Nonstationarity and conjugacy: utilities for data patch work

Jon F. Claerbout

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ABSTRACT

I design and explain programs for parceling a planar data set into an array of patches (small planes) that may overlap. The conjugate takes the patches and adds them back together into a data plane. Because of overlap, the original data set is not recovered unless weighting functions are used. Any weighting function can be used in any patch. I provide a seamless reconstruction with code in which you can incorporate any linear operator. Finally, I code time and space variable 2-D filtering using invariant filtering in patches, taking care that filters do not run off the boundaries of each patch and using triangular weighting functions to merge patches.