Atomic Decomposition by Basis Pursuit
SIAM Review
Seismic Denoising with Nonuniformly Sampled Curvelets
Computing in Science and Engineering
Sparse reconstruction by separable approximation
IEEE Transactions on Signal Processing
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
Nonlinear regularization techniques for seismic tomography
Journal of Computational Physics
Interpolation and extrapolation using a high-resolution discreteFourier transform
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
Color plane interpolation using alternating projections
IEEE Transactions on Image Processing
An EM algorithm for wavelet-based image restoration
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration
IEEE Transactions on Image Processing
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Interpolating the missing traces of regularly or irregularly sampled seismic record is an exceedingly important issue in the geophysical community. Many modern acquisition and reconstruction methods are designed to exploit the transform domain sparsity of the few randomly recorded but informative seismic data using thresholding techniques. In this paper, to regularize randomly sampled seismic data, we introduce two accelerated, analysis-based two-step interpolation algorithms, the analysis-based FISTA (fast iterative shrinkage-thresholding algorithm) and the FPOCS (fast projection onto convex sets) algorithm from the IST (iterative shrinkage-thresholding) algorithm and the POCS (projection onto convex sets) algorithm. A MATLAB package is developed for the implementation of these thresholding-related interpolation methods. Based on this package, we compare the reconstruction performance of these algorithms, using synthetic and real seismic data. Combined with several thresholding strategies, the accelerated convergence of the proposed methods is also highlighted.