Zhong, W., Chen, Y., Gan, S. and Yuan, J., 2016. Li, norm regularization for 3D seismic data interpolation. Journal of Seismic Exploration, 25: 257-267. Sparse reconstruction of seismic data aims to reconstruct the missing traces from noise-contaminated or incomplete seismic datasets with a sparsity regularization. The Lo and L, 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, regularization, the traditional approach cannot get the optimal solutions to the seismic interpolation problems. We propose a novel Lip 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 Lip 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 Lo and L, 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.