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The common-reflection surface (CRS) method is a sophisticated alternative to the traditional common-midpoint stacking because its traveltime approximation allows for the use of more traces than the normal moveout. This in turn requires more parameters for the moveout description, thus increasing the computational burden of the parameter estimation. In the literature, a suboptimal strategy is often used, which decreases the complexity but, as we found in this work, compromises the accuracy of the parameters in some cases. To cope with this problem, in this work, we have devised detailed information for efficient estimation of the CRS parameters using the differential evolution (DE) global optimization algorithm. Because we used data sets with low fold and low signal-to-noise ratio, from which no reliable velocity analysis could be easily performed, we applied this algorithm in a fully automatic global search, i.e., without any velocity guide. The results for a 2D real data set from Brazil indicated that the global strategy yielded good results, both in terms of image quality as in the quality of the parameter volumes, especially the stacking velocity estimates, while keeping the computational costs relatively low. We also developed a convergence and a sensitivity analysis of the DE that shows its computational efficiency and the robustness of the optimization method with respect to the choice of the control parameters of the algorithm.

The choice of an appropriate frame, or dictionary, is a crucial step in the sparse representation of a given class of signals. Traditional dictionary learning techniques generally lead to unstructured dictionaries which are costly to deploy and train, and do not scale well to higher dimensional signals. In order to overcome such limitation, we propose a learning algorithm that constrains the dictionary to be a sum of Kronecker products of smaller sub-dictionaries. This approach, named SuKro, is demonstrated experimentally on an image denoising application.

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