Learning dictionary in the approximately flattened structure domain

Dictionary learning provides an adaptive way to optimally represent a given dataset. In dictionary learning, the basis function is adapted according to the given data instead of being fixed in many analytical sparse transforms. The application of the dictionary learning techniques in seismic data processing has been popular in the past decade. However, most dictionary learning algorithms are directly taken from the image processing community and thus are not suitable for seismic data. Considering that the seismic data is spatially coherent, the dictionary should better be learned according to the coherency information in the seismic data. We found the dictionary learning performs better when the spatial correlation is stronger and thus we propose an approximately flattening operator to help learn the dictionary in an approximately flattened structure domain, where the strong spatial coherence helps construct a dictionary that follows better the structural pattern inof the seismic data. The presented dictionary learning in the approximately flattened structure domain (DLAF) thus has a stronger capability in separating signal and noise. We use both synthetic and field data examples to demonstrate the superb performance of the proposed method.