L1/2 NORM REGULARIZATION FOR 3D SEISMIC DATA INTERPOLATION

Sparse reconstruction of seismic data aims to reconstruct the missing traces from noise-contaminated or incomplete seismic datasets with a sparsity regularization. The L-0 and L-1 regularizations are the two most widely used methods to constrain the transform-domain coefficients. However, because of the NP-hard difficulty of Lo regularization and non-sparsest solution of L-1 regularization, the traditional approach cannot get the optimal solutions to the seismic interpolation problems. We propose a novel L-1/2 regularization model to solve the seismic interpolation problem and borrow the efficient iterative half-thresholding solver from the signal-processing field to solve the proposed L-1/2 regularization model. Both 3D irregularly sampled synthetic data and field seismic data with 50% randomly missing traces show accurate reconstructions using the proposed approach. Comparisons with the traditional L-0 and L-1 regularizations also confirm the effectiveness of the proposed approach. Because of the simple and efficient implementation of the iterative half-thresholding algorithm, the proposed approach can be conveniently used in the industry.