Interpolation with Fourier-radial adaptive thresholding
William J. Curry · 2009
Many interpolation methods are suited for either regular sampling or for randomly-sampled data, while the spatial sampling of field data is typically neither regular nor random. Fourier-Radial Adaptive Thresholding (FRAT) is a sparsity-promoting method where the interpolated result is both sparse in the frequency-wavenumber domain and is also coherent in a manner consistent with that of a collection of unaliased plane waves. Both the sparsity and the desired pattern in the f-k domain are promoted by iterative soft thresholding and adaptive weighting, where the data in the f-k domain are transformed to polar coordinates followed by low-pass filtering along the radial axis to generate the nonlinear weight. I demonstrate this method on both a simple synthetic example as well as a shot gather from the Sigsbee2A synthetic model.