Graph regularized seismic dictionary learning

A graph-based regularization for geophysical inversion is proposed that offers a more efficient way to solve inverse denoising problems by dictionary learning methods designed to find a sparse signal representation that adaptively captures prominent characteristics in a given data. Most traditional dictionary learning methods convert 2D seismic data patches or 3D data volumes into 1D vectors for training or learning, but this conversion breaks down the inherent geometric structure of the data. To overcome this problem, two algorithms of graph regularization for dictionary learning based on clustering and SVD methods, named FDL-Graph and SDL-Graph, are proposed. First, the clustering-based dictionary learning method divides the training patches into regions/clusters of similar geometric structures employing a simplified principal component analysis method or L2 distance function to effectively perform such a clustering. Next, the clusters are used to learn a basis or a frame that best describes the patches. Besides employing an adapted dictionary for sparse data representation we also consider the local geometric structures of the seismic data using a Laplacian graph. Since this novel denoising model adds a graph regularization to the sparse representation model to emphasize correlations among data patches, the proposed method leads to smoother results and can achieve better denoising performance than existing methods without graph regularization, both in terms of peak signal-to-noise ratio values and visual estimation of weak-even preservation. Comparisons of experimental results on synthetic and recorded seismic data using traditional FX deconvolution and curvelet thresholding methods are also provided.