Sparse Reconstruction of Regional Gravity Signal Based on Stabilized Orthogonal Matching Pursuit (SOMP)

Abstract

The main role of gravity field recovery is the study of dynamic processes in the interior of the Earth especially in exploration geophysics. In this paper, the Stabilized Orthogonal Matching Pursuit (SOMP) algorithm is introduced for sparse reconstruction of regional gravity signals of the Earth. In practical applications, ill-posed problems may be encountered regarding unknown parameters that are sensitive to the data perturbations. Therefore, an appropriate regularization method needs to be applied to find a stabilized solution. The SOMP algorithm aims to regularize the norm of the solution vector, while also minimizing the norm of the corresponding residual vector. In this procedure, a convergence point of the algorithm that specifies optimal sparsity-level of the problem is determined. The results show that the SOMP algorithm finds the stabilized solution for the ill-posed problem at the optimal sparsity-level, improving upon existing sparsity based approaches.

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