Nonstationary Predictive Deconvolution

A partition of unity (POU) is a discrete set of usually overlapping windows that sum exactly to one for a finite interval on the real line. Multiplying a signal by the POU decomposes it into a set of temporally localized signals or Gabor slices. Applying any stationary operator to these slices and allowing the operator to depend upon the slice defines a nonstationary operator. We apply a stationary prediction operator to each slice and by summing construct a time-domain nonstationary deconvolution method based on gapped prediction filtering. We call this new method slicedecon because it operates directly on the individual Gabor slices. We also prescribe the construction of nonstationary autocorrelation functions as an analysis tool. We then compare slicedecon with the more established Gabor deconvolution or gabordecon. When the prediction filtering is unit-lag, we show that slicedecon achieves results comparable to gabordecon on a nonstationary (Q attenuation) synthetic. For lags greater than unity slicedecon appears to suppress, though not eliminate, periodicities in the nonstationary autocorrelation of a signal. Testing on a synthetic with multiples has not yet indicated any dramatic elimination of the unwanted multiple reflections.