This thesis covers two methods of separating noise and signal. The first method is removing noise by prediction filtering. Examples of this method are the traditional predictive deconvolution, Canales' and Gulunay's fx-decon techniques, and the t-x prediction techniques discussed in this thesis and in Hornbostel 1991. The second method is to separate the signal and noise using a least-squares inversion method to predict the signal or the noise.
Additionally, a preprocessing step of removing high-amplitude noise is presented to condition data in preparation for these two methods. Since high-amplitude noise corrupts the calculation of a prediction filter and can overwhelm the least-squares inversions used to predict the signal or noise, this process is an important step in signal and noise separation. As an extension to the signal and noise separation problem, missing data may be predicted with a modification of the inversion method. This prediction of missing data is useful, since high-amplitude noise, which would otherwise overwhelm the least-squares calculations, can be removed and later recovered by the inversion.