Texture synthesis and prediction error filtering

The spectrum of a prediction-error filter (PEF) tends toward the inverse spectrum of the data from which it is estimated. I compute 2-D PEF’s from known “training images” and use them to synthesize similar-looking textures from random numbers via helix deconvolution. Compared to a similar technique employing Fourier transforms, the PEF-based method is generally more flexible, due to its ability to handle missing data, a fact which I illustrate with an example. Applying PEF-based texture synthesis to a stacked 2-D seismic section, I note that the residual error in the PEF estimation forms the basis for “coherency” analysis by highlighting discontinuities in the data, and may also serve as a measure of the quality of a given migration velocity model. Last, I relate the notion of texture synthesis to missing data interpolation and show an example.