Seismic reconstruction via constrained dictionary learning

Seismic reconstruction is to fill the irregularly missing traces in the measurement and recover the data in a regular grid (the recovery). Transform-based sparse inversion has been introduced in seismic reconstruction and the significant results have been achieved. Most methods mainly focus on the sparse representation of the recovery in fixed transform (dictionary), such as Fourier or curvelet transform. In this paper, in the context of machine learning, we present an alternative method via constrained dictionary learning, where the dictionary is learned directly from the measurement and is data-driven. Apart from the l₁ -norm induced sparsity of the coefficients, the sparsity of dictionary atoms in fixed transform domain is additionally explored to suppress the noise contained in the dictionary. The alternating optimization scheme is used to update the sparse coefficients and the dictionary separately. The results of complex synthetic model and field data show that the obtained dictionary is quite fitting to the recovery and provides sparser representation, which renders the effective reconstruction of seismic data.