SINGLE‐CHANNEL WHITE‐NOISE ESTIMATORS FOR DECONVOLUTION

Abstract

The Wiener filtering approach to deconvolution is limited by certain modeling assumptions, which may not always be valid. We develop a Kalman filtering approach to deconvolution which permits more flexible modeling assumptions than the Wiener filtering approach. Our approach is applicable to time‐varying or time‐invariant wavelets as well as to nonstationary or stationary noise processes. We develop equations herein for minimum‐variance estimates of the reflection coefficient sequence, as well as error variances associated with these estimates. Our estimators are compared with an ad hoc “prediction error filter,” which has recently been reported on in the geophysics literature. We show that our estimators perform better than the prediction error filter. Simulation results are included, for both time‐invariant and time‐varying situations, which support our theoretical developments.