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In combination with compressive sensing, a successful reconstruction scheme called Curvelet-based Recovery by Sparsity-promoting Inversion (CRSI) has been developed, and has proven to be useful for seismic data processing. One of the most important issues for CRSI is the sampling scheme, which can greatly affect the quality of reconstruction. Unlike usual regular undersampling, stochastic sampling can convert aliases to easy-to-eliminate noise. Some stochastic sampling methods have been developed for CRSI, e.g. jittered sampling, however most have only been applied to 1D sampling along a line. Seismic datasets are usually higher dimensional and very large, thus it is desirable and often necessary to develop higher dimensional sampling methods to deal with these data.
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