Streaming prediction-error filters

Abstract

Prediction-error filters (PEFs) are essential in seismic deconvolution and other geophysical estimation problems. We show that non-stationary multidimensional PEFs can be computed in a “streaming” manner, where the filter gets updated incrementally by accepting one new data point at a time. The computational cost of estimating a streaming PEF reduces to the cost of a single convolution. In other words, the cost of PEF design while filtering equals the cost of applying the filter. Moreover, the non-linear operation of finding and applying a streaming PEF is invertible at a similar cost, which enables a fast approach to missing data interpolation.