A residual dictionary learning method for footprint removal from seismic data

We introduce a novel dictionary learning strategy for removal of footprint patterns and random noise in seismic data. To this end, we construct an augmented dictionary based solely on the atoms learned from the coherenceconstrained dictionary learning (CDL), a method that is very effective on attenuating random noise. It turns out that when seismic data is contaminated with acquisition and/or processing footprint, the atoms of the learned dictionary are contaminated by coherent noise patterns. Hence, it is necessary to carry out a morphological and/or texture attribute classification of the atoms for effective footprint removal. Instead, the method that we propose relies on an augmented dictionary that is constructed using a simple data-driven empirical mode decomposition (EMD) algorithm, which leads to a dictionary that contains signal atoms and a residual dictionary that contains footprint atoms. This avoids the use of complex statistical classifications strategies to segregate the atoms of the learned dictionary. As in CDL, the proposed method does not require the user to know or adjust the noise level or the sparsity of the solution for each data set. Further, it only requires one pass of CDL dictionary learning and is shown to produce successful transfer learning results in field data. This leads to a speed-up of the denoising processing, since random and coherent noise can be removed without calculating the augmented dictionary for each time slice of the 3D data volume. Results on field data demonstrate effective footprint removal with accurate edge preservation on time slices of 3D seismic poststack data.