Seismic Data Regularization on Nonequispaced Grid via a Joint Sparsity-Promotion Method

The seismic data regularization problem is vital to seismic data processing. We propose a joint sparsity-promotion method based on the compressive sensing theory named the curvelet-data-driven-tight-frame-based sparsity-promoting (CDSP) method. The CDSP method regularizes the seismic data directly on the nonequispaced grid along the spatial dimension. The joint sparsity is exploited in the curvelet and data-driven tight frame transform simultaneously on the projected regular spatial grid. The projection from the nonequispaced grid to the equispaced grid is achieved by the nonequispaced discretized Fourier transform. Comparing with the curvelet-sparsity-promotion-based (CSP) regularization method, CDSP combines the advantage of the predefined curvelet transform and adaptive-learned sparse transform into one single optimization model. An alternative directional method of multipliers (ADMM) is applied to solve the optimization problem. One synthetic and two field examples show that the CDSP method performs better on the preservation of the continuity of events and produces less artifacts than the CSP method.