While a PEF at every sample works well for destroying the data, it is not the best choice for reconstructing it; interpolation with PEFs estimated at every data point gives poor results and requires extravagant memory allocation. One answer is just that zero is not the correct value of in (5); but we can greatly improve the results and decrease the memory usage without adding equations, by using very small patches, such as ; small enough that the assumption of stationarity within a patch is reasonable. This is similar to putting an extra roughener in the damping equation, in that it is essentially an infinite penalty on variations of between small groups of samples, and it has the important economizing effect of reducing the memory allocation. In the method where the patches are independent Crawley (1998), the number of filter coefficients puts a lower bound on patch size; the problem has to stay well overdetermined to produce a useful PEF. Using smoothly varying filters effectively reduces the minimum patch size, so that the filter estimation problem can be underdetermined, and still produce useful PEFs.

4/20/1999