sampling4 and we will demonstrate that these randomized schemes perform better than the wellestablished regular sampling protocol.