Streaming prediction-error filters

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