Interpolation of Irregularly-sampled Data With Non-stationary, Multi-scale Prediction-error Filters

Data interpolation can be cast as an inverse problem where th known data remains constant, and the empty bins are regulari zed to constrain the null space. A two-stage linear approach was developed (Claerbout, 1999) where a prediction-error filter ( PEF) is estimated on known data, and is then used to constrain the unk nown data by minimizing the output of the model after convolution with the PEF. When the data is not stationary, a non-stationary fil ter has been used to fill the unknown data (Crawley, 2000). This usual ly produces better results than a patching approach, where the da a is broken up into separate patches that are assumed to be statio nary and are treated as independent problems.