Interpolation of Irregularly Sampled Data by Matching Pursuit

While several methods exist that aim to interpolate between regularly sampled traces or reconstruct traces missing from a dataset that is sampled on a regular grid, there are few techniques designed to handle truly irregular sampling. We introduce a new iterative method (IMAP) to regularize irregularly sampled seismic data, based on the matching pursuit technique. In this technique, the data are modeled as a sum of basis functions characterized by a set of parameters. At each iteration, the optimal new basis function is found to reduce the residual at the measurement points. If sinusoids are used as basis functions, it turns out that the optimal wavenumber to use is given by the maximum of the Lomb periodogram, which is considered the state-of-the-art method for computing the spectrum of unevenly sample data. As the IMAP method is iterative, it improves on the original Lomb spectrum result. The new technique is demonstrated using a finite-difference synthetic data example with severe sampling irregularity.