Statics Preserving Sparse Radon Transform

Abstract

This paper develops a Statics Preserving Sparse Radon transform (SPSR) algorithm.The de-coloration power of Radon basis functions depends on different factors. The most important one is statics. Statics decrease the sparsity of Radon models. To tackle this problem, it is necessary to include statics into the Radon bases functions. SPSR algorithm includes statics into the Radon bases functions, allowing for a sparse representation of statics contaminated data in the Radon domain. SPSR algorithm formulated as an $L_2- L_1$ optimization problem and solved via alternating minimization method. Real data examples used to test the performance of the proposed method in multiple and noise attenuation in the presence of statics.