Structured Dictionary Learning for Interpolation of Aliased Seismic Data

We present a new dictionary learning method for seismic data interpolation. Dictionary learning methods train a set of basis vectors on the data to capture the morphology of the redundant signal. The basis vectors are called atoms, and the set is referred to as the dictionary. Learned dictionaries are very effective for representing the data as sparse linear combinations of their atoms. In conventional dictionary learning, the atoms are unstructured and do not have an analytic expression. In the proposed method, the atoms are constrained to represent linear events of known slopes. Using the slope information, theatoms can be easily interpolated. Hence, a regularly sampled data can be interpolated over a finer grid by learning a dictionaryon the data, finding a sparse representation of the data in the dictionary domain, interpolating the dictionary, and finallytaking the sparse representation of the data in the interpolated dictionary domain. The sparsity constraint ensures that atomswith well-fitting slopes are chosen to represent the data, and it hence prevents from aliasing and noise representation. Onsynthetic and field data, we observe that the proposed method performs a near to exact interpolation of linear events and anaccurate interpolation of curved events, and that it is robust to noise.