Data denoising and interpolation using synthesis and analysis sparse regularization

Missing trace reconstruction is a challenge in seismic processing due to incomplete and irregular acquisition. Noise is a concern, due to the many sources of noise that occur during seismic acquisition. Most of the recent research on denoising and interpolation focuses on transform domain approaches using L1 norm minimization. A specific kind of constraint, called the synthesis approach, is widely used in geophysical problems. The analysis approach, which can be considered as the synthesis’ dual problem, is an alternative for sparsityconstrained inversion. Although less popular than the synthesis solution, the analysis approach is more effective in several problems, such as denoising of natural images. We compare and contrast the analysis and synthesis approaches as sparsity constraints for the missing trace reconstruction and denoising problems. We show that the analysis approach yields more accurate results than the synthesis approach, which makes it a viable approach for sparsity-constrained inversion for noise related geophysical problems.