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Sparse least squares migration (SLSM) estimates the reflectivity distribution that honors a sparsity condition. This problem can be reformulated by finding both the sparse coefficients and basics functions from the data to predict the migration image. This is designated as neural network least squares migration (NLSM), which is a more general formulation of SLSM. This reformulation opens up new thinking for improving SLSM by adapting ideas from the machine learning community.